1
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van Swol F, Douglas Frink LJ, Malanoski AP, Petsev DN. Diffusion in inhomogeneous fluids: Hard spheres to polymer coatings. J Chem Phys 2023; 159:084705. [PMID: 37622595 DOI: 10.1063/5.0164257] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2023] [Accepted: 08/07/2023] [Indexed: 08/26/2023] Open
Abstract
We investigate diffusion in fluids near surfaces that may be coated with polymer films. We first consider diffusion in hard sphere fluids near a planar hard wall. We specifically consider color diffusion, where hard spheres are labeled A or B but are otherwise identical in all respects. In this inhomogeneous fluid, we consider a surface reaction-diffusion problem. At the left wall, a particle of species A is converted to one of species B upon a wall collision. At the opposing wall, the reverse reaction takes place: B → A. Using molecular dynamics simulation, we study the steady state of this system. We demonstrate that in the homogeneous region, a diffusing particle is subject to an equilibrium oscillatory force, the solvation force, that arises from the interfacial structuring of the fluid at the wall. For the hard sphere/hard wall system, the solvation force can be determined in various ways. We use the solvation force [the potential of mean force (PMF)] to solve the continuum diffusion equation. This provides an adequate and accurate description of the reaction-diffusion problem. The analysis is then extended to consider both color diffusion in the presence of a slowly varying one-body field such as gravity and a more applied problem of diffusion of free species through a surface film consisting of tethered chains. In both cases, the PMF experienced by the free particles is affected, but the diffusion problem can be treated in the same way as for the simpler hard sphere color diffusion case.
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Affiliation(s)
- Frank van Swol
- Department of Chemical and Biological Engineering and Center for Microengineered Materials, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Laura J Douglas Frink
- Department of Chemical and Biological Engineering and Center for Microengineered Materials, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Anthony P Malanoski
- United States Naval Research Laboratory, Center for Biomolecular Science and Engineering, Washington, DC 20375, USA
| | - Dimiter N Petsev
- Department of Chemical and Biological Engineering and Center for Microengineered Materials, University of New Mexico, Albuquerque, New Mexico 87131, USA
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2
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Ro S, Yi J, Kim YW. Target searches of interacting Brownian particles in dilute systems. Phys Rev E 2023; 107:064143. [PMID: 37464617 DOI: 10.1103/physreve.107.064143] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2022] [Accepted: 06/05/2023] [Indexed: 07/20/2023]
Abstract
We study the target searches of interacting Brownian particles in a finite domain, focusing on the effect of interparticle interactions on the search time. We derive the integral equation for the mean first-passage time and acquire its solution as a series expansion in the orders of the Mayer function. We analytically obtain the leading order correction to the search time for dilute systems, which are most relevant to target search problems and prove a universal relation given by the particle density and the second virial coefficient. Finally, we validate our theoretical prediction by Langevin dynamics simulations for the various types of the interaction potential.
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Affiliation(s)
- Sunghan Ro
- Department of Physics, Technion-Israel Institute of Technology, Haifa 3200003, Israel
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Juyeon Yi
- Department of Physics, Pusan National University, Busan 46241, Korea
| | - Yong Woon Kim
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Physics, Korea Advanced Institute of Science and Technology, Deajeon 34141, Korea
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3
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Chen J. Why Should the Reaction Order of a Bimolecular Reaction be 2.33 Instead of 2? J Phys Chem A 2022; 126:9719-9725. [PMID: 36520427 PMCID: PMC9805503 DOI: 10.1021/acs.jpca.2c07500] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
Predicting the reaction kinetics, that is, how fast a reaction can happen in a solution, is essential information for many processes, such as industrial chemical manufacturing, refining, synthesis and separation of petroleum products, environmental processes in air and water, biological reactions in cells, biosensing, and drug delivery. Collision theory was originally developed to explain the reaction kinetics of gas reactions with no dilution. For a reaction in a diluted inert gas solution or a diluted liquid solution, diffusion often dominates the collision process. Thus, it is necessary to include diffusion in such a calculation. Traditionally, the classical Smoluchowski rate is used as a starting point to predict the collision frequency of two molecules in a diluted solution. In this report, a different collision model is derived from the adsorption of molecules on a flat surface. A surprising result is obtained, showing that the reaction order for bimolecular reactions should be 2 and 1/3 instead of 2, following a fractal reaction kinetics.
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Affiliation(s)
- Jixin Chen
- Department of Chemistry and Biochemistry, Nanoscale and Quantum Phenomena Institute, Ohio University, Athens, OH 45701, USA
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4
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Beck C, Grimaldo M, Lopez H, Da Vela S, Sohmen B, Zhang F, Oettel M, Barrat JL, Roosen-Runge F, Schreiber F, Seydel T. Short-Time Transport Properties of Bidisperse Suspensions of Immunoglobulins and Serum Albumins Consistent with a Colloid Physics Picture. J Phys Chem B 2022; 126:7400-7408. [PMID: 36112146 PMCID: PMC9527755 DOI: 10.1021/acs.jpcb.2c02380] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
![]()
The crowded environment of biological systems such as
the interior
of living cells is occupied by macromolecules with a broad size distribution.
This situation of polydispersity might influence the dependence of
the diffusive dynamics of a given tracer macromolecule in a monodisperse
solution on its hydrodynamic size and on the volume fraction. The
resulting size dependence of diffusive transport crucially influences
the function of a living cell. Here, we investigate a simplified model
system consisting of two constituents in aqueous solution, namely,
of the proteins bovine serum albumin (BSA) and bovine polyclonal gamma-globulin
(Ig), systematically depending on the total volume fraction and ratio
of these constituents. From high-resolution quasi-elastic neutron
spectroscopy, the separate apparent short-time diffusion coefficients
for BSA and Ig in the mixture are extracted, which show substantial
deviations from the diffusion coefficients measured in monodisperse
solutions at the same total volume fraction. These deviations can
be modeled quantitatively using results from the short-time rotational
and translational diffusion in a two-component hard sphere system
with two distinct, effective hydrodynamic radii. Thus, we find that
a simple colloid picture well describes short-time diffusion in binary
mixtures as a function of the mixing ratio and the total volume fraction.
Notably, the self-diffusion of the smaller protein BSA in the mixture
is faster than the diffusion in a pure BSA solution, whereas the self-diffusion
of Ig in the mixture is slower than in the pure Ig solution.
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Affiliation(s)
- Christian Beck
- Institut für Angewandte Physik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
- Institut Max von Laue─Paul Langevin (ILL), CS 20156, F-38042 Grenoble Cedex 9, France
| | - Marco Grimaldo
- Institut Max von Laue─Paul Langevin (ILL), CS 20156, F-38042 Grenoble Cedex 9, France
| | - Hender Lopez
- School of Physics and Optometric & Clinical Sciences, Technological University Dublin, D07 XT95 Grangegorman, Ireland
| | - Stefano Da Vela
- Institut für Angewandte Physik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
| | - Benedikt Sohmen
- Institut für Angewandte Physik, Universität Tübingen, 72076 Tübingen, Germany
| | - Fajun Zhang
- Institut für Angewandte Physik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
| | - Martin Oettel
- Institut für Angewandte Physik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
| | | | - Felix Roosen-Runge
- Department of Biomedical Science and Biofilms-Research Center for Biointerfaces (BRCB), Malmö University, 20506 Malmö, Sweden
| | - Frank Schreiber
- Institut für Angewandte Physik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
| | - Tilo Seydel
- Institut Max von Laue─Paul Langevin (ILL), CS 20156, F-38042 Grenoble Cedex 9, France
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5
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Nicoletti G, Busiello DM. Mutual information in changing environments: Nonlinear interactions, out-of-equilibrium systems, and continuously varying diffusivities. Phys Rev E 2022; 106:014153. [PMID: 35974654 DOI: 10.1103/physreve.106.014153] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2022] [Accepted: 07/14/2022] [Indexed: 06/15/2023]
Abstract
Biochemistry, ecology, and neuroscience are examples of prominent fields aiming at describing interacting systems that exhibit nontrivial couplings to complex, ever-changing environments. We have recently shown that linear interactions and a switching environment are encoded separately in the mutual information of the overall system. Here we first generalize these findings to a broad class of nonlinear interacting models. We find that a new term in the mutual information appears, quantifying the interplay between nonlinear interactions and environmental changes, and leading to either constructive or destructive information interference. Furthermore, we show that a higher mutual information emerges in out-of-equilibrium environments with respect to an equilibrium scenario. Finally, we generalize our framework to the case of continuously varying environments. We find that environmental changes can be mapped exactly into an effective spatially varying diffusion coefficient, shedding light on modeling of biophysical systems in inhomogeneous media.
