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Lauber N, Tichacek O, Narayanankutty K, De Martino D, Ruiz-Mirazo K. Collective catalysis under spatial constraints: Phase separation and size-scaling effects on mass action kinetics. Phys Rev E 2023; 108:044410. [PMID: 37978605 DOI: 10.1103/physreve.108.044410] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2023] [Accepted: 09/07/2023] [Indexed: 11/19/2023]
Abstract
Chemical reactions are usually studied under the assumption that both substrates and catalysts are well-mixed (WM) throughout the system. Although this is often applicable to test-tube experimental conditions, it is not realistic in cellular environments, where biomolecules can undergo liquid-liquid phase separation (LLPS) and form condensates, leading to important functional outcomes, including the modulation of catalytic action. Similar processes may also play a role in protocellular systems, like primitive coacervates, or in membrane-assisted prebiotic pathways. Here we explore whether the demixing of catalysts could lead to the formation of microenvironments that influence the kinetics of a linear (multistep) reaction pathway, as compared to a WM system. We implemented a general lattice model to simulate LLPS of a collection of different catalysts and extended it to include diffusion and a sequence of reactions of small substrates. We carried out a quantitative analysis of how the phase separation of the catalysts affects reaction times depending on the affinity between substrates and catalysts, the length of the reaction pathway, the system size, and the degree of homogeneity of the condensate. A key aspect underlying the differences reported between the two scenarios is that the scale invariance observed in the WM system is broken by condensation processes. The main theoretical implications of our results for mean-field chemistry are drawn, extending the mass action kinetics scheme to include substrate initial "hitting times" to reach the catalysts condensate. We finally test this approach by considering open nonlinear conditions, where we successfully predict, through microscopic simulations, that phase separation inhibits chemical oscillatory behavior, providing a possible explanation for the marginal role that this complex dynamic behavior plays in real metabolisms.
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Affiliation(s)
- Nino Lauber
- Biofisika Institute (CSIC, UPV/EHU), 48940 Leioa, Spain
- Donostia International Physics Center, 20018 Donostia-San Sebastian, Spain
- Department of Philosophy, University of the Basque Country, 20018 Donostia-San Sebastian, Spain
| | - Ondrej Tichacek
- Institute of Organic Chemistry and Biochemistry of the Czech Academy of Sciences, 160 00 Prague, Czech Republic
| | - Krishnadev Narayanankutty
- Biofisika Institute (CSIC, UPV/EHU), 48940 Leioa, Spain
- Department of Molecular Biology and Biochemistry, University of the Basque Country, 48940 Leioa, Spain
| | - Daniele De Martino
- Biofisika Institute (CSIC, UPV/EHU), 48940 Leioa, Spain
- Ikerbasque Foundation, 48009 Bilbao, Spain
| | - Kepa Ruiz-Mirazo
- Biofisika Institute (CSIC, UPV/EHU), 48940 Leioa, Spain
- Department of Philosophy, University of the Basque Country, 20018 Donostia-San Sebastian, Spain
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2
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Kumar P, Chakrabarti R. Dynamics of self-propelled tracer particles inside a polymer network. Phys Chem Chem Phys 2023; 25:1937-1946. [PMID: 36541408 DOI: 10.1039/d2cp04253c] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
The transport of tracer particles through mesh-like environments such as biological hydrogels and polymer matrices is ubiquitous in nature. These tracers can be passive, such as colloids, or active (self-propelled), for example, synthetic nanomotors or bacteria. Computer simulations in principle could be extremely useful in exploring the mechanism of the active transport of tracer particles through mesh-like environments. Therefore, we construct a polymer network on a diamond lattice and use computer simulations to investigate the dynamics of spherical self-propelled particles inside the network. Our main objective is to elucidate the effect of the self-propulsion on the tracer particle dynamics as a function of the tracer size and the stiffness of the polymer network. We compute the time-averaged mean-squared displacement (MSD) and the van-Hove correlations of the tracer. On the one hand, in the case of a bigger sticky particle, the caging caused by the network particles wins over the escape assisted by the self-propulsion. This results an intermediate-time subdiffusion. On the other hand, smaller tracers or tracers with high self-propulsion velocities can easily escape from the cages and show intermediate-time superdiffusion. The stiffer the network, the slower the dynamics of the tracer, and bigger tracers exhibit longer lived intermediate time superdiffusion, since the persistence time scales as ∼σ3, where σ is the diameter of the tracer. At the intermediate time, non-Gaussianity is more pronounced for active tracers. At the long time, the dynamics of the tracer, if passive or weakly active, becomes Gaussian and diffusive, but remains flat for tracers with high self-propulsion, accounting for their seemingly unrestricted motion inside the network.
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Affiliation(s)
- Praveen Kumar
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai 400076, India.
| | - Rajarshi Chakrabarti
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai 400076, India.
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3
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Scott S, Weiss M, Selhuber-Unkel C, Barooji YF, Sabri A, Erler JT, Metzler R, Oddershede LB. Extracting, quantifying, and comparing dynamical and biomechanical properties of living matter through single particle tracking. Phys Chem Chem Phys 2023; 25:1513-1537. [PMID: 36546878 DOI: 10.1039/d2cp01384c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
A panoply of new tools for tracking single particles and molecules has led to an explosion of experimental data, leading to novel insights into physical properties of living matter governing cellular development and function, health and disease. In this Perspective, we present tools to investigate the dynamics and mechanics of living systems from the molecular to cellular scale via single-particle techniques. In particular, we focus on methods to measure, interpret, and analyse complex data sets that are associated with forces, materials properties, transport, and emergent organisation phenomena within biological and soft-matter systems. Current approaches, challenges, and existing solutions in the associated fields are outlined in order to support the growing community of researchers at the interface of physics and the life sciences. Each section focuses not only on the general physical principles and the potential for understanding living matter, but also on details of practical data extraction and analysis, discussing limitations, interpretation, and comparison across different experimental realisations and theoretical frameworks. Particularly relevant results are introduced as examples. While this Perspective describes living matter from a physical perspective, highlighting experimental and theoretical physics techniques relevant for such systems, it is also meant to serve as a solid starting point for researchers in the life sciences interested in the implementation of biophysical methods.
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Affiliation(s)
- Shane Scott
- Institute of Physiology, Kiel University, Hermann-Rodewald-Straße 5, 24118 Kiel, Germany
| | - Matthias Weiss
- Experimental Physics I, University of Bayreuth, Universitätsstr. 30, D-95447 Bayreuth, Germany
| | - Christine Selhuber-Unkel
- Institute for Molecular Systems Engineering, Heidelberg University, D-69120 Heidelberg, Germany.,Max Planck School Matter to Life, Jahnstraße 29, D-69120 Heidelberg, Germany
| | - Younes F Barooji
- Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen, Denmark.
| | - Adal Sabri
- Experimental Physics I, University of Bayreuth, Universitätsstr. 30, D-95447 Bayreuth, Germany
| | - Janine T Erler
- BRIC, University of Copenhagen, Ole Maaløes Vej 5, DK-2200 Copenhagen, Denmark.
| | - Ralf Metzler
- Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht Str. 24/25, D-14476 Potsdam, Germany.,Asia Pacific Center for Theoretical Physics, Pohang 37673, Republic of Korea
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4
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Sahoo R, Theeyancheri L, Chakrabarti R. Transport of a self-propelled tracer through a hairy cylindrical channel: interplay of stickiness and activity. SOFT MATTER 2022; 18:1310-1318. [PMID: 35060583 DOI: 10.1039/d1sm01693h] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Active transport of biomolecules assisted by motor proteins is imperative for the proper functioning of cellular activities. Inspired by the diffusion of active agents in crowded cellular channels, we computationally investigate the transport of an active tracer through a polymer grafted cylindrical channel by varying the activity of the tracer and stickiness of the tracer to the polymers. Our results reveal that the passive tracer exhibits profound subdiffusion with increasing stickiness by exploring deep into the grafted polymeric zone, while purely repulsive one prefers to diffuse through the pore-like space created along the cylindrical axis of the channel. In contrast, the active tracer shows faster dynamics and intermediate superdiffusion even though the tracer preferentially stays close to the dense polymeric region. This observation is further supported by the sharp peaks in the density profile of the probability of radial displacement of the tracer. We discover that the activity plays an important role in deciding the pathway that the tracer takes through the narrow channel. Interestingly, increasing the activity washes out the effect of stickiness. Adding to this, van-Hove functions manifest that the active tracer dynamics deviates from Gaussianity, and the degree of deviation grows with the activity. Our work has direct implications on how effective transportation and delivery of cargo can be achieved through a confined medium where activity, interactions, and crowding are interplaying. Looking ahead, these factors will be crucial for understanding the mechanism of artificial self-powered machines navigating through the cellular channels and performing in vivo challenging tasks.
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Affiliation(s)
- Rajiblochan Sahoo
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai 400076, India.
| | - Ligesh Theeyancheri
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai 400076, India.
| | - Rajarshi Chakrabarti
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai 400076, India.
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5
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Maestri S, Merelli E, Pettini M. Agent-based models for detecting the driving forces of biomolecular interactions. Sci Rep 2022; 12:1878. [PMID: 35115584 PMCID: PMC8814177 DOI: 10.1038/s41598-021-04205-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2021] [Accepted: 12/16/2021] [Indexed: 11/22/2022] Open
Abstract
Agent-based modelling and simulation have been effectively applied to the study of complex biological systems, especially when composed of many interacting entities. Representing biomolecules as autonomous agents allows this approach to bring out the global behaviour of biochemical processes as resulting from local molecular interactions. In this paper, we leverage the capabilities of the agent paradigm to construct an in silico replica of the glycolytic pathway; the aim is to detect the role that long-range electrodynamic forces might have on the rate of glucose oxidation. Experimental evidences have shown that random encounters and short-range potentials might not be sufficient to explain the high efficiency of biochemical reactions in living cells. However, while the latest in vitro studies are limited by present-day technology, agent-based simulations provide an in silico support to the outcomes hitherto obtained and shed light on behaviours not yet well understood. Our results grasp properties hard to uncover through other computational methods, such as the effect of electromagnetic potentials on glycolytic oscillations.
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Affiliation(s)
- Stefano Maestri
- School of Science and Technology, University of Camerino, 62032, Camerino, Italy
- Aix-Marseille Univ, Université de Toulon, CNRS, Centre de Physique Théorique, 163 Avenue de Luminy, 13288, Marseille Cedex 9, France
| | - Emanuela Merelli
- School of Science and Technology, University of Camerino, 62032, Camerino, Italy.
| | - Marco Pettini
- Aix-Marseille Univ, Université de Toulon, CNRS, Centre de Physique Théorique, 163 Avenue de Luminy, 13288, Marseille Cedex 9, France
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6
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Speckner K, Weiss M. Single-Particle Tracking Reveals Anti-Persistent Subdiffusion in Cell Extracts. ENTROPY (BASEL, SWITZERLAND) 2021; 23:892. [PMID: 34356433 PMCID: PMC8303845 DOI: 10.3390/e23070892] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/15/2021] [Revised: 07/06/2021] [Accepted: 07/09/2021] [Indexed: 01/08/2023]
Abstract
Single-particle tracking (SPT) has become a powerful tool to quantify transport phenomena in complex media with unprecedented detail. Based on the reconstruction of individual trajectories, a wealth of informative measures become available for each particle, allowing for a detailed comparison with theoretical predictions. While SPT has been used frequently to explore diffusive transport in artificial fluids and inside living cells, intermediate systems, i.e., biochemically active cell extracts, have been studied only sparsely. Extracts derived from the eggs of the clawfrog Xenopus laevis, for example, are known for their ability to support and mimic vital processes of cells, emphasizing the need to explore also the transport phenomena of nano-sized particles in such extracts. Here, we have performed extensive SPT on beads with 20 nm radius in native and chemically treated Xenopus extracts. By analyzing a variety of distinct measures, we show that these beads feature an anti-persistent subdiffusion that is consistent with fractional Brownian motion. Chemical treatments did not grossly alter this finding, suggesting that the high degree of macromolecular crowding in Xenopus extracts equips the fluid with a viscoelastic modulus, hence enforcing particles to perform random walks with a significant anti-persistent memory kernel.
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Affiliation(s)
| | - Matthias Weiss
- Experimental Physics I, University of Bayreuth, Universitätsstr. 30, D-95447 Bayreuth, Germany;
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7
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Angeles-Martinez L, Hatzimanikatis V. The influence of the crowding assumptions in biofilm simulations. PLoS Comput Biol 2021; 17:e1009158. [PMID: 34292941 PMCID: PMC8297847 DOI: 10.1371/journal.pcbi.1009158] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2020] [Accepted: 06/07/2021] [Indexed: 12/02/2022] Open
Abstract
Microorganisms are frequently organized into crowded structures that affect the nutrients diffusion. This reduction in metabolite diffusion could modify the microbial dynamics, meaning that computational methods for studying microbial systems need accurate ways to model the crowding conditions. We previously developed a computational framework, termed CROMICS, that incorporates the effect of the (time-dependent) crowding conditions on the spatio-temporal modeling of microbial communities, and we used it to demonstrate the crowding influence on the community dynamics. To further identify scenarios where crowding should be considered in microbial modeling, we herein applied and extended CROMICS to simulate several environmental conditions that could potentially boost or dampen the crowding influence in biofilms. We explore whether the nutrient supply (rich- or low-nutrient media), the cell-packing configuration (square or hexagonal spherical cell arrangement), or the cell growing conditions (planktonic state or biofilm) modify the crowding influence on the growth of Escherichia coli. Our results indicate that the growth rate, the abundance and appearance time of different cell phenotypes as well as the amount of by-products secreted to the medium are sensitive to some extent to the local crowding conditions in all scenarios tested, except in rich-nutrient media. Crowding conditions enhance the formation of nutrient gradient in biofilms, but its effect is only appreciated when cell metabolism is controlled by the nutrient limitation. Thus, as soon as biomass (and/or any other extracellular macromolecule) accumulates in a region, and cells occupy more than 14% of the volume fraction, the crowding effect must not be underestimated, as the microbial dynamics start to deviate from the ideal/expected behaviour that assumes volumeless cells or when a homogeneous (reduced) diffusion is applied in the simulation. The modeling and simulation of the interplay between the species diversity (cell shape and metabolism) and the environmental conditions (nutrient quality, crowding conditions) can help to design effective strategies for the optimization and control of microbial systems.
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Affiliation(s)
- Liliana Angeles-Martinez
- Laboratory of Computational Systems Biotechnology, École Polytechnique Fédérale de Lausanne, EPFL, Lausanne, Switzerland
| | - Vassily Hatzimanikatis
- Laboratory of Computational Systems Biotechnology, École Polytechnique Fédérale de Lausanne, EPFL, Lausanne, Switzerland
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8
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Tenner B, Getz M, Ross B, Ohadi D, Bohrer CH, Greenwald E, Mehta S, Xiao J, Rangamani P, Zhang J. Spatially compartmentalized phase regulation of a Ca 2+-cAMP-PKA oscillatory circuit. eLife 2020; 9:e55013. [PMID: 33201801 PMCID: PMC7671691 DOI: 10.7554/elife.55013] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2020] [Accepted: 10/07/2020] [Indexed: 01/31/2023] Open
Abstract
Signaling networks are spatiotemporally organized to sense diverse inputs, process information, and carry out specific cellular tasks. In β cells, Ca2+, cyclic adenosine monophosphate (cAMP), and Protein Kinase A (PKA) exist in an oscillatory circuit characterized by a high degree of feedback. Here, we describe a mode of regulation within this circuit involving a spatial dependence of the relative phase between cAMP, PKA, and Ca2+. We show that in mouse MIN6 β cells, nanodomain clustering of Ca2+-sensitive adenylyl cyclases (ACs) drives oscillations of local cAMP levels to be precisely in-phase with Ca2+ oscillations, whereas Ca2+-sensitive phosphodiesterases maintain out-of-phase oscillations outside of the nanodomain. Disruption of this precise phase relationship perturbs Ca2+ oscillations, suggesting the relative phase within an oscillatory circuit can encode specific functional information. This work unveils a novel mechanism of cAMP compartmentation utilized for localized tuning of an oscillatory circuit and has broad implications for the spatiotemporal regulation of signaling networks.
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Affiliation(s)
- Brian Tenner
- Department of Biophysics and Biophysical Chemistry, The Johns Hopkins University School of MedicineBaltimoreUnited States
- Department of Pharmacology, University of California, San DiegoLa JollaUnited States
| | - Michael Getz
- Chemical Engineering Graduate Program, University of California, San DiegoLa JollaUnited States
| | - Brian Ross
- Department of Pharmacology, University of California, San DiegoLa JollaUnited States
| | - Donya Ohadi
- Department of Mechanical and Aerospace Engineering, University of California, San DiegoLa JollaUnited States
| | - Christopher H Bohrer
- Department of Biophysics and Biophysical Chemistry, The Johns Hopkins University School of MedicineBaltimoreUnited States
| | - Eric Greenwald
- Department of Pharmacology, University of California, San DiegoLa JollaUnited States
| | - Sohum Mehta
- Department of Pharmacology, University of California, San DiegoLa JollaUnited States
| | - Jie Xiao
- Department of Biophysics and Biophysical Chemistry, The Johns Hopkins University School of MedicineBaltimoreUnited States
| | - Padmini Rangamani
- Chemical Engineering Graduate Program, University of California, San DiegoLa JollaUnited States
- Department of Mechanical and Aerospace Engineering, University of California, San DiegoLa JollaUnited States
| | - Jin Zhang
- Department of Pharmacology, University of California, San DiegoLa JollaUnited States
- Department of Chemistry and Biochemistry, University of California, San DiegoLa JollaUnited States
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9
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Novikov S. Two-dimensional bimolecular recombination in amorphous organic semiconductors. Phys Chem Chem Phys 2020; 22:1174-1180. [PMID: 31848542 DOI: 10.1039/c9cp05511h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We consider the two-dimensional bimolecular recombination of charge carriers in amorphous organic semiconductors having the lamellar structure. We calculate the dependence of the effective recombination rate constant on the carrier density taking into account the correlated nature of the energetic disorder typical for organic semiconductors. The resulting recombination kinetics demonstrates a very rich variety of behaviors depending on the correlation properties of the particular semiconductor and relevant charge density range.
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Affiliation(s)
- Sergey Novikov
- A.N. Frumkin Institute of Physical Chemistry and Electrochemistry, Leninsky prosp. 31, Moscow 119071, Russia. and National Research University Higher School of Economics, Myasnitskaya Ulitsa 20, Moscow 101000, Russia
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10
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Kari J, Christensen SJ, Andersen M, Baiget SS, Borch K, Westh P. A practical approach to steady-state kinetic analysis of cellulases acting on their natural insoluble substrate. Anal Biochem 2019; 586:113411. [PMID: 31520594 DOI: 10.1016/j.ab.2019.113411] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2019] [Revised: 08/26/2019] [Accepted: 08/28/2019] [Indexed: 10/26/2022]
Abstract
Measurement of steady-state rates (vSS) is straightforward in standard enzymology with soluble substrate, and it has been instrumental for comparative biochemical analyses within this area. For insoluble substrate, however, experimental values of vss remain controversial, and this has strongly limited the amount and quality of comparative analyses for cellulases and other enzymes that act on the surface of an insoluble substrate. In the current work, we have measured progress curves over a wide range of conditions for two cellulases, TrCel6A and TrCel7A from Trichoderma reesei, acting on their natural, insoluble substrate, cellulose. Based on this, we consider practical compromises for the determination of experimental vSS values, and propose a basic protocol that provides representative reaction rates and is experimentally simple so that larger groups of enzymes and conditions can be readily assayed with standard laboratory equipment. We surmise that the suggested experimental approach can be useful in comparative biochemical studies of cellulases; an area that remains poorly developed.