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Affiliation(s)
- Giorgio Nicoletti
- Laboratory of Interdisciplinary Physics, Department of Physics and Astronomy "G. Galilei," University of Padova, Padova 35121, Italy
| | - Daniel Maria Busiello
- Institute of Physics, École Polytechnique Fédérale de Lausanne-EPFL, 1015 Lausanne, Switzerland
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6
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The Impact of Membrane Protein Diffusion on GPCR Signaling. Cells 2022; 11:cells11101660. [PMID: 35626696 PMCID: PMC9139411 DOI: 10.3390/cells11101660] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2022] [Revised: 05/12/2022] [Accepted: 05/14/2022] [Indexed: 12/10/2022] Open
Abstract
Spatiotemporal signal shaping in G protein-coupled receptor (GPCR) signaling is now a well-established and accepted notion to explain how signaling specificity can be achieved by a superfamily sharing only a handful of downstream second messengers. Dozens of Gs-coupled GPCR signals ultimately converge on the production of cAMP, a ubiquitous second messenger. This idea is almost always framed in terms of local concentrations, the differences in which are maintained by means of spatial separation. However, given the dynamic nature of the reaction-diffusion processes at hand, the dynamics, in particular the local diffusional properties of the receptors and their cognate G proteins, are also important. By combining some first principle considerations, simulated data, and experimental data of the receptors diffusing on the membranes of living cells, we offer a short perspective on the modulatory role of local membrane diffusion in regulating GPCR-mediated cell signaling. Our analysis points to a diffusion-limited regime where the effective production rate of activated G protein scales linearly with the receptor–G protein complex’s relative diffusion rate and to an interesting role played by the membrane geometry in modulating the efficiency of coupling.
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7
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Rizkallah P, Sarracino A, Bénichou O, Illien P. Microscopic Theory for the Diffusion of an Active Particle in a Crowded Environment. PHYSICAL REVIEW LETTERS 2022; 128:038001. [PMID: 35119883 DOI: 10.1103/physrevlett.128.038001] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2021] [Accepted: 12/13/2021] [Indexed: 06/14/2023]
Abstract
We calculate the diffusion coefficient of an active tracer in a schematic crowded environment, represented as a lattice gas of passive particles with hardcore interactions. Starting from the master equation of the problem, we put forward a closure approximation that goes beyond trivial mean field and provides the diffusion coefficient for an arbitrary density of crowders in the system. We show that our approximation is accurate for a very wide range of parameters, and that it correctly captures numerous nonequilibrium effects, which are the signature of the activity in the system. In addition to the determination of the diffusion coefficient of the tracer, our approach allows us to characterize the perturbation of the environment induced by the displacement of the active tracer. Finally, we consider the asymptotic regimes of low and high densities, in which the expression of the diffusion coefficient of the tracer becomes explicit, and which we argue to be exact.
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Affiliation(s)
- Pierre Rizkallah
- Sorbonne Université, CNRS, Laboratoire de Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux (PHENIX), 4 Place Jussieu, 75005 Paris, France
| | - Alessandro Sarracino
- Dipartimento di Ingegneria, Università della Campania "Luigi Vanvitelli", 81031 Aversa (CE), Italy
| | - Olivier Bénichou
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), 4 Place Jussieu, 75005 Paris, France
| | - Pierre Illien
- Sorbonne Université, CNRS, Laboratoire de Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux (PHENIX), 4 Place Jussieu, 75005 Paris, France
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8
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Lee S. Operator algebraic methods in the theory of
diffusion‐influenced
reaction kinetics. B KOREAN CHEM SOC 2021. [DOI: 10.1002/bkcs.12448] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Sangyoub Lee
- Professor Sangyoub Lee, Department of Chemistry Seoul National University Seoul South Korea
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9
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Kim R, Radhakrishnan ML. Macromolecular crowding effects on electrostatic binding affinity: Fundamental insights from theoretical, idealized models. J Chem Phys 2021; 154:225101. [PMID: 34241219 DOI: 10.1063/5.0042082] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The crowded cellular environment can affect biomolecular binding energetics, with specific effects depending on the properties of the binding partners and the local environment. Often, crowding effects on binding are studied on particular complexes, which provide system-specific insights but may not provide comprehensive trends or a generalized framework to better understand how crowding affects energetics involved in molecular recognition. Here, we use theoretical, idealized molecules whose physical properties can be systematically varied along with samplings of crowder placements to understand how electrostatic binding energetics are altered through crowding and how these effects depend on the charge distribution, shape, and size of the binding partners or crowders. We focus on electrostatic binding energetics using a continuum electrostatic framework to understand effects due to depletion of a polar, aqueous solvent in a crowded environment. We find that crowding effects can depend predictably on a system's charge distribution, with coupling between the crowder size and the geometry of the partners' binding interface in determining crowder effects. We also explore the effect of crowder charge on binding interactions as a function of the monopoles of the system components. Finally, we find that modeling crowding via a lowered solvent dielectric constant cannot account for certain electrostatic crowding effects due to the finite size, shape, or placement of system components. This study, which comprehensively examines solvent depletion effects due to crowding, complements work focusing on other crowding aspects to help build a holistic understanding of environmental impacts on molecular recognition.
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Affiliation(s)
- Rachel Kim
- Department of Chemistry, Wellesley College, Wellesley, Massachusetts 02481, USA
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10
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de Graaff DR, van Loosdrecht MCM, Pronk M. Trehalose as an osmolyte in Candidatus Accumulibacter phosphatis. Appl Microbiol Biotechnol 2020; 105:379-388. [PMID: 33074418 PMCID: PMC7778627 DOI: 10.1007/s00253-020-10947-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2020] [Revised: 09/30/2020] [Accepted: 10/04/2020] [Indexed: 11/30/2022]
Abstract
Abstract Candidatus Accumulibacter phosphatis is an important microorganism for enhanced biological phosphorus removal (EBPR). In a previous study, we found a remarkable flexibility regarding salinity, since this same microorganism could thrive in both freshwater- and seawater-based environments, but the mechanism for the tolerance to saline conditions remained unknown. Here, we identified and described the role of trehalose as an osmolyte in Ca. Accumulibacter phosphatis. A freshwater-adapted culture was exposed to a single batch cycle of hyperosmotic and hypo-osmotic shock, which led to the release of trehalose up to 5.34 mg trehalose/g volatile suspended solids (VSS). Long-term adaptation to 30% seawater-based medium in a sequencing batch reactor (SBR) gave a stable operation with complete anaerobic uptake of acetate and propionate along with phosphate release of 0.73 Pmol/Cmol, and complete aerobic uptake of phosphate. Microbial analysis showed Ca. Accumulibacter phosphatis clade I as the dominant organism in both the freshwater- and seawater-adapted cultures (> 90% presence). Exposure of the seawater-adapted culture to a single batch cycle of hyperosmotic incubation and hypo-osmotic shock led to an increase in trehalose release upon hypo-osmotic shock when higher salinity is used for the hyperosmotic incubation. Maximum trehalose release upon hypo-osmotic shock was achieved after hyperosmotic incubation with 3× salinity increase relative to the salinity in the SBR adaptation reactor, resulting in the release of 11.9 mg trehalose/g VSS. Genome analysis shows the possibility of Ca. Accumulibacter phosphatis to convert glycogen into trehalose by the presence of treX, treY, and treZ genes. Addition of trehalose to the reactor led to its consumption, both during anaerobic and aerobic phases. These results indicate the flexibility of the metabolism of Ca. Accumulibacter phosphatis towards variations in salinity. Key points • Trehalose is identified as an osmolyte in Candidatus Accumulibacter phosphatis. • Ca. Accumulibacter phosphatis can convert glycogen into trehalose. • Ca. Accumulibacter phosphatis clade I is present and active in both seawater and freshwater. Electronic supplementary material The online version of this article (10.1007/s00253-020-10947-8) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Danny R de Graaff
- Department of Biotechnology, Delft University of Technology, van der Maasweg 9, 2629 HZ, Delft, The Netherlands
| | - Mark C M van Loosdrecht
- Department of Biotechnology, Delft University of Technology, van der Maasweg 9, 2629 HZ, Delft, The Netherlands
| | - Mario Pronk
- Department of Biotechnology, Delft University of Technology, van der Maasweg 9, 2629 HZ, Delft, The Netherlands. .,Royal HaskoningDHV, Laan1914 35, 3800 AL, Amersfoort, The Netherlands.