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Affiliation(s)
- Jeppe Kari
- Department of Biotechnology and Biomedicine, Technical University of Denmark, Søltofts Plads, Building 224, DK-2800, Kgs. Lyngby, Denmark
| | - Stefan Jarl Christensen
- Department of Science and Environment, Roskilde University, Universitetsvej, Build. 28.C, DK-4000, Roskilde, Denmark
| | - Morten Andersen
- Department of Science and Environment, Roskilde University, Universitetsvej, Build. 28.C, DK-4000, Roskilde, Denmark
| | | | - Kim Borch
- Novozymes A/S, Krogshøjvej 36, DK-2880, Bagsværd, Denmark
| | - Peter Westh
- Department of Biotechnology and Biomedicine, Technical University of Denmark, Søltofts Plads, Building 224, DK-2800, Kgs. Lyngby, Denmark.
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11
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Gschwend GC, Kazmierczak M, Olaya AJ, Brevet PF, Girault HH. Two dimensional diffusion-controlled triplet-triplet annihilation kinetics. Chem Sci 2019; 10:7633-7640. [PMID: 31588315 PMCID: PMC6761882 DOI: 10.1039/c9sc00957d] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2019] [Accepted: 06/28/2019] [Indexed: 01/14/2023] Open
Abstract
Diffusion controlled chemical reactions are usually observed in three dimensional media. In contrast, planar bimolecular reactions taking place between reagents adsorbed at a soft interface are two-dimensional and therefore cannot be studied within the same formalism. Indeed, soft interfaces allow the adsorbed species to freely diffuse in a liquid-like manner. Here, we present the first experimental observation of a diffusion-controlled reaction in an environment that is planar at the ångström scale. By means of time-resolved surface second harmonic generation, an inherently surface sensitive technique, we observed that the kinetics of the diffusion of the reagents in the plane decreases as the surface concentration of adsorbed species increases. This is of course not the case for bulk reactions where the rates always increase with the reactant concentration. Such changes in the kinetics regime were rationalised as the evolution from a regular 2D free diffusion regime to a geometry-controlled scheme.
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Affiliation(s)
- Grégoire C Gschwend
- Laboratoire d'Électrochimie Physique et Analytique , École Polytechnique Fédérale de Lausanne , Rue de l'Industrie 17 , CH-1951 Sion , Switzerland .
| | - Morgan Kazmierczak
- Laboratoire d'Électrochimie Physique et Analytique , École Polytechnique Fédérale de Lausanne , Rue de l'Industrie 17 , CH-1951 Sion , Switzerland .
- École Normale Supérieure , Département de Chimie , PSL Research University , 75005 , Paris , France
| | - Astrid J Olaya
- Laboratoire d'Électrochimie Physique et Analytique , École Polytechnique Fédérale de Lausanne , Rue de l'Industrie 17 , CH-1951 Sion , Switzerland .
| | - Pierre-François Brevet
- Institut Lumière Matière , UMR CNRS 5306 , Université Claude Bernard Lyon 1 , Campus LyonTech La Doua , 10 Rue Ada Byron , 69622 Villeurbanne Cedex , France
| | - Hubert H Girault
- Laboratoire d'Électrochimie Physique et Analytique , École Polytechnique Fédérale de Lausanne , Rue de l'Industrie 17 , CH-1951 Sion , Switzerland .
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12
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13
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Chew WX, Kaizu K, Watabe M, Muniandy SV, Takahashi K, Arjunan SNV. Surface reaction-diffusion kinetics on lattice at the microscopic scale. Phys Rev E 2019; 99:042411. [PMID: 31108654 DOI: 10.1103/physreve.99.042411] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2018] [Indexed: 01/06/2023]
Abstract
Microscopic models of reaction-diffusion processes on the cell membrane can link local spatiotemporal effects to macroscopic self-organized patterns often observed on the membrane. Simulation schemes based on the microscopic lattice method (MLM) can model these processes at the microscopic scale by tracking individual molecules, represented as hard spheres, on fine lattice voxels. Although MLM is simple to implement and is generally less computationally demanding than off-lattice approaches, its accuracy and consistency in modeling surface reactions have not been fully verified. Using the Spatiocyte scheme, we study the accuracy of MLM in diffusion-influenced surface reactions. We derive the lattice-based bimolecular association rates for two-dimensional (2D) surface-surface reaction and one-dimensional (1D) volume-surface adsorption according to the Smoluchowski-Collins-Kimball model and random walk theory. We match the time-dependent rates on lattice with off-lattice counterparts to obtain the correct expressions for MLM parameters in terms of physical constants. The expressions indicate that the voxel size needs to be at least 0.6% larger than the molecule to accurately simulate surface reactions on triangular lattice. On square lattice, the minimum voxel size should be even larger, at 5%. We also demonstrate the ability of MLM-based schemes such as Spatiocyte to simulate a reaction-diffusion model that involves all dimensions: three-dimensional (3D) diffusion in the cytoplasm, 2D diffusion on the cell membrane, and 1D cytoplasm-membrane adsorption. With the model, we examine the contribution of the 2D reaction pathway to the overall reaction rate at different reactant diffusivity, reactivity, and concentrations.
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Affiliation(s)
- Wei-Xiang Chew
- Laboratory for Biologically Inspired Computing, RIKEN Center for Biosystems Dynamics Research, Suita, Osaka, Japan.,Department of Physics, Faculty of Science, University of Malaya, 50603, Kuala Lumpur, Malaysia
| | - Kazunari Kaizu
- Laboratory for Biologically Inspired Computing, RIKEN Center for Biosystems Dynamics Research, Suita, Osaka, Japan
| | - Masaki Watabe
- Laboratory for Biologically Inspired Computing, RIKEN Center for Biosystems Dynamics Research, Suita, Osaka, Japan
| | - Sithi V Muniandy
- Department of Physics, Faculty of Science, University of Malaya, 50603, Kuala Lumpur, Malaysia
| | - Koichi Takahashi
- Laboratory for Biologically Inspired Computing, RIKEN Center for Biosystems Dynamics Research, Suita, Osaka, Japan
| | - Satya N V Arjunan
- Laboratory for Biologically Inspired Computing, RIKEN Center for Biosystems Dynamics Research, Suita, Osaka, Japan
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14
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Du Y, Jiang H, Hou Z. Study of active Brownian particle diffusion in polymer solutions. SOFT MATTER 2019; 15:2020-2031. [PMID: 30724318 DOI: 10.1039/c8sm02292e] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The diffusion behavior of an active Brownian particle (ABP) in polymer solutions is studied using Langevin dynamics simulations. We find that the long time diffusion coefficient D can show a non-monotonic dependence on the particle size R if the active force Fa is large enough, wherein a bigger particle would diffuse faster than a smaller one which is quite counterintuitive. By analyzing the short time dynamics in comparison to the passive one, we find that such non-trivial dependence results from the competition between persistent motion of the ABP and the length-scale dependent effective viscosity that the particle experiences in the polymer solution. We have also introduced an effective viscosity ηeff experienced by the ABP phenomenologically. Such an active ηeff is found to be larger than a passive one and strongly depends on R and Fa. In addition, we find that the dependence of D on propelling force Fa presents a good power-law scaling at a fixed R and the scaling factor changes non-monotonically with R. Such results demonstrate that the active process plays rather subtle roles in the diffusion of nano-particles in complex solutions.
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Affiliation(s)
- Yunfei Du
- Department of Chemical Physics and Hefei National Laboratory for Physical Sciences at Microscales, iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China.
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15
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Anand R, Agrawal M, Mattaparthi VS, Swaminathan R, Santra SB. Consequences of Heterogeneous Crowding on an Enzymatic Reaction: A Residence Time Monte Carlo Approach. ACS OMEGA 2019; 4:727-736. [PMID: 31459357 PMCID: PMC6649177 DOI: 10.1021/acsomega.8b02863] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2018] [Accepted: 12/26/2018] [Indexed: 05/06/2023]
Abstract
Translational diffusion of a free substrate in crowded metabolically active spaces such as cell cytoplasm or mitochondrial matrix is punctuated by collisions and nonspecific interactions with soluble/immobile macromolecules/macrostructures in a variety of shapes/sizes. It is not understood how such disruptions alter enzyme reaction kinetics in such spaces. A novel Monte Carlo (MC) technique, "residence time MC", has been developed to study the kinetics of a simple enzyme-substrate reaction in a crowded milieu using a single immobile enzyme in the midst of diffusing substrates and products. The reaction time lost while the substrate nonspecifically interacts or is transiently trapped with ambient macromolecules is quantified by introducing the residence time "tau". Tau scales with the size of crowding macromolecules but makes the knowledge of their shape redundant. The residence time thus presents a convenient parameter to realistically mimic the sticky surroundings encountered by a diffusing substrate in heterogeneously crowded physiological spaces. Results reveal that for identical substrate concentration and excluded volume, increase in tau significantly diminished enzymatic product yield and reaction rate, slowed down substrate/product diffusion, and prolonged their relaxation times. A smooth transition from the anomalous subdiffusive motion to normal diffusion at long time limits was observed irrespective of the value of tau. The predictions from the model are shown to be in qualitative agreement with in vitro experimental data revealing the rate of alkaline phosphatase-catalyzed hydrolysis of p-nitrophenyl phosphate in the midst of 40/500/2000 kDa dextrans. Our findings from the residence time MC model also attempt to rationalize previously unexplained experimental observations in crowded enzyme kinetics literature. Furthermore, major insights to emerge from this study are the reasons why free diffusion of the substrate in crowded physiological spaces is detrimental to enzyme function. It is argued that organized enzyme clusters such as "metabolon" may perhaps exist to regulate the substrate translocation in such sticky physiological spaces to maintain optimal enzyme function. In summary, this work provides key insights explaining why absence of substrate channeling can dramatically slow down enzyme reaction rate in crowded metabolically active spaces.