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11
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Lee K, Lee S. Interplay of reactive interference and crowding effects in the diffusion-influenced reaction kinetics. J Chem Phys 2020; 153:044129. [PMID: 32752726 DOI: 10.1063/5.0016269] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
We investigate the interplay of reactive interference and crowding effects in the irreversible diffusion-influenced bimolecular reactions of the type A+B→P+B by using the Brownian dynamics simulation method. It is known that the presence of nonreactive crowding agents retards the reaction rate when the volume fraction of the crowding agents is large enough. On the other hand, a high concentration of B is known to increase the reaction rate more than expected from the mass action law, although the B's may also act as crowders. Therefore, it would be interesting to see which effect dominates when the number density of B as well as the number density of the crowders increases. We will present an approximate theory that provides a reasonable account for the Brownian dynamics simulation results.
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Affiliation(s)
- Kyusup Lee
- Department of Chemistry, Seoul National University, Seoul 151-747, South Korea
| | - Sangyoub Lee
- Department of Chemistry, Seoul National University, Seoul 151-747, South Korea
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12
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Dibak M, Fröhner C, Noé F, Höfling F. Diffusion-influenced reaction rates in the presence of pair interactions. J Chem Phys 2019; 151:164105. [PMID: 31675872 DOI: 10.1063/1.5124728] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
The kinetics of bimolecular reactions in solution depends, among other factors, on intermolecular forces such as steric repulsion or electrostatic interaction. Microscopically, a pair of molecules first has to meet by diffusion before the reaction can take place. In this work, we establish an extension of Doi's volume reaction model to molecules interacting via pair potentials, which is a key ingredient for interacting-particle-based reaction-diffusion (iPRD) simulations. As a central result, we relate model parameters and macroscopic reaction rate constants in this situation. We solve the corresponding reaction-diffusion equation in the steady state and derive semi-analytical expressions for the reaction rate constant and the local concentration profiles. Our results apply to the full spectrum from well-mixed to diffusion-limited kinetics. For limiting cases, we give explicit formulas, and we provide a computationally inexpensive numerical scheme for the general case, including the intermediate, diffusion-influenced regime. The obtained rate constants decompose uniquely into encounter and formation rates, and we discuss the effect of the potential on both subprocesses, exemplified for a soft harmonic repulsion and a Lennard-Jones potential. The analysis is complemented by extensive stochastic iPRD simulations, and we find excellent agreement with the theoretical predictions.
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Affiliation(s)
- Manuel Dibak
- Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 6, 14195 Berlin, Germany
| | - Christoph Fröhner
- Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 6, 14195 Berlin, Germany
| | - Frank Noé
- Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 6, 14195 Berlin, Germany
| | - Felix Höfling
- Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 6, 14195 Berlin, Germany
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13
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Del Razo MJ, Qian H, Noé F. Grand canonical diffusion-influenced reactions: A stochastic theory with applications to multiscale reaction-diffusion simulations. J Chem Phys 2018; 149:044102. [PMID: 30068197 DOI: 10.1063/1.5037060] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
Abstract
Smoluchowski-type models for diffusion-influenced reactions (A + B → C) can be formulated within two frameworks: the probabilistic-based approach for a pair A, B of reacting particles and the concentration-based approach for systems in contact with a bath that generates a concentration gradient of B particles that interact with A. Although these two approaches are mathematically similar, it is not straightforward to establish a precise mathematical relationship between them. Determining this relationship is essential to derive particle-based numerical methods that are quantitatively consistent with bulk concentration dynamics. In this work, we determine the relationship between the two approaches by introducing the grand canonical Smoluchowski master equation (GC-SME), which consists of a continuous-time Markov chain that models an arbitrary number of B particles, each one of them following Smoluchowski's probabilistic dynamics. We show that the GC-SME recovers the concentration-based approach by taking either the hydrodynamic or the large copy number limit. In addition, we show that the GC-SME provides a clear statistical mechanical interpretation of the concentration-based approach and yields an emergent chemical potential for nonequilibrium spatially inhomogeneous reaction processes. We further exploit the GC-SME robust framework to accurately derive multiscale/hybrid numerical methods that couple particle-based reaction-diffusion simulations with bulk concentration descriptions, as described in detail through two computational implementations.
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Affiliation(s)
- Mauricio J Del Razo
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Hong Qian
- Department of Applied Mathematics, University of Washington, Seattle, Washington 98195-3925, USA
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
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14
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Roa R, Siegl T, Kim WK, Dzubiella J. Product interactions and feedback in diffusion-controlled reactions. J Chem Phys 2018; 148:064705. [PMID: 29448770 DOI: 10.1063/1.5016608] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Steric or attractive interactions among reactants or between reactants and inert crowders can substantially influence the total rate of a diffusion-influenced reaction in the liquid phase. However, the role of the product species, which has typically different physical properties than the reactant species, has been disregarded so far. Here we study the effects of reactant-product and product-product interactions as well as asymmetric diffusion properties on the rate of diffusion-controlled reactions in the classical Smoluchowski-setup for chemical transformations at a perfect catalytic sphere. For this, we solve the diffusion equation with appropriate boundary conditions coupled by a mean-field approach on the second virial level to account for the particle interactions. We find that all particle spatial distributions and the total rate can change significantly, depending on the diffusion and interaction properties of the accumulated products. Complex competing and self-regulating (homeostatic) or self-amplifying effects are observed for the system, leading to both decrease and increase in the rates, as the presence of interacting products feeds back to the reactant flux and thus the rate with which the products are generated.