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Affiliation(s)
- Rajat Anand
- Department of Biosciences and Bioengineering and Department of
Physics, Indian Institute of Technology
Guwahati, Guwahati 781039, Assam, India
| | - Manish Agrawal
- Department of Biosciences and Bioengineering and Department of
Physics, Indian Institute of Technology
Guwahati, Guwahati 781039, Assam, India
| | - Venkata Satish
Kumar Mattaparthi
- Department of Biosciences and Bioengineering and Department of
Physics, Indian Institute of Technology
Guwahati, Guwahati 781039, Assam, India
| | - Rajaram Swaminathan
- Department of Biosciences and Bioengineering and Department of
Physics, Indian Institute of Technology
Guwahati, Guwahati 781039, Assam, India
- E-mail:
| | - Sitangshu Bikas Santra
- Department of Biosciences and Bioengineering and Department of
Physics, Indian Institute of Technology
Guwahati, Guwahati 781039, Assam, India
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16
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Montagnaro F, Balsamo M. Modelling CO2 adsorption dynamics onto amine-functionalised sorbents: A fractal-like kinetic perspective. Chem Eng Sci 2018. [DOI: 10.1016/j.ces.2018.08.009] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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17
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Woringer M, Darzacq X. Protein motion in the nucleus: from anomalous diffusion to weak interactions. Biochem Soc Trans 2018; 46:945-956. [PMID: 30065106 PMCID: PMC6103463 DOI: 10.1042/bst20170310] [Citation(s) in RCA: 38] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2018] [Revised: 05/02/2018] [Accepted: 05/14/2018] [Indexed: 12/12/2022]
Abstract
Understanding how transcription factors (TFs) regulate mammalian gene expression in space and time is a central topic in biology. To activate a gene, a TF has first to diffuse in the available space of the nucleus until it reaches a target DNA sequence or protein (target site). This eventually results in the recruitment of the whole transcriptional machinery. All these processes take place in the mammalian nucleoplasm, a highly organized and dynamic environment, in which some complexes transiently assemble and break apart, whereas others appear more stable. This diversity of dynamic behaviors arises from the number of biomolecules that make up the nucleoplasm and their pairwise interactions. Indeed, interactions energies that span several orders of magnitude, from covalent bounds to transient and dynamic interactions, can shape nuclear landscapes. Thus, the nuclear environment determines how frequently and how fast a TF contacts its target site, and it indirectly regulates gene expression. How exactly transient interactions are involved in the regulation of TF diffusion is unclear, but are reflected by live cell imaging techniques, including single-particle tracking (SPT). Overall, the macroscopic result of these microscopic interactions is almost always anomalous diffusion, a phenomenon widely studied and modeled. Here, we review the connections between the anomalous diffusion of a TF observed by SPT and the microscopic organization of the nucleus, including recently described topologically associated domains and dynamic phase-separated compartments. We propose that anomalous diffusion found in SPT data result from weak and transient interactions with dynamic nuclear substructures, and that SPT data analysis would benefit from a better description of such structures.
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Affiliation(s)
- Maxime Woringer
- Department of Molecular and Cell Biology, Li Ka Shing Center for Biomedical and Health Sciences, CIRM Center of Excellence, University of California, Berkeley, CA 94720, U.S.A.
- Unité Imagerie et Modélisation, Institut Pasteur, 25 rue du Docteur Roux, 75015 Paris, France
- Sorbonne Universités, CNRS, F-75005 Paris, France
| | - Xavier Darzacq
- Department of Molecular and Cell Biology, Li Ka Shing Center for Biomedical and Health Sciences, CIRM Center of Excellence, University of California, Berkeley, CA 94720, U.S.A.
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18
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Mohammadi Y, Penlidis A. “Optimulation” in Chemical Reaction Engineering: Oxidative Coupling of Methane as a Case Study. Ind Eng Chem Res 2018. [DOI: 10.1021/acs.iecr.8b01424] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Affiliation(s)
- Yousef Mohammadi
- Petrochemical Research and Technology Company (NPC-rt), National Petrochemical Company (NPC), P.O. Box 14358-84711, Tehran, Iran
| | - Alexander Penlidis
- Department of Chemical Engineering, Institute for Polymer Research (IPR), University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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19
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Multiscale Modeling of Diffusion in a Crowded Environment. Bull Math Biol 2017; 79:2672-2695. [PMID: 28924915 DOI: 10.1007/s11538-017-0346-6] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2016] [Accepted: 09/06/2017] [Indexed: 10/18/2022]
Abstract
We present a multiscale approach to model diffusion in a crowded environment and its effect on the reaction rates. Diffusion in biological systems is often modeled by a discrete space jump process in order to capture the inherent noise of biological systems, which becomes important in the low copy number regime. To model diffusion in the crowded cell environment efficiently, we compute the jump rates in this mesoscopic model from local first exit times, which account for the microscopic positions of the crowding molecules, while the diffusing molecules jump on a coarser Cartesian grid. We then extract a macroscopic description from the resulting jump rates, where the excluded volume effect is modeled by a diffusion equation with space-dependent diffusion coefficient. The crowding molecules can be of arbitrary shape and size, and numerical experiments demonstrate that those factors together with the size of the diffusing molecule play a crucial role on the magnitude of the decrease in diffusive motion. When correcting the reaction rates for the altered diffusion we can show that molecular crowding either enhances or inhibits chemical reactions depending on local fluctuations of the obstacle density.
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20
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Stefferson MW, Norris SL, Vernerey FJ, Betterton MD, Hough LE. Effects of soft interactions and bound mobility on diffusion in crowded environments: a model of sticky and slippery obstacles. Phys Biol 2017; 14:045008. [PMID: 28597848 DOI: 10.1088/1478-3975/aa7869] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Crowded environments modify the diffusion of macromolecules, generally slowing their movement and inducing transient anomalous subdiffusion. The presence of obstacles also modifies the kinetics and equilibrium behavior of tracers. While previous theoretical studies of particle diffusion have typically assumed either impenetrable obstacles or binding interactions that immobilize the particle, in many cellular contexts bound particles remain mobile. Examples include membrane proteins or lipids with some entry and diffusion within lipid domains and proteins that can enter into membraneless organelles or compartments such as the nucleolus. Using a lattice model, we studied the diffusive movement of tracer particles which bind to soft obstacles, allowing tracers and obstacles to occupy the same lattice site. For sticky obstacles, bound tracer particles are immobile, while for slippery obstacles, bound tracers can hop without penalty to adjacent obstacles. In both models, binding significantly alters tracer motion. The type and degree of motion while bound is a key determinant of the tracer mobility: slippery obstacles can allow nearly unhindered diffusion, even at high obstacle filling fraction. To mimic compartmentalization in a cell, we examined how obstacle size and a range of bound diffusion coefficients affect tracer dynamics. The behavior of the model is similar in two and three spatial dimensions. Our work has implications for protein movement and interactions within cells.
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Affiliation(s)
- Michael W Stefferson
- Department of Physics, University of Colorado, Boulder, United States of America
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21
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Kari J, Andersen M, Borch K, Westh P. An Inverse Michaelis–Menten Approach for Interfacial Enzyme Kinetics. ACS Catal 2017. [DOI: 10.1021/acscatal.7b00838] [Citation(s) in RCA: 71] [Impact Index Per Article: 10.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jeppe Kari
- Dept.
of Science and Environment, Roskilde University, 1 Universitetsvej, Building 28, DK-4000 Roskilde, Denmark
| | - Morten Andersen
- Dept.
of Science and Environment, Roskilde University, 1 Universitetsvej, Building 28, DK-4000 Roskilde, Denmark
| | - Kim Borch
- Novozymes A/S, Krogshøjvej
36, DK-2880 Bagsværd, Denmark
| | - Peter Westh
- Dept.
of Science and Environment, Roskilde University, 1 Universitetsvej, Building 28, DK-4000 Roskilde, Denmark
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22
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Garland J. Unravelling the complexity of signalling networks in cancer: A review of the increasing role for computational modelling. Crit Rev Oncol Hematol 2017; 117:73-113. [PMID: 28807238 DOI: 10.1016/j.critrevonc.2017.06.004] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2016] [Revised: 06/01/2017] [Accepted: 06/08/2017] [Indexed: 02/06/2023] Open
Abstract
Cancer induction is a highly complex process involving hundreds of different inducers but whose eventual outcome is the same. Clearly, it is essential to understand how signalling pathways and networks generated by these inducers interact to regulate cell behaviour and create the cancer phenotype. While enormous strides have been made in identifying key networking profiles, the amount of data generated far exceeds our ability to understand how it all "fits together". The number of potential interactions is astronomically large and requires novel approaches and extreme computation methods to dissect them out. However, such methodologies have high intrinsic mathematical and conceptual content which is difficult to follow. This review explains how computation modelling is progressively finding solutions and also revealing unexpected and unpredictable nano-scale molecular behaviours extremely relevant to how signalling and networking are coherently integrated. It is divided into linked sections illustrated by numerous figures from the literature describing different approaches and offering visual portrayals of networking and major conceptual advances in the field. First, the problem of signalling complexity and data collection is illustrated for only a small selection of known oncogenes. Next, new concepts from biophysics, molecular behaviours, kinetics, organisation at the nano level and predictive models are presented. These areas include: visual representations of networking, Energy Landscapes and energy transfer/dissemination (entropy); diffusion, percolation; molecular crowding; protein allostery; quinary structure and fractal distributions; energy management, metabolism and re-examination of the Warburg effect. The importance of unravelling complex network interactions is then illustrated for some widely-used drugs in cancer therapy whose interactions are very extensive. Finally, use of computational modelling to develop micro- and nano- functional models ("bottom-up" research) is highlighted. The review concludes that computational modelling is an essential part of cancer research and is vital to understanding network formation and molecular behaviours that are associated with it. Its role is increasingly essential because it is unravelling the huge complexity of cancer induction otherwise unattainable by any other approach.