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Affiliation(s)
- Rafael Roa
- Física Aplicada I, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain
| | - Toni Siegl
- Institut für Weiche Materie und Funktionale Materialien, Helmholtz-Zentrum Berlin für Materialien und Energie, 14109 Berlin, Germany
| | - Won Kyu Kim
- Institut für Weiche Materie und Funktionale Materialien, Helmholtz-Zentrum Berlin für Materialien und Energie, 14109 Berlin, Germany
| | - Joachim Dzubiella
- Institut für Weiche Materie und Funktionale Materialien, Helmholtz-Zentrum Berlin für Materialien und Energie, 14109 Berlin, Germany
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15
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Sozza A, Piazza F, Cencini M, De Lillo F, Boffetta G. Point-particle method to compute diffusion-limited cellular uptake. Phys Rev E 2018; 97:023301. [PMID: 29548108 DOI: 10.1103/physreve.97.023301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2017] [Indexed: 11/07/2022]
Abstract
We present an efficient point-particle approach to simulate reaction-diffusion processes of spherical absorbing particles in the diffusion-limited regime, as simple models of cellular uptake. The exact solution for a single absorber is used to calibrate the method, linking the numerical parameters to the physical particle radius and uptake rate. We study the configurations of multiple absorbers of increasing complexity to examine the performance of the method by comparing our simulations with available exact analytical or numerical results. We demonstrate the potential of the method to resolve the complex diffusive interactions, here quantified by the Sherwood number, measuring the uptake rate in terms of that of isolated absorbers. We implement the method in a pseudospectral solver that can be generalized to include fluid motion and fluid-particle interactions. As a test case of the presence of a flow, we consider the uptake rate by a particle in a linear shear flow. Overall, our method represents a powerful and flexible computational tool that can be employed to investigate many complex situations in biology, chemistry, and related sciences.
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Affiliation(s)
- A Sozza
- Department of Physics, Università di Torino & INFN, via P. Giuria 1, 10125 Torino, Italy
| | - F Piazza
- Centre de Biophysique Moléculaire, CNRS-UPR 4301 and Université d'Orléans, F-45071 Orléans Cedex, France
| | - M Cencini
- Istituto dei Sistemi Complessi, CNR, via dei Taurini 19 Roma, Italy and INFN Sezione di "Tor Vergata," Roma, Italy
| | - F De Lillo
- Department of Physics, Università di Torino & INFN, via P. Giuria 1, 10125 Torino, Italy
| | - G Boffetta
- Department of Physics, Università di Torino & INFN, via P. Giuria 1, 10125 Torino, Italy
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16
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Chen W, Young LJ, Lu M, Zaccone A, Ströhl F, Yu N, Kaminski Schierle GS, Kaminski CF. Fluorescence Self-Quenching from Reporter Dyes Informs on the Structural Properties of Amyloid Clusters Formed in Vitro and in Cells. NANO LETTERS 2017; 17:143-149. [PMID: 28073262 PMCID: PMC5338000 DOI: 10.1021/acs.nanolett.6b03686] [Citation(s) in RCA: 37] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2016] [Revised: 10/26/2016] [Indexed: 05/26/2023]
Abstract
The characterization of the aggregation kinetics of protein amyloids and the structural properties of the ensuing aggregates are vital in the study of the pathogenesis of many neurodegenerative diseases and the discovery of therapeutic targets. In this article, we show that the fluorescence lifetime of synthetic dyes covalently attached to amyloid proteins informs on the structural properties of amyloid clusters formed both in vitro and in cells. We demonstrate that the mechanism behind such a "lifetime sensor" of protein aggregation is based on fluorescence self-quenching and that it offers a good dynamic range to report on various stages of aggregation without significantly perturbing the process under investigation. We show that the sensor informs on the structural density of amyloid clusters in a high-throughput and quantitative manner and in these aspects the sensor outperforms super-resolution imaging techniques. We demonstrate the power and speed of the method, offering capabilities, for example, in therapeutic screenings that monitor biological self-assembly. We investigate the mechanism and advantages of the lifetime sensor in studies of the K18 protein fragment of the Alzheimer's disease related protein tau and its amyloid aggregates formed in vitro. Finally, we demonstrate the sensor in the study of aggregates of polyglutamine protein, a model used in studies related to Huntington's disease, by performing correlative fluorescence lifetime imaging microscopy and structured-illumination microscopy experiments in cells.
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17
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Lin X, Noel JK, Wang Q, Ma J, Onuchic JN. Lowered pH Leads to Fusion Peptide Release and a Highly Dynamic Intermediate of Influenza Hemagglutinin. J Phys Chem B 2016; 120:9654-60. [PMID: 27541202 DOI: 10.1021/acs.jpcb.6b06775] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Hemagglutinin (HA), the membrane-bound fusion protein of the influenza virus, enables the entry of virus into host cells via a structural rearrangement. There is strong evidence that the primary trigger for this rearrangement is the low pH environment of a late endosome. To understand the structural basis and the dynamic consequences of the pH trigger, we employed explicit-solvent molecular dynamics simulations to investigate the initial stages of the HA transition. Our results indicate that lowered pH destabilizes HA and speeds up the dissociation of the fusion peptides (FPs). A buried salt bridge between the N-terminus and Asp1122 of HA stem domain locks the FPs and may act as one of the pH sensors. In line with recent observations from simplified protein models, we find that, after the dissociation of FPs, a structural order-disorder transition in a loop connecting the central coiled-coil to the C-terminal domains produces a highly mobile HA. This motion suggests the existence of a long-lived asymmetric or "symmetry-broken" intermediate during the HA conformational change. This intermediate conformation is consistent with models of hemifusion, and its early formation during the conformational change has implications for the aggregation seen in HA activity.
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Affiliation(s)
- Xingcheng Lin
- Center for Theoretical Biological Physics, Rice University , Houston, Texas 77030, United States.,Department of Physics and Astronomy, Rice University , Houston, Texas 77005, United States
| | - Jeffrey K Noel
- Max Delbrück Center for Molecular Medicine , Berlin 13125, Germany.,Fritz Haber Institute of the Max Planck Society , Berlin 14195, Germany
| | - Qinghua Wang
- Verna and Marrs McLean Department of Biochemistry and Molecular Biology, Baylor College of Medicine , Houston 77030, Texas, United States
| | - Jianpeng Ma
- Center for Theoretical Biological Physics, Rice University , Houston, Texas 77030, United States.,Verna and Marrs McLean Department of Biochemistry and Molecular Biology, Baylor College of Medicine , Houston 77030, Texas, United States.,Department of Bioengineering, Rice University , Houston, Texas 77005, United States
| | - José N Onuchic
- Center for Theoretical Biological Physics, Rice University , Houston, Texas 77030, United States.,Department of Physics and Astronomy, Rice University , Houston, Texas 77005, United States.,Departments of Chemistry and Biosciences, Rice University , Houston, Texas 77005, United States
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18
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Antoine C, Talbot J. Effect of crowding and confinement on first-passage times: A model study. Phys Rev E 2016; 93:062120. [PMID: 27415221 DOI: 10.1103/physreve.93.062120] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2016] [Indexed: 06/06/2023]
Abstract
We study the "color dynamics" of a hard-disk fluid confined in an annulus, as well as the corresponding hard-sphere system in three dimensions, using event-driven simulation in order to explore the effect of confinement and self-crowding on the search for targets. We compute the mean first-passage times (MFPTs) of red particles transiting from the outer to the inner boundary as well as those of blue particles passing from the inner to the outer boundary for different packing fractions and geometries. In the steady state the reaction rate, defined as the rate of collision of red particles with the inner boundary, is inversely proportional to the sum of the MFPTs. The reaction rate is wall mediated (ballistic) at low densities and diffusion controlled at higher densities and displays a maximum at intermediate densities. At moderate to high densities, the presence of layering has a strong influence on the search process. The numerical results for the reaction rate and MFPTs are compared with a ballistic model at low densities and a Smoluchowski approach with uniform diffusivities at higher densities. We discuss the reasons for the limited validity of the theoretical approaches. The maximum in the reaction rate is qualitatively well rendered by a Bosanquet-like approach that interpolates between the two regimes. Finally, we compute the position-dependent diffusivity from the MFPTs and observe that it is out of phase with the radial density.
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Affiliation(s)
- C Antoine
- Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, Sorbonne Universités, 4 place Jussieu, 75252 Paris Cedex 05, France
| | - J Talbot
- Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, Sorbonne Universités, 4 place Jussieu, 75252 Paris Cedex 05, France
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19
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Galanti M, Fanelli D, Traytak SD, Piazza F. Theory of diffusion-influenced reactions in complex geometries. Phys Chem Chem Phys 2016; 18:15950-4. [PMID: 27241805 DOI: 10.1039/c6cp01147k] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Chemical transformations involving the diffusion of reactants and subsequent chemical fixation steps are generally termed "diffusion-influenced reactions" (DIR). Virtually all biochemical processes in living media can be counted among them, together with those occurring in an ever-growing number of emerging nano-technologies. The role of the environment's geometry (obstacles, compartmentalization) and distributed reactivity (competitive reactants, traps) is key in modulating the rate constants of DIRs, and is therefore a prime design parameter. Yet, it is a formidable challenge to build a comprehensive theory that is able to describe the environment's "reactive geometry". Here we show that such a theory can be built by unfolding this many-body problem through addition theorems for special functions. Our method is powerful and general and allows one to study a given DIR reaction occurring in arbitrary "reactive landscapes", made of multiple spherical boundaries of given size and reactivity. Importantly, ready-to-use analytical formulas can be derived easily in most cases.
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Affiliation(s)
- Marta Galanti
- Università degli Studi di Firenze, Dipartimento di Fisica e Astronomia and CSDC, via G. Sansone 1, IT-50019 Sesto Fiorentino, Firenze, Italia.
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20
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Berezhkovskii AM, Szabo A. Theory of Crowding Effects on Bimolecular Reaction Rates. J Phys Chem B 2016; 120:5998-6002. [PMID: 27096470 DOI: 10.1021/acs.jpcb.6b01892] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
An analytical expression for the rate constant of a diffusion-influenced bimolecular reaction in a crowded environment is derived in the framework of a microscopic model that accounts for: (1) the slowdown of diffusion due to crowding and the dependence of the diffusivity on the distance between the reactants, (2) a crowding-induced attractive short-range potential of mean force, and (3) nonspecific reversible binding to the crowders. This expression spans the range from reaction to diffusion control. Crowding can increase the reaction-controlled rate by inducing an effective attraction between reactants but decrease the diffusion-controlled rate by reducing their relative diffusivity.
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Affiliation(s)
- Alexander M Berezhkovskii
- Mathematical and Statistical Computing Laboratory, Division of Computational Bioscience, Center for Information Technology, National Institutes of Health , Bethesda, Maryland 20892, United States
| | - Attila Szabo
- Laboratory of Chemical Physics, National institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health , Bethesda, Maryland 20892, United States
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21
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Brady KT, Reiner JE. Improving the prospects of cleavage-based nanopore sequencing engines. J Chem Phys 2015; 143:074904. [DOI: 10.1063/1.4928647] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kyle T. Brady
- Department of Physics, Virginia Commonwealth University, Richmond, Virginia 23284, USA
| | - Joseph E. Reiner
- Department of Physics, Virginia Commonwealth University, Richmond, Virginia 23284, USA
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22
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Palinkas A, Bulik S, Bockmayr A, Holzhütter HG. Sequential metabolic phases as a means to optimize cellular output in a constant environment. PLoS One 2015; 10:e0118347. [PMID: 25786979 PMCID: PMC4365075 DOI: 10.1371/journal.pone.0118347] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2014] [Accepted: 01/14/2015] [Indexed: 11/25/2022] Open
Abstract
Temporal changes of gene expression are a well-known regulatory feature of all cells, which is commonly perceived as a strategy to adapt the proteome to varying external conditions. However, temporal (rhythmic and non-rhythmic) changes of gene expression are also observed under virtually constant external conditions. Here we hypothesize that such changes are a means to render the synthesis of the metabolic output more efficient than under conditions of constant gene activities. In order to substantiate this hypothesis, we used a flux-balance model of the cellular metabolism. The total time span spent on the production of a given set of target metabolites was split into a series of shorter time intervals (metabolic phases) during which only selected groups of metabolic genes are active. The related flux distributions were calculated under the constraint that genes can be either active or inactive whereby the amount of protein related to an active gene is only controlled by the number of active genes: the lower the number of active genes the more protein can be allocated to the enzymes carrying non-zero fluxes. This concept of a predominantly protein-limited efficiency of gene expression clearly differs from other concepts resting on the assumption of an optimal gene regulation capable of allocating to all enzymes and transporters just that fraction of protein necessary to prevent rate limitation. Applying this concept to a simplified metabolic network of the central carbon metabolism with glucose or lactate as alternative substrates, we demonstrate that switching between optimally chosen stationary flux modes comprising different sets of active genes allows producing a demanded amount of target metabolites in a significantly shorter time than by a single optimal flux mode at fixed gene activities. Our model-based findings suggest that temporal expression of metabolic genes can be advantageous even under conditions of constant external substrate supply.
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Affiliation(s)
- Aljoscha Palinkas
- FB Mathematik und Informatik, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
- * E-mail:
| | - Sascha Bulik
- Institute of Biochemistry, University Medicine—Charite, Chariteplatz 1 Sitz: Virchowweg 6, 10117 Berlin, Germany
| | - Alexander Bockmayr
- FB Mathematik und Informatik, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Hermann-Georg Holzhütter
- Institute of Biochemistry, University Medicine—Charite, Chariteplatz 1 Sitz: Virchowweg 6, 10117 Berlin, Germany
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23
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Dewavrin JY, Abdurrahiem M, Blocki A, Musib M, Piazza F, Raghunath M. Synergistic Rate Boosting of Collagen Fibrillogenesis in Heterogeneous Mixtures of Crowding Agents. J Phys Chem B 2015; 119:4350-8. [DOI: 10.1021/jp5077559] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jean-Yves Dewavrin
- Department
of Biomedical Engineering, Faculty of Engineering, National University of Singapore, 117510 Singapore
- NUS
Tissue Engineering Programme, Life Sciences Institute, National University of Singapore, 117510 Singapore
- NUS Graduate School
for Integrative Sciences and Engineering: Centre for Life Sciences, #05-01, 28 Medical Drive, 117456 Singapore
| | - Muhammed Abdurrahiem
- Department
of Biomedical Engineering, Faculty of Engineering, National University of Singapore, 117510 Singapore
- NUS
Tissue Engineering Programme, Life Sciences Institute, National University of Singapore, 117510 Singapore
| | - Anna Blocki
- Singapore Bioimaging
Consortium, A*STAR, 138667 Singapore
| | - Mrinal Musib
- Department
of Biomedical Engineering, Faculty of Engineering, National University of Singapore, 117510 Singapore
| | - Francesco Piazza
- Université d’Orléans and Centre de Biophysique Moléculaire, rue Charles Sadron, F-45071, Orléans, France
| | - Michael Raghunath
- Department
of Biomedical Engineering, Faculty of Engineering, National University of Singapore, 117510 Singapore
- NUS
Tissue Engineering Programme, Life Sciences Institute, National University of Singapore, 117510 Singapore
- Department
of Biochemistry, Yong Loo Lin School of Medicine, National University of Singapore, 117599 Singapore
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24
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Goldt SD, Terentjev EM. Role of the potential landscape on the single-file diffusion through channels. J Chem Phys 2014; 141:224901. [PMID: 25494767 DOI: 10.1063/1.4903175] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Transport of colloid particles through narrow channels is ubiquitous in cell biology as well as becoming increasingly important for microfluidic applications or targeted drug delivery. Membrane channels in cells are useful models for artificial designs because of their high efficiency, selectivity, and robustness to external fluctuations. Here, we model the passive channels that let cargo simply diffuse through them, affected by a potential profile along the way. Passive transporters achieve high levels of efficiency and specificity from binding interactions with the cargo inside the channel. This however leads to a paradox: why should channels which are so narrow that they are blocked by their cargo evolve to have binding regions for their cargo if that will effectively block them? Using Brownian dynamics simulations, we show that different potentials, notably symmetric, increase the flux through narrow passive channels - and investigate how shape and depth of potentials influence the flux. We find that there exist optimal depths for certain potential shapes and that it is most efficient to apply a small force over an extended region of the channel. On the other hand, having several spatially discrete binding pockets will not alter the flux significantly. We also explore the role of many-particle effects arising from pairwise particle interactions with their neighbours and demonstrate that the relative changes in flux can be accounted for by the kinetics of the absorption reaction at the end of the channel.