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Affiliation(s)
- John Garland
- Manchester Interdisciplinary Biocentre, Manchester University, Manchester, UK.
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23
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Meinecke L, Eriksson M. Excluded volume effects in on- and off-lattice reaction-diffusion models. IET Syst Biol 2017; 11:55-64. [PMID: 28476973 PMCID: PMC8687331 DOI: 10.1049/iet-syb.2016.0021] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2016] [Revised: 10/24/2016] [Accepted: 10/25/2016] [Indexed: 04/05/2024] Open
Abstract
Mathematical models are important tools to study the excluded volume effects on reaction-diffusion systems, which are known to play an important role inside living cells. Detailed microscopic simulations with off-lattice Brownian dynamics become computationally expensive in crowded environments. In this study, the authors therefore investigate to which extent on-lattice approximations, the so-called cellular automata models, can be used to simulate reactions and diffusion in the presence of crowding molecules. They show that the diffusion is most severely slowed down in the off-lattice model, since randomly distributed obstacles effectively exclude more volume than those ordered on an artificial grid. Crowded reaction rates can be both increased and decreased by the grid structure and it proves important to model the molecules with realistic sizes when excluded volume is taken into account. The grid artefacts increase with increasing crowder density and they conclude that the computationally more efficient on-lattice simulations are accurate approximations only for low crowder densities.
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Affiliation(s)
- Lina Meinecke
- Department of Information Technology, Uppsala University, Uppsala, Sweden.
| | - Markus Eriksson
- Department of Information Technology, Uppsala University, Uppsala, Sweden
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24
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Smith S, Grima R. Fast simulation of Brownian dynamics in a crowded environment. J Chem Phys 2017; 146:024105. [DOI: 10.1063/1.4973606] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Affiliation(s)
- Stephen Smith
- School of Biological Sciences, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JR, Scotland, United Kingdom
| | - Ramon Grima
- School of Biological Sciences, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JR, Scotland, United Kingdom
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25
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Cianci C, Smith S, Grima R. Molecular finite-size effects in stochastic models of equilibrium chemical systems. J Chem Phys 2016; 144:084101. [PMID: 26931675 DOI: 10.1063/1.4941583] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Abstract
The reaction-diffusion master equation (RDME) is a standard modelling approach for understanding stochastic and spatial chemical kinetics. An inherent assumption is that molecules are point-like. Here, we introduce the excluded volume reaction-diffusion master equation (vRDME) which takes into account volume exclusion effects on stochastic kinetics due to a finite molecular radius. We obtain an exact closed form solution of the RDME and of the vRDME for a general chemical system in equilibrium conditions. The difference between the two solutions increases with the ratio of molecular diameter to the compartment length scale. We show that an increase in the fraction of excluded space can (i) lead to deviations from the classical inverse square root law for the noise-strength, (ii) flip the skewness of the probability distribution from right to left-skewed, (iii) shift the equilibrium of bimolecular reactions so that more product molecules are formed, and (iv) strongly modulate the Fano factors and coefficients of variation. These volume exclusion effects are found to be particularly pronounced for chemical species not involved in chemical conservation laws. Finally, we show that statistics obtained using the vRDME are in good agreement with those obtained from Brownian dynamics with excluded volume interactions.
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Affiliation(s)
- Claudia Cianci
- School of Biological Sciences, University of Edinburgh, Mayfield Road Edinburgh EH93JR Scotland,United Kingdom
| | - Stephen Smith
- School of Biological Sciences, University of Edinburgh, Mayfield Road Edinburgh EH93JR Scotland,United Kingdom
| | - Ramon Grima
- School of Biological Sciences, University of Edinburgh, Mayfield Road Edinburgh EH93JR Scotland,United Kingdom
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26
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Lenzi EK, Ribeiro HV, Tateishi AA, Zola RS, Evangelista LR. Anomalous diffusion and transport in heterogeneous systems separated by a membrane. Proc Math Phys Eng Sci 2016; 472:20160502. [PMID: 27956877 DOI: 10.1098/rspa.2016.0502] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Diffusion of particles in a heterogeneous system separated by a semipermeable membrane is investigated. The particle dynamics is governed by fractional diffusion equations in the bulk and by kinetic equations on the membrane, which characterizes an interface between two different media. The kinetic equations are solved by incorporating memory effects to account for anomalous diffusion and, consequently, non-Debye relaxations. A rich variety of behaviours for the particle distribution at the interface and in the bulk may be found, depending on the choice of characteristic times in the boundary conditions and on the fractional index of the modelling equations.
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Affiliation(s)
- E K Lenzi
- Departamento de Física , Universidade Estadual de Ponta Grossa , Ponta Grossa, Paraná 87030-900, Brazil
| | - H V Ribeiro
- Departamento de Física , Universidade Estadual de Maringá , Maringá, Paraná 87020-900, Brazil
| | - A A Tateishi
- Departamento de Física , Universidade Tecnológica Federal do Paraná , Pato Branco, Paraná 85503-390, Brazil
| | - R S Zola
- Departamento de Física, Universidade Estadual de Maringá, Maringá, Paraná 87020-900, Brazil; Departamento de Física, Universidade Tecnológica Federal do Paraná, Apucarana, Paraná 86812-460, Brazil
| | - L R Evangelista
- Departamento de Física , Universidade Estadual de Maringá , Maringá, Paraná 87020-900, Brazil
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27
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Feng X, Chen A, Wang J, Zhao N, Hou Z. Understanding Protein Diffusion in Polymer Solutions: A Hydration with Depletion Model. J Phys Chem B 2016; 120:10114-10123. [DOI: 10.1021/acs.jpcb.6b06248] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Affiliation(s)
- Xiaoqing Feng
- College
of Chemistry, Sichuan University, Chengdu 610064, China
| | - Anpu Chen
- College
of Chemistry, Sichuan University, Chengdu 610064, China
| | - Juan Wang
- College
of Chemistry, Sichuan University, Chengdu 610064, China
| | - Nanrong Zhao
- College
of Chemistry, Sichuan University, Chengdu 610064, China
| | - Zhonghuai Hou
- Hefei National Laboratory for Physical Sciences at the Microscale & Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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28
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Wang ZW, Xu F, Manchala KR, Sun Y, Li Y. Fractal-like kinetics of the solid-state anaerobic digestion. WASTE MANAGEMENT (NEW YORK, N.Y.) 2016; 53:55-61. [PMID: 27132655 DOI: 10.1016/j.wasman.2016.04.019] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2016] [Revised: 04/13/2016] [Accepted: 04/15/2016] [Indexed: 06/05/2023]
Abstract
Total solid content (TS) negatively impacts the methane production efficiency (MPE) of solid-state anaerobic digestion (SS-AD), to which the classic mass action-based kinetics failed to provide a unified explanation. This study revealed that SS-AD reactions actually follow the fractal-like kinetics in light of the surface reactions in crowded SS-AD environment packed with heterogeneous media. The fractal characteristics of the SS-AD kinetics were found increasingly pronounced as TS increased. This study represents the first attempt to resolve the dilemma in SS-AD kinetics with the application of fractal theory. Employing this new concept allows explaining the reduced MPE at high TS and offers an easy assessment of the fractal characteristics of the SS-AD media.
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Affiliation(s)
- Zhi-Wu Wang
- Department of Civil and Environmental Engineering, Virginia Tech, Occoquan Laboratory, 9408 Prince William Street, Manassas, VA 20110, USA.
| | - Fuqing Xu
- Department of Food, Agricultural and Biological Engineering, The Ohio State University/Ohio Agricultural Research and Development Center, 1680 Madison Ave., Wooster, OH 44691, USA
| | - Karthik R Manchala
- Department of Civil and Environmental Engineering, Virginia Tech, Occoquan Laboratory, 9408 Prince William Street, Manassas, VA 20110, USA
| | - Yewei Sun
- Department of Civil and Environmental Engineering, Virginia Tech, Occoquan Laboratory, 9408 Prince William Street, Manassas, VA 20110, USA
| | - Yebo Li
- Department of Food, Agricultural and Biological Engineering, The Ohio State University/Ohio Agricultural Research and Development Center, 1680 Madison Ave., Wooster, OH 44691, USA
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29
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Mourão MA, Hakim JB, Schnell S. Connecting the dots: the effects of macromolecular crowding on cell physiology. Biophys J 2016; 107:2761-2766. [PMID: 25517143 DOI: 10.1016/j.bpj.2014.10.051] [Citation(s) in RCA: 97] [Impact Index Per Article: 12.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2014] [Revised: 10/17/2014] [Accepted: 10/23/2014] [Indexed: 10/25/2022] Open
Abstract
The physicochemical properties of cellular environments with a high macromolecular content have been systematically characterized to explain differences observed in the diffusion coefficients, kinetics parameters, and thermodynamic properties of proteins inside and outside of cells. However, much less attention has been given to the effects of macromolecular crowding on cell physiology. Here, we review recent findings that shed some light on the role of crowding in various cellular processes, such as reduction of biochemical activities, structural reorganization of the cytoplasm, cytoplasm fluidity, and cellular dormancy. We conclude by presenting some unresolved problems that require the attention of biophysicists, biochemists, and cell physiologists. Although it is still underappreciated, macromolecular crowding plays a critical role in life as we know it.