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Affiliation(s)
- S D Goldt
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - E M Terentjev
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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25
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Kim M, Lee S, Kim JH. Concentration effects on the rates of irreversible diffusion-influenced reactions. J Chem Phys 2014; 141:084101. [PMID: 25172999 DOI: 10.1063/1.4893340] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We formulate a new theory of the effects of like-particle interactions on the irreversible diffusion-influenced bimolecular reactions of the type A + B → P + B by considering the evolution equation of the triplet ABB number density field explicitly. The solution to the evolution equation is aided by a recently proposed method for solving the Fredholm integral equation of the second kind. We evaluate the theory by comparing its predictions with the results of extensive computer simulations. The present theory provides a reasonable explanation of the simulation results.
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Affiliation(s)
- Minjung Kim
- Department of Chemistry, Seoul National University, Seoul 151-747, South Korea
| | - Sangyoub Lee
- Department of Chemistry, Seoul National University, Seoul 151-747, South Korea
| | - Ji-Hyun Kim
- Department of Chemistry and Institute of Innovative Functional Imaging, Chung-Ang University, Seoul 156-756, South Korea
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26
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Kelkar AV, Franses EI, Corti DS. Nonideal diffusion effects and short-range ordering lead to higher aggregation rates in concentrated hard-sphere dispersions. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2014; 30:3647-3657. [PMID: 24646405 DOI: 10.1021/la500176t] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Brownian aggregation in concentrated hard-sphere dispersions is studied using models and Brownian dynamics (BD) simulations. Two new theoretical models are presented and compared to several existing approaches and BD simulation results, which serve as benchmarks. The first new model is an improvement over an existing local density approximation (LDA)-based model. The other is based on the more rigorous Fundamental measure theory (FMT) applied to the "liquid-state" dynamic density-functional theory (DDFT). Both models provide significant improvements over the classical Smoluchowski model. The predictions of the new FM-DDFT-based model for aggregation kinetics are in excellent agreement with BD simulation results for dispersions with initial particle volume fractions, ϕ, up to 0.35 (close to the hard-sphere freezing transition at ϕ = 0.494). In contrast to previous approaches, the nonideal particle diffusion effects and the initial and time-dependent short-range ordering in concentrated dispersions due to entropic packing effects are explicitly considered here, in addition to the unsteady-state effects. The greater accuracy of the FM-DDFT-based model compared to that of the LDA-based models indicates that nonlocal contributions to particle diffusion (only accounted for in the former) play important roles in aggregation. At high concentrations, the FM-DDFT-based model predicts aggregation half-times and gelation times that are up to 2 orders of magnitude shorter than those of the Smoluchowski model. Moreover, the FM-DDFT-based model predicts asymmetric cluster-cluster aggregation rate constants, at least for short times. Overall, a rigorous mechanistic understanding of the enhancement of aggregation kinetics in concentrated dispersions is provided.
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Affiliation(s)
- Aniruddha V Kelkar
- School of Chemical Engineering, Purdue University , West Lafayette, Indiana 47907, United States
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27
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Cohen SIA, Rajah L, Yoon CH, Buell AK, White DA, Sperling RA, Vendruscolo M, Terentjev EM, Dobson CM, Weitz DA, Knowles TPJ. Spatial propagation of protein polymerization. PHYSICAL REVIEW LETTERS 2014; 112:098101. [PMID: 24655282 DOI: 10.1103/physrevlett.112.098101] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2013] [Indexed: 06/03/2023]
Abstract
We consider the spatial dependence of filamentous protein self-assembly. Through studying the cases where the spreading of aggregated material is dominated either by diffusion or by growth, we derive analytical results for the spatial evolution of filamentous protein aggregation, which we validate against Monte Carlo simulations. Moreover, we compare the predictions of our theory with experimental measurements of two systems for which we identify the propagation as either growth or diffusion controlled. Our results connect the macroscopic observables that characterize the spatial propagation of protein self-assembly with the underlying microscopic processes and provide physical limits on spatial propagation and prionlike behavior associated with protein aggregation.
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Affiliation(s)
- S I A Cohen
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom and School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - L Rajah
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - C H Yoon
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - A K Buell
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - D A White
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - R A Sperling
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - M Vendruscolo
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - E M Terentjev
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - C M Dobson
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - D A Weitz
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA and Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - T P J Knowles
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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28
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Reigh SY. Effect of an external electric field on the diffusion-influenced geminate reversible reaction of a neutral particle and a charged particle in three dimensions. IV. Excited-state ABCD reaction. J Chem Phys 2014; 140:064502. [DOI: 10.1063/1.4864202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
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29
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Ryabov A, Chvosta P. Tracer dynamics in a single-file system with absorbing boundary. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:022132. [PMID: 25353447 DOI: 10.1103/physreve.89.022132] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2013] [Indexed: 06/04/2023]
Abstract
The paper addresses the single-file diffusion in the presence of an absorbing boundary. The emphasis is on an interplay between the hard-core interparticle interaction and the absorption process. The resulting dynamics exhibits several qualitatively new features. First, starting with the exact probability density function for a given particle (a tracer), we study the long-time asymptotics of its moments. Both the mean position and the mean-square displacement are controlled by dynamical exponents which depend on the initial order of the particle in the file. Second, conditioning on nonabsorption, we study the distribution of long-living particles. In the conditioned framework, the dynamical exponents are the same for all particles, however, a given particle possesses an effective diffusion coefficient which depends on its initial order. After performing the thermodynamic limit, the conditioned dynamics of the tracer is subdiffusive, the generalized diffusion coefficient D(1/2) being different from that reported for the system without absorbing boundary.
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Affiliation(s)
- Artem Ryabov
- Department of Macromolecular Physics, Faculty of Mathematics and Physics, Charles University in Prague, V Holešovičkách 2, 18000 Praha 8, Czech Republic
| | - Petr Chvosta
- Department of Macromolecular Physics, Faculty of Mathematics and Physics, Charles University in Prague, V Holešovičkách 2, 18000 Praha 8, Czech Republic
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30
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Piazza F, Dorsaz N, De Michele C, De Los Rios P, Foffi G. Diffusion-limited reactions in crowded environments: a local density approximation. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:375104. [PMID: 23963402 DOI: 10.1088/0953-8984/25/37/375104] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
In the real world, diffusion-limited reactions in chemistry and biology mostly occur in crowded environments, such as macromolecular complex formation in the cell. Despite the paramount importance of such phenomena, theoretical approaches still mainly rely on the Smoluchowski theory, only valid in the infinite dilution limit. In this paper we introduce a novel theoretical framework to describe the encounter rate and the stationary density profiles for encounters between an immobilized target and a fluid of interacting spherical particles, valid in the local density approximation. A comparison with numerical simulations performed for a fluid of hard spheres and square well attractive hard spheres confirms the accuracy of our treatment.
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31
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Angulo G, Cuetos A, Rosspeintner A, Vauthey E. Experimental Evidence of the Relevance of Orientational Correlations in Photoinduced Bimolecular Reactions in Solution. J Phys Chem A 2013; 117:8814-25. [DOI: 10.1021/jp407203r] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Affiliation(s)
- Gonzalo Angulo
- Institute
of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224
Warsaw, Poland
| | - Alejandro Cuetos
- Department of Physical,
Chemical and Natural Systems, Universidad Pablo Olavide, 41013 Sevilla, Spain
| | - Arnulf Rosspeintner
- Department of Physical
Chemistry, University of Geneva, 30 Quai Ernest-Ansermet, 1211 Geneva 4, Switzerland
| | - Eric Vauthey
- Department of Physical
Chemistry, University of Geneva, 30 Quai Ernest-Ansermet, 1211 Geneva 4, Switzerland
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32
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33
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Klann M, Koeppl H. Reaction schemes, escape times and geminate recombinations in particle-based spatial simulations of biochemical reactions. Phys Biol 2013; 10:046005. [DOI: 10.1088/1478-3975/10/4/046005] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
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34
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Piazza F, Foffi G, De Michele C. Irreversible bimolecular reactions with inertia: from the trapping to the target setting at finite densities. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:245101. [PMID: 23670209 DOI: 10.1088/0953-8984/25/24/245101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We investigate numerically pseudo-first-order irreversible bimolecular reactions of the type A + B → B between hard spheres undergoing event-driven Brownian dynamics. We study the encounter rate and the survival probability of A particles as functions of the packing fraction ϕ in the trapping (a single particle diffusing among static non-overlapping traps) and target (many traps diffusing in the presence of a single static target particle) settings, as well as in the case of diffusing traps and particles (full mobility). We show that, since inertial effects are accounted for in our simulation protocol, the standard Smoluchowski theory of coagulation of non-interacting colloids is recovered only at times greater than a characteristic time Δt, marking the transition from the under-damped to the over-damped regime. We show that the survival probability S(t) decays exponentially during this first stage, with a rate 1/τ0 is proportional to φ. Furthermore, we work out a simple analytical expression that is able to capture to an excellent extent the numerical results for t < Δt at low and intermediate densities. Moreover, we demonstrate that the time constant of the asymptotic exponential decay of S(t) for diffusing traps and particles is k(S)(-1), where kS = 4π(DA + DB)Rρ is the Smoluchowski rate. Detailed analyses of the effective decay exponent β = d [log(-logS(t))]/d (logt) and of the steady-state encounter rate reveal that the full mobility and trapping problem are characterized by very similar kinetics, rather different from the target problem. Our results do not allow one to ascertain whether the prediction S(t) is proportional to exp(-at(3/2)) (a = const.) as t → ∞ for the trapping problem in 3D is indeed recovered. In fact, at high density, S(t) is dominated by short encounter times, which makes it exceedingly hard to record the events corresponding to the exploration of large, trap-free regions. As a consequence, at high densities the steady-state rate simply tends to 1/τ0. Finally, we work out an analytical formula for the rate that shows a remarkable agreement with the numerics up φ = 0.4.
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Affiliation(s)
- Francesco Piazza
- Centre de Biophysique Moléculaire, CNRS-UPR 4301, Université d'Orléans, Orléans, France.
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Zaccone A. Note: slowing-down of diffusion-controlled reactions in dense liquid matter. J Chem Phys 2013; 138:186101. [PMID: 23676075 DOI: 10.1063/1.4804417] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Xu Y, Wang H, Nussinov R, Ma B. Protein charge and mass contribute to the spatio-temporal dynamics of protein-protein interactions in a minimal proteome. Proteomics 2013; 13:1339-51. [PMID: 23420643 PMCID: PMC3762602 DOI: 10.1002/pmic.201100540] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2011] [Revised: 12/10/2012] [Accepted: 01/31/2013] [Indexed: 11/07/2022]
Abstract
We constructed and simulated a "minimal proteome" model using Langevin dynamics. It contains 206 essential protein types that were compiled from the literature. For comparison, we generated six proteomes with randomized concentrations. We found that the net charges and molecular weights of the proteins in the minimal genome are not random. The net charge of a protein decreases linearly with molecular weight, with small proteins being mostly positively charged and large proteins negatively charged. The protein copy numbers in the minimal genome have the tendency to maximize the number of protein-protein interactions in the network. Negatively charged proteins that tend to have larger sizes can provide a large collision cross-section allowing them to interact with other proteins; on the other hand, the smaller positively charged proteins could have higher diffusion speed and are more likely to collide with other proteins. Proteomes with random charge/mass populations form less stable clusters than those with experimental protein copy numbers. Our study suggests that "proper" populations of negatively and positively charged proteins are important for maintaining a protein-protein interaction network in a proteome. It is interesting to note that the minimal genome model based on the charge and mass of Escherichia coli may have a larger protein-protein interaction network than that based on the lower organism Mycoplasma pneumoniae.
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Affiliation(s)
- Yu Xu
- Institute of Chinese Minority Traditional Medicine, Minzu University of China, Beijing 100081, People’s Republic of China
| | - Hong Wang
- Institute of Chinese Minority Traditional Medicine, Minzu University of China, Beijing 100081, People’s Republic of China
| | - Ruth Nussinov
- Basic Science Program, SAIC - Frederick, Inc. Center for Cancer Research Nanobiology Program, Frederick National Laboratory, NCI, Frederick, MD 21702, Tel: 301-846-6540, Fax: 301-846-5598
- Sackler Inst. of Molecular Medicine, Department of Human Genetics and Molecular Medicine, Sackler School of Medicine, Tel Aviv University, Tel Aviv 69978, Israel, Tel: 301-846-5579, Fax: 301-846-5598
| | - Buyong Ma
- Basic Science Program, SAIC - Frederick, Inc. Center for Cancer Research Nanobiology Program, Frederick National Laboratory, NCI, Frederick, MD 21702, Tel: 301-846-6540, Fax: 301-846-5598
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Höfling F, Franosch T. Anomalous transport in the crowded world of biological cells. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2013; 76:046602. [PMID: 23481518 DOI: 10.1088/0034-4885/76/4/046602] [Citation(s) in RCA: 584] [Impact Index Per Article: 53.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
A ubiquitous observation in cell biology is that the diffusive motion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarizing their densely packed and heterogeneous structures. The most familiar phenomenon is a sublinear, power-law increase of the mean-square displacement (MSD) as a function of the lag time, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations in time, non-Gaussian distributions of spatial displacements, heterogeneous diffusion and a fraction of immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarize some widely used theoretical models: Gaussian models like fractional Brownian motion and Langevin equations for visco-elastic media, the continuous-time random walk model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Particular emphasis is put on the spatio-temporal properties of the transport in terms of two-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even if the MSDs are identical. Then, we review the theory underlying commonly applied experimental techniques in the presence of anomalous transport like single-particle tracking, fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP). We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where a variety of model systems mimic physiological crowding conditions. Finally, computer simulations are discussed which play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.
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Affiliation(s)
- Felix Höfling
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, and Institut für Theoretische Physik IV, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
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Severe osmotic compression triggers a slowdown of intracellular signaling, which can be explained by molecular crowding. Proc Natl Acad Sci U S A 2013; 110:5725-30. [PMID: 23493557 DOI: 10.1073/pnas.1215367110] [Citation(s) in RCA: 133] [Impact Index Per Article: 12.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Abstract
Regulation of the cellular volume is fundamental for cell survival and function. Deviations from equilibrium trigger dedicated signaling and transcriptional responses that mediate water homeostasis and volume recovery. Cells are densely packed with proteins, and molecular crowding may play an important role in cellular processes. Indeed, increasing molecular crowding has been shown to modify the kinetics of biochemical reactions in vitro; however, the effects of molecular crowding in living cells are mostly unexplored. Here, we report that, in yeast, a sudden reduction in cellular volume, induced by severe osmotic stress, slows down the dynamics of several signaling cascades, including the stress-response pathways required for osmotic adaptation. We show that increasing osmotic compression decreases protein mobility and can eventually lead to a dramatic stalling of several unrelated signaling and cellular processes. The rate of these cellular processes decreased exponentially with protein density when approaching stalling osmotic compression. This suggests that, under compression, the cytoplasm behaves as a soft colloid undergoing a glass transition. Our results shed light on the physical mechanisms that force cells to cope with volume fluctuations to maintain an optimal protein density compatible with cellular functions.