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Affiliation(s)
- Márcio A Mourão
- Mathematical Biosciences Institute, Ohio State University, Columbus, Ohio
| | - Joe B Hakim
- Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland; Department of Molecular & Integrative Physiology, University of Michigan Medical School, Ann Arbor, Michigan
| | - Santiago Schnell
- Department of Molecular & Integrative Physiology, University of Michigan Medical School, Ann Arbor, Michigan; Department of Computational Medicine & Bioinformatics, University of Michigan Medical School, Ann Arbor, Michigan; Brehm Center for Diabetes Research, University of Michigan Medical School, Ann Arbor, Michigan.
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30
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Rohrs JA, Wang P, Finley SD. Predictive Model of Lymphocyte-Specific Protein Tyrosine Kinase (LCK) Autoregulation. Cell Mol Bioeng 2016; 9:351-367. [PMID: 27547268 PMCID: PMC4978775 DOI: 10.1007/s12195-016-0438-7] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2016] [Accepted: 04/12/2016] [Indexed: 12/29/2022] Open
Abstract
Lymphocyte-specific protein tyrosine kinase (LCK) is a key activator of T cells; however, little is known about the specific autoregulatory mechanisms that control its activity. We have constructed a model of LCK autophosphorylation and phosphorylation by the regulating kinase CSK. The model was fit to existing experimental data in the literature that presents an in vitro reconstituted membrane system, which provides more physiologically relevant kinetic measurements than traditional solution-based systems. The model is able to predict a robust mechanism of LCK autoregulation. It provides insights into the molecular causes of key site-specific phosphorylation differences between distinct experimental conditions. Probing the model also provides new hypotheses regarding the influence of individual binding and catalytic rates, which can be tested experimentally. This minimal model is required to elucidate the mechanistic interactions of LCK and CSK and can be further expanded to better understand T cell activation from a systems perspective. Our computational model enables the evaluation of LCK protein interactions that mediate T cell activation on a more quantitative level, providing new insights and testable hypotheses.
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Affiliation(s)
- Jennifer A Rohrs
- Department of Biomedical Engineering, University of Southern California, 1042 Downey Way, DRB 140, Los Angeles, CA 90089 USA
| | - Pin Wang
- Department of Biomedical Engineering, University of Southern California, 1042 Downey Way, DRB 140, Los Angeles, CA 90089 USA ; Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, CA USA
| | - Stacey D Finley
- Department of Biomedical Engineering, University of Southern California, 1042 Downey Way, DRB 140, Los Angeles, CA 90089 USA ; Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, CA USA
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31
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Angeles-Martinez L, Theodoropoulos C. A Lattice-Boltzmann scheme for the simulation of diffusion in intracellular crowded systems. BMC Bioinformatics 2015; 16:353. [PMID: 26530635 PMCID: PMC4632338 DOI: 10.1186/s12859-015-0769-8] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2014] [Accepted: 10/08/2015] [Indexed: 11/10/2022] Open
Abstract
Background The intracellular environment is a complex and crowded medium where the diffusion of proteins, metabolites and other molecules can be decreased. One of the most popular methodologies for the simulation of diffusion in crowding systems is the Monte Carlo algorithm (MC) which tracks the movement of each particle. This can, however, be computationally expensive for a system comprising a large number of molecules. On the other hand, the Lattice Boltzmann Method (LBM) tracks the movement of collections of molecules, which represents significant savings in computational time. Nevertheless in the classical manifestation of such scheme the crowding conditions are neglected. Methods In this paper we use Scaled Particle Theory (SPT) to approximate the probability to find free space for the displacement of hard-disk molecules and in this way to incorporate the crowding effect to the LBM. This new methodology which couples SPT and LBM is validated using a kinetic Monte Carlo (kMC) algorithm, which is used here as our "computational experiment". Results The results indicate that LBM over-predicts the diffusion in 2D crowded systems, while the proposed coupled SPT-LBM predicts the same behaviour as the kinetic Monte Carlo (kMC) algorithm but with a significantly reduced computational effort. Despite the fact that small deviations between the two methods were observed, in part due to the mesoscopic and microscopic nature of each method, respectively, the agreement was satisfactory both from a qualitative and a quantitative point of view. Conclusions A crowding-adaptation to LBM has been developed using SPT, allowing fast simulations of diffusion-systems of different size hard-disk molecules in two-dimensional space. This methodology takes into account crowding conditions; not only the space fraction occupied by the crowder molecules but also the influence of the size of the crowder which can affect the displacement of molecules across the lattice system. Electronic supplementary material The online version of this article (doi:10.1186/s12859-015-0769-8) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Liliana Angeles-Martinez
- School of Chemical Engineering and Analytical Science, University of Manchester, Manchester, M13 9PL, UK.
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32
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Ernst D, Köhler J, Weiss M. Probing the type of anomalous diffusion with single-particle tracking. Phys Chem Chem Phys 2015; 16:7686-91. [PMID: 24651929 DOI: 10.1039/c4cp00292j] [Citation(s) in RCA: 68] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Many reactions in complex fluids, e.g. signaling cascades in the cytoplasm of living cells, are governed by a diffusion-driven encounter of reactants. Yet, diffusion in complex fluids often exhibits an anomalous characteristic ('subdiffusion'). Since different types of subdiffusion have distinct effects on timing and equilibria of chemical reactions, a thorough determination of the reactants' type of random walk is key to a quantitative understanding of reactions in complex fluids. Here we introduce a straightforward and simple approach for determining the type of subdiffusion from single-particle tracking data. Unlike previous approaches, our method also is sensitive to transient subdiffusion phenomena, e.g. obstructed diffusion below the percolation threshold. We validate our strategy with data from experiment and simulation.
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Affiliation(s)
- Dominique Ernst
- Experimental Physics IV, University of Bayreuth, 95440 Bayreuth, Germany.
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Alarcón T. Stochastic quasi-steady state approximations for asymptotic solutions of the chemical master equation. J Chem Phys 2015; 140:184109. [PMID: 24832255 DOI: 10.1063/1.4874653] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this paper, we propose two methods to carry out the quasi-steady state approximation in stochastic models of enzyme catalytic regulation, based on WKB asymptotics of the chemical master equation or of the corresponding partial differential equation for the generating function. The first of the methods we propose involves the development of multiscale generalisation of a WKB approximation of the solution of the master equation, where the separation of time scales is made explicit which allows us to apply the quasi-steady state approximation in a straightforward manner. To the lowest order, the multi-scale WKB method provides a quasi-steady state, Gaussian approximation of the probability distribution. The second method is based on the Hamilton-Jacobi representation of the stochastic process where, as predicted by large deviation theory, the solution of the partial differential equation for the corresponding characteristic function is given in terms of an effective action functional. The optimal transition paths between two states are then given by those paths that maximise the effective action. Such paths are the solutions of the Hamilton equations for the Hamiltonian associated to the effective action functional. The quasi-steady state approximation is applied to the Hamilton equations thus providing an approximation to the optimal transition paths and the transition time between two states. Using this approximation we predict that, unlike the mean-field quasi-steady approximation result, the rate of enzyme catalysis depends explicitly on the initial number of enzyme molecules. The accuracy and validity of our approximated results as well as that of our predictions regarding the behaviour of the stochastic enzyme catalytic models are verified by direct simulation of the stochastic model using Gillespie stochastic simulation algorithm.
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Affiliation(s)
- Tomás Alarcón
- Centre de Recerca Matemàtica, Edifici C, Campus de Bellaterra, 08193 Bellaterra (Barcelona), Spain
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Abstract
An appreciable part of enzymes operating in vivo is associated with lipid membranes. The function of such enzymes can be influenced by the presence of domains containing proteins and/or composed of different lipids. The corresponding experimental model-system studies can be performed under well controlled conditions, e.g., on a planar supported lipid bilayer or surface-immobilized vesicles. To clarify what may happen in such systems, we propose general kinetic equations describing the enzyme-catalyzed substrate conversion occurring via the Michaelis-Menten (MM) mechanism on a membrane with domains which do not directly participate in reaction. For two generic situations when a relatively slow reaction takes place primarily in or outside domains, we take substrate saturation and lateral substrate-substrate interactions at domains into account and scrutinize the dependence of the reaction rate on the average substrate coverage. With increasing coverage, depending on the details, the reaction rate reaches saturation via an inflection point or monotonously as in the conventional MM case. In addition, we show analytically the types of reaction kinetics occurring primarily at domain boundaries. In the physically interesting situation when the domain growth is fast on the reaction time scale, the latter kinetics are far from conventional. The opposite situation when the reaction is fast and controlled by diffusion has been studied by using the Monte Carlo technique. The corresponding results indicate that the dependence of the reaction kinetics on the domain size may be weak.
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Affiliation(s)
- Vladimir P Zhdanov
- Division of Biological Physics, Department of Applied Physics, Chalmers University of Technology, SE-41296 Göteborg, Sweden. Boreskov Institute of Catalysis, Russian Academy of Sciences, Novosibirsk 630090, Russia
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ElKalaawy N, Wassal A. Methodologies for the modeling and simulation of biochemical networks, illustrated for signal transduction pathways: a primer. Biosystems 2015; 129:1-18. [PMID: 25637875 DOI: 10.1016/j.biosystems.2015.01.008] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2014] [Revised: 01/23/2015] [Accepted: 01/23/2015] [Indexed: 01/30/2023]
Abstract
Biochemical networks depict the chemical interactions that take place among elements of living cells. They aim to elucidate how cellular behavior and functional properties of the cell emerge from the relationships between its components, i.e. molecules. Biochemical networks are largely characterized by dynamic behavior, and exhibit high degrees of complexity. Hence, the interest in such networks is growing and they have been the target of several recent modeling efforts. Signal transduction pathways (STPs) constitute a class of biochemical networks that receive, process, and respond to stimuli from the environment, as well as stimuli that are internal to the organism. An STP consists of a chain of intracellular signaling processes that ultimately result in generating different cellular responses. This primer presents the methodologies used for the modeling and simulation of biochemical networks, illustrated for STPs. These methodologies range from qualitative to quantitative, and include structural as well as dynamic analysis techniques. We describe the different methodologies, outline their underlying assumptions, and provide an assessment of their advantages and disadvantages. Moreover, publicly and/or commercially available implementations of these methodologies are listed as appropriate. In particular, this primer aims to provide a clear introduction and comprehensive coverage of biochemical modeling and simulation methodologies for the non-expert, with specific focus on relevant literature of STPs.
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Affiliation(s)
- Nesma ElKalaawy
- Department of Computer Engineering, Faculty of Engineering, Cairo University, Giza 12613, Egypt.
| | - Amr Wassal
- Department of Computer Engineering, Faculty of Engineering, Cairo University, Giza 12613, Egypt.
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36
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Aon MA, Cortassa S. Function of metabolic and organelle networks in crowded and organized media. Front Physiol 2015; 5:523. [PMID: 25653618 PMCID: PMC4300868 DOI: 10.3389/fphys.2014.00523] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2014] [Accepted: 12/19/2014] [Indexed: 11/13/2022] Open
Abstract
(Macro)molecular crowding and the ability of the ubiquitous cytoskeleton to dynamically polymerize–depolymerize are prevalent cytoplasmic conditions in prokaryotic and eukaryotic cells. Protein interactions, enzymatic or signaling reactions - single, sequential or in complexes - whole metabolic pathways and organelles can be affected by crowding, the type and polymeric status of cytoskeletal proteins (e.g., tubulin, actin), and their imparted organization. The self-organizing capability of the cytoskeleton can orchestrate metabolic fluxes through entire pathways while its fractal organization can frame the scaling of activities in several levels of organization. The intracellular environment dynamics (e.g., biochemical reactions) is dominated by the orderly cytoskeleton and the intrinsic randomness of molecular crowding. Existing evidence underscores the inherent capacity of intracellular organization to generate emergent global behavior. Yet unknown is the relative impact on cell function provided by organelle or functional compartmentation based on transient proteins association driven by weak interactions (quinary structures) under specific environmental challenges or functional conditions (e.g., hypoxia, division, differentiation). We propose a qualitative, integrated structural–functional model of cytoplasmic organization based on a modified version of the Sierspinsky–Menger–Mandelbrot sponge, a 3D representation of a percolation cluster, and examine its capacity to accommodate established experimental facts.
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Affiliation(s)
- Miguel A Aon
- Department of Medicine, School of Medicine, Johns Hopkins University Baltimore, MD, USA
| | - Sonia Cortassa
- Department of Medicine, School of Medicine, Johns Hopkins University Baltimore, MD, USA
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Stiehl O, Weidner-Hertrampf K, Weiss M. Macromolecular crowding impacts on the diffusion and conformation of DNA hairpins. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:012703. [PMID: 25679639 DOI: 10.1103/physreve.91.012703] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2014] [Indexed: 06/04/2023]
Abstract
Biochemical reactions in crowded fluids differ significantly from those in dilute solutions. Both, excluded-volume interactions with surrounding macromolecules ("crowders") and an enhanced rebinding of reaction partners due to crowding-induced viscoelasticity and subdiffusion have been hypothesized to shift chemical equilibria towards the associated state. We have explored the impact of both cues in an experimentally tunable system by monitoring the steady-state fraction of open DNA hairpins in crowded fluids with varying viscoelastic characteristics but similar occupied volume fractions. As a result, we observed an increased fraction of closed DNA hairpins in viscoelastic crowded fluids. Our observations compare favorably to a simple statistical model that considers both facets of crowding, while preferential interactions between crowders and DNA hairpins appear to have little influence.
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Affiliation(s)
- Olivia Stiehl
- Experimental Physics I, University of Bayreuth, Universitätsstrasse 30, D-95440 Bayreuth, Germany
| | | | - Matthias Weiss
- Experimental Physics I, University of Bayreuth, Universitätsstrasse 30, D-95440 Bayreuth, Germany
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Echeverria C, Kapral R. Enzyme kinetics and transport in a system crowded by mobile macromolecules. Phys Chem Chem Phys 2015; 17:29243-50. [DOI: 10.1039/c5cp05056a] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The dynamics of an elastic network model for the enzyme 4-oxalocrotonate tautomerase is studied in a system crowded by mobile macromolecules, also modeled by elastic networks.
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Affiliation(s)
- Carlos Echeverria
- Chemical Physics Theory Group
- Department of Chemistry
- University of Toronto
- Toronto
- Canada
| | - Raymond Kapral
- Chemical Physics Theory Group
- Department of Chemistry
- University of Toronto
- Toronto
- Canada
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Berry H, Soula HA. Spatial distributions at equilibrium under heterogeneous transient subdiffusion. Front Physiol 2014; 5:437. [PMID: 25429273 PMCID: PMC4228838 DOI: 10.3389/fphys.2014.00437] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2014] [Accepted: 10/27/2014] [Indexed: 11/18/2022] Open
Abstract
Experimental measurements of the mobility of macromolecules, especially proteins, in cells and their membranes consistently report transient subdiffusion with possibly position-dependent—non-homogeneous—properties. However, the spatiotemporal dynamics of protein mobility when transient subdiffusion is restricted to a subregion of space is still unclear. Here, we investigated the spatial distribution at equilibrium of proteins undergoing transient subdiffusion due to continuous-time random walks (CTRW) in a restricted subregion of a two-dimensional space. Our Monte-Carlo simulations suggest that this process leads to a non-homogeneous spatial distribution of the proteins at equilibrium, where proteins increasingly accumulate in the CTRW subregion as its anomalous properties are increasingly marked. In the case of transient CTRW, we show that this accumulation is dictated by the asymptotic Brownian regime and not by the initial anomalous transient dynamics. Moreover, our results also show that this dominance of the asymptotic Brownian regime cannot be simply generalized to other scenarios of transient subdiffusion. In particular, non-homogeneous transient subdiffusion due to hindrance by randomly-located immobile obstacles does not lead to such a strong local accumulation. These results suggest that, even though they exhibit the same time-dependence of the mean-squared displacement, the different scenarios proposed to account for subdiffusion in the cell lead to different protein distribution in space, even at equilibrium and without coupling with reaction.
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Affiliation(s)
- Hugues Berry
- Beagle, Institut National de Recherche en Informatique et en Automatique Villeurbanne, France ; Laboratoire d'InfoRmatique en Image et Systèmes d'information, UMR 5205 CNRS-INSA, Université de Lyon Villeurbanne, France
| | - Hédi A Soula
- Beagle, Institut National de Recherche en Informatique et en Automatique Villeurbanne, France ; Institut Multidisciplinaire de Biochimie des Lipides, Inserm UMR1060, Université de Lyon Villeurbanne, France
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Furlan G, Minowa T, Hanagata N, Kataoka-Hamai C, Kaizuka Y. Phosphatase CD45 both positively and negatively regulates T cell receptor phosphorylation in reconstituted membrane protein clusters. J Biol Chem 2014; 289:28514-25. [PMID: 25128530 DOI: 10.1074/jbc.m114.574319] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Abstract
T cell receptor (TCR) phosphorylation requires the kinase Lck and phosphatase CD45. CD45 activates Lck by dephosphorylating an inhibitory tyrosine of Lck to relieve autoinhibition. However, CD45 also dephosphorylates the TCR, and the spatial exclusion of CD45 from TCR clustering in the plasma membrane appears to attenuate this negative effect of CD45. To further investigate the role of CD45 in signal initiation, we reconstituted membrane TCR clusters in vitro on supported lipid bilayers. Fluorescence microscopy of single clusters showed that incorporation of CD45 enhanced phosphorylation of TCR clusters, but only when Lck co-clustered with TCR. We found that clustered Lck autophosphorylated the inhibitory tyrosine and thus could be activated by CD45, whereas diffusive Lck molecules did not. In the TCR-Lck clusters and at low CD45 density, we speculate that the effect of Lck activation may overcome dephosphorylation of TCR, resulting in a net positive regulation. The CD45 density in physiological TCR clusters is also low because of the exclusion of CD45. Thus, we propose that the spatial organization of TCR/Lck/CD45 in T cell membranes is important not only for modulating the negative role of CD45 but also for creating conditions in which CD45 has a positive role in signal initiation.
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Affiliation(s)
- Gabriela Furlan
- From the International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan
| | - Takashi Minowa
- From the International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan
| | - Nobutaka Hanagata
- From the International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan
| | - Chiho Kataoka-Hamai
- From the International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan
| | - Yoshihisa Kaizuka
- From the International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan
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41
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Basit H, Lopez SG, Keyes TE. Fluorescence correlation and lifetime correlation spectroscopy applied to the study of supported lipid bilayer models of the cell membrane. Methods 2014; 68:286-99. [DOI: 10.1016/j.ymeth.2014.02.005] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2013] [Revised: 01/21/2014] [Accepted: 02/06/2014] [Indexed: 10/25/2022] Open
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Soula H, Caré B, Beslon G, Berry H. Anomalous versus slowed-down Brownian diffusion in the ligand-binding equilibrium. Biophys J 2014; 105:2064-73. [PMID: 24209851 DOI: 10.1016/j.bpj.2013.07.023] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2013] [Revised: 07/04/2013] [Accepted: 07/16/2013] [Indexed: 01/06/2023] Open
Abstract
Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes.
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Affiliation(s)
- Hédi Soula
- EPI Beagle, INRIA Rhône-Alpes, F-69603, Villeurbanne, France; Université de Lyon, Inserm UMR1060, CarMeN, F-69621 Villeurbanne, France.
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43
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Shang BZ, Chu JW. Kinetic Modeling at Single-Molecule Resolution Elucidates the Mechanisms of Cellulase Synergy. ACS Catal 2014. [DOI: 10.1021/cs500126q] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Affiliation(s)
- Barry Z. Shang
- Department
of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, United States
| | - Jhih-Wei Chu
- Department
of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, United States
- Department
of Biological Science and Technology, National Chiao Tung University, Hsinchu, Taiwan, ROC
- Institute
of Bioinformatics and Systems Biology, National Chiao Tung University, Hsinchu, Taiwan, ROC
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Pitulice L, Vilaseca E, Pastor I, Madurga S, Garcés JL, Isvoran A, Mas F. Monte Carlo simulations of enzymatic reactions in crowded media. Effect of the enzyme-obstacle relative size. Math Biosci 2014; 251:72-82. [DOI: 10.1016/j.mbs.2014.03.012] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2013] [Revised: 02/23/2014] [Accepted: 03/18/2014] [Indexed: 01/21/2023]
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Balcells C, Pastor I, Vilaseca E, Madurga S, Cascante M, Mas F. Macromolecular crowding effect upon in vitro enzyme kinetics: mixed activation-diffusion control of the oxidation of NADH by pyruvate catalyzed by lactate dehydrogenase. J Phys Chem B 2014; 118:4062-8. [PMID: 24660904 DOI: 10.1021/jp4118858] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Abstract
Enzyme kinetics studies have been usually designed as dilute solution experiments, which differ substantially from in vivo conditions. However, cell cytosol is crowded with a high concentration of molecules having different shapes and sizes. The consequences of such crowding in enzymatic reactions remain unclear. The aim of the present study is to understand the effect of macromolecular crowding produced by dextran of different sizes and at diverse concentrations in the well-known reaction of oxidation of NADH by pyruvate catalyzed by L-lactate dehydrogenase (LDH). Our results indicate that the reaction rate is determined by both the occupied volume and the relative size of dextran obstacles with respect to the enzyme present in the reaction. Moreover, we analyzed the influence of macromolecular crowding on the Michaelis-Menten constants, vmax and Km. The obtained results show that only high concentrations and large sizes of dextran reduce both constants suggesting a mixed activation-diffusion control of this enzymatic reaction due to the dextran crowding action. From our knowledge, this is the first experimental study that depicts mixed activation-diffusion control in an enzymatic reaction due to the effect of crowding.
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Affiliation(s)
- Cristina Balcells
- Department of Physical Chemistry and Research Institute of Theoretical and Computational Chemistry (IQTCUB), University of Barcelona (UB) , 08028 Barcelona, Spain
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Berry H, Chaté H. Anomalous diffusion due to hindering by mobile obstacles undergoing Brownian motion or Orstein-Ulhenbeck processes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:022708. [PMID: 25353510 DOI: 10.1103/physreve.89.022708] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2013] [Indexed: 06/04/2023]
Abstract
In vivo measurements of the passive movements of biomolecules or vesicles in cells consistently report "anomalous diffusion," where mean-squared displacements scale as a power law of time with exponent α<1 (subdiffusion). While the detailed mechanisms causing such behaviors are not always elucidated, movement hindrance by obstacles is often invoked. However, our understanding of how hindered diffusion leads to subdiffusion is based on diffusion amidst randomly located immobile obstacles. Here, we have used Monte Carlo simulations to investigate transient subdiffusion due to mobile obstacles with various modes of mobility. Our simulations confirm that the anomalous regimes rapidly disappear when the obstacles move by Brownian motion. By contrast, mobile obstacles with more confined displacements, e.g., Orstein-Ulhenbeck motion, are shown to preserve subdiffusive regimes. The mean-squared displacement of tracked protein displays convincing power laws with anomalous exponent α that varies with the density of Orstein-Ulhenbeck (OU) obstacles or the relaxation time scale of the OU process. In particular, some of the values we observed are significantly below the universal value predicted for immobile obstacles in two dimensions. Therefore, our results show that subdiffusion due to mobile obstacles with OU type of motion may account for the large variation range exhibited by experimental measurements in living cells and may explain that some experimental estimates are below the universal value predicted for immobile obstacles.
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Affiliation(s)
- Hugues Berry
- EPI Beagle, INRIA Rhône-Alpes, F-69603, Villeurbanne, France and LIRIS, Université de Lyon, UMR 5205 CNRS-INSA, F-69621, Villeurbanne, France
| | - Hugues Chaté
- Service de Physique de l'Etat Condensé, URA2464, CEA-Saclay, 91191 Gif-sur-Yvette, France
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47
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Weiss M. Crowding, Diffusion, and Biochemical Reactions. INTERNATIONAL REVIEW OF CELL AND MOLECULAR BIOLOGY 2014; 307:383-417. [DOI: 10.1016/b978-0-12-800046-5.00011-4] [Citation(s) in RCA: 79] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/03/2022]
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48
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Mourão M, Kreitman D, Schnell S. Unravelling the impact of obstacles in diffusion and kinetics of an enzyme catalysed reaction. Phys Chem Chem Phys 2014; 16:4492-503. [DOI: 10.1039/c3cp52417e] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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49
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Tummler K, Lubitz T, Schelker M, Klipp E. New types of experimental data shape the use of enzyme kinetics for dynamic network modeling. FEBS J 2013; 281:549-71. [PMID: 24034816 DOI: 10.1111/febs.12525] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2013] [Revised: 08/27/2013] [Accepted: 09/10/2013] [Indexed: 01/21/2023]
Abstract
Since the publication of Leonor Michaelis and Maude Menten's paper on the reaction kinetics of the enzyme invertase in 1913, molecular biology has evolved tremendously. New measurement techniques allow in vivo characterization of the whole genome, proteome or transcriptome of cells, whereas the classical enzyme essay only allows determination of the two Michaelis-Menten parameters V and K(m). Nevertheless, Michaelis-Menten kinetics are still commonly used, not only in the in vitro context of enzyme characterization but also as a rate law for enzymatic reactions in larger biochemical reaction networks. In this review, we give an overview of the historical development of kinetic rate laws originating from Michaelis-Menten kinetics over the past 100 years. Furthermore, we briefly summarize the experimental techniques used for the characterization of enzymes, and discuss web resources that systematically store kinetic parameters and related information. Finally, describe the novel opportunities that arise from using these data in dynamic mathematical modeling. In this framework, traditional in vitro approaches may be combined with modern genome-scale measurements to foster thorough understanding of the underlying complex mechanisms.
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Affiliation(s)
- Katja Tummler
- Theoretical Biophysics, Humboldt-Universität zu Berlin, Germany
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50
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Vasilescu C, Olteanu M, Flondor P, Calin GA. Fractal-like kinetics of intracellular enzymatic reactions: a chemical framework of endotoxin tolerance and a possible non-specific contribution of macromolecular crowding to cross-tolerance. Theor Biol Med Model 2013; 10:55. [PMID: 24034421 PMCID: PMC3849556 DOI: 10.1186/1742-4682-10-55] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2013] [Accepted: 09/10/2013] [Indexed: 12/26/2022] Open
Abstract
BACKGROUND The response to endotoxin (LPS), and subsequent signal transduction lead to the production of cytokines such as tumor necrosis factor-α (TNF-α) by innate immune cells. Cells or organisms pretreated with endotoxin enter into a transient state of hyporesponsiveness, referred to as endotoxin tolerance (ET) which represents a particular case of negative preconditioning. Despite recent progress in understanding the molecular basis of ET, there is no consensus yet on the primary mechanism responsible for ET and for the more complex cases of cross tolerance. In this study, we examined the consequences of the macromolecular crowding (MMC) and of fractal-like kinetics (FLK) of intracellular enzymatic reactions on the LPS signaling machinery. We hypothesized that this particular type of enzyme kinetics may explain the development of ET phenomenon. METHOD Our aim in the present study was to characterize the chemical kinetics framework in ET and determine whether fractal-like kinetics explains, at least in part, ET. We developed an ordinary differential equations (ODE) mathematical model that took into account the links between the MMC and the LPS signaling machinery leading to ET. We proposed that the intracellular fractal environment (MMC) contributes to ET and developed two mathematical models of enzyme kinetics: one based on Kopelman's fractal-like kinetics framework and the other based on Savageau's power law model. RESULTS Kopelman's model provides a good image of the potential influence of a fractal intracellular environment (MMC) on ET. The Savageau power law model also partially explains ET. The computer simulations supported the hypothesis that MMC and FLK may play a role in ET. CONCLUSION The model highlights the links between the organization of the intracellular environment, MMC and the LPS signaling machinery leading to ET. Our FLK-based model does not minimize the role of the numerous negative regulatory factors. It simply draws attention to the fact that macromolecular crowding can contribute significantly to the induction of ET by imposing geometric constrains and a particular chemical kinetic for the intracellular reactions.
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Affiliation(s)
- Catalin Vasilescu
- Fundeni Clinical Institute, Carol Davila University of Medicine and Pharmacy, 258 Fundeni Street, Bucharest, Romania.
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