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Abstract
Macromolecular crowding decreases the diffusion rate, shifts the equilibrium of protein-protein and protein-substrate interactions, and changes protein conformational dynamics. Collectively, these effects contribute to enzyme catalysis. Here we describe how crowding may bias the conformational change and dynamics of enzyme populations and in this way affect catalysis. Crowding effects have been studied using artificial crowding agents and in vivo-like environments. These studies revealed a correlation between protein dynamics and function in the crowded environment. We suggest that crowded environments be classified into uniform crowding and structured crowding. Uniform crowding represents random crowding conditions created by synthetic particles with a narrow size distribution. Structured crowding refers to the highly coordinated cellular environment, where proteins and other macromolecules are clustered and organized. In structured crowded environments the perturbation of protein thermal stability may be lower; however, it may still be able to modulate functions effectively and dynamically. Dynamic, allosteric enzymes could be more sensitive to cellular perturbations if their free energy landscape is flatter around the native state; on the other hand, if their free energy landscape is rougher, with high kinetic barriers separating deep minima, they could be more robust. Above all, cells are structured; and this holds both for the cytosol and for the membrane environment. The crowded environment is organized, which limits the search, and the crowders are not necessarily inert. More likely, they too transmit allosteric effects, and as such play important functional roles. Overall, structured cellular crowding may lead to higher enzyme efficiency and specificity.
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Affiliation(s)
- Judith Klinman
- Department of Chemistry Department of Molecular and Cell Biology, University of California The california institute for Quantitativ, Berkeley, CA, USA
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40
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Qin S, Cai L, Zhou HX. A method for computing association rate constants of atomistically represented proteins under macromolecular crowding. Phys Biol 2012. [PMID: 23197255 DOI: 10.1088/1478-3975/9/6/066008] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
In cellular environments, two protein molecules on their way to form a specific complex encounter many bystander macromolecules. The latter molecules, or crowders, affect both the energetics of the interaction between the test molecules and the dynamics of their relative motion. In earlier work (Zhou and Szabo 1991 J. Chem. Phys. 95 5948-52), it has been shown that, in modeling the association kinetics of the test molecules, the presence of crowders can be accounted for by their energetic and dynamic effects. The recent development of the transient-complex theory for protein association in dilute solutions makes it possible to easily incorporate the energetic and dynamic effects of crowders. The transient complex refers to a late on-pathway intermediate, in which the two protein molecules have near-native relative separation and orientation, but have yet to form the many short-range specific interactions of the native complex. The transient-complex theory predicts the association rate constant as k(a) = k(a0)exp(-ΔG*(el)/k(B)T), where k(a0) is the 'basal' rate constant for reaching the transient complex by unbiased diffusion, and the Boltzmann factors captures the influence of long-range electrostatic interactions between the protein molecules. Crowders slow down the diffusion, therefore reducing the basal rate constant (to k(ac0)), and induce an effective interaction energy ΔG(c). We show that the latter interaction energy for atomistic proteins in the presence of spherical crowders is 'long'-ranged, allowing the association rate constant under crowding to be computed as k(ac) = k(ac0)exp[-(ΔG*(el) + ΔG*(c))/k(B)T]. Applications demonstrate that this computational method allows for realistic modeling of protein association kinetics under crowding.
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Affiliation(s)
- Sanbo Qin
- Department of Physics and Institute of Molecular Biophysics, Florida State University, Tallahassee, FL 32306, USA
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Stepanyan R, Lebouille JGJL, Slot JJM, Tuinier R, Stuart MAC. Controlled nanoparticle formation by diffusion limited coalescence. PHYSICAL REVIEW LETTERS 2012; 109:138301. [PMID: 23030126 DOI: 10.1103/physrevlett.109.138301] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2012] [Indexed: 06/01/2023]
Abstract
Polymeric nanoparticles (NPs) have great application potential in science and technology. Their functionality strongly depends on their size. We present a theory for the size of NPs formed by precipitation of polymers into a bad solvent in the presence of a stabilizing surfactant. The analytical theory is based upon diffusion-limited coalescence kinetics of the polymers. Two relevant time scales, a mixing and a coalescence time, are identified and their ratio is shown to determine the final NP diameter. The size is found to scale in a universal manner and is predominantly sensitive to the mixing time and the polymer concentration if the surfactant concentration is sufficiently high. The model predictions are in good agreement with experimental data. Hence the theory provides a solid framework for tailoring NPs with a priori determined size.
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Affiliation(s)
- R Stepanyan
- DSM Research, PO Box 18, NL-6160 MD Geleen, The Netherlands
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Zhu PW. Nonequilibrium polymer chains induced by conformational transitions in densely interfacial layers. J Chem Phys 2012; 137:104903. [PMID: 22979886 DOI: 10.1063/1.4751479] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Nonequilibrium poly(N-isopropylacrylamide) (PNIPAM) chains are generated by temperature-induced conformational transitions in the densely interfacial PNIPAM layer at high adsorbed amounts in aqueous solution. The interleaving chains relax in a spatially heterogeneous space of adsorbed layer which is filled with the domains via the hydrogen bonding and hydrophobic interactions. The relaxation dynamics of interleaving chains is changed from the weekly stretched exponential behaviour at the lower adsorbed amount to the strongly stretched exponential behaviour at the higher adsorbed amount. The kinetic constraints for the relaxation dynamics depend on the segment density of the adsorbed layer which is controlled by the temperature. The stretched exponential relaxation is related to an ensemble of relaxations confined in the domains with different physical origins for the heterogeneous dynamics. The range of energy barriers for the relaxation is estimated from the stretched exponent based on the random first order transition theory.
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Affiliation(s)
- Peng-Wei Zhu
- Cooperative Research Centre for Polymers, Melbourne, Australia
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Zaccone A, Terentjev EM. Theory of molecular crowding in Brownian hard-sphere liquids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:061202. [PMID: 23005079 DOI: 10.1103/physreve.85.061202] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2011] [Indexed: 06/01/2023]
Abstract
We derive an analytical pair potential of mean force for Brownian molecules in the liquid state. Our approach accounts for many-particle correlations of crowding particles of the liquid and for diffusive transport across the spatially modulated local density of crowders in the dense environment. Focusing on the limit of equal-size particles, we show that this diffusive transport leads to additional density- and structure-dependent terms in the interaction potential and to a much stronger attraction (by a factor of ≈4 at average volume fraction of crowders φ{0}=0.25) than in the standard depletion interaction where the diffusive effects are neglected. As an illustration of the theory, we use it to study the size of a polymer chain in a solution of inert crowders. Even in the case of an athermal background solvent, when a classical chain should be fully swollen, we find a sharp coil-globule transition of the ideal chain collapsing at a critical value of the crowder volume fraction φ{c}≈0.145.
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Affiliation(s)
- Alessio Zaccone
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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Ryabov A, Chvosta P. Survival of interacting Brownian particles in crowded one-dimensional environment. J Chem Phys 2012; 136:064114. [DOI: 10.1063/1.3684954] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Zaccone A, Terentjev EM. Theory of thermally activated ionization and dissociation of bound states. PHYSICAL REVIEW LETTERS 2012; 108:038302. [PMID: 22400791 DOI: 10.1103/physrevlett.108.038302] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2011] [Indexed: 05/31/2023]
Abstract
Calculating the microscopic dissociation rate of a bound state, such as a classical diatomic molecule, has been difficult so far. The problem was that standard theories require an energy barrier over which the bound particle (or state) escapes into the preferred low-energy state. This is not the case when the long-range repulsion responsible for the barrier is either absent or screened (as in Cooper pairs, plasmas, or biomolecular complexes). We solve this classical problem by accounting for entropic driving forces at the microscopic level. The theory predicts dissociation rates for arbitrary potentials and is successfully tested on the example of plasma, where it yields an estimate of ionization in the core of the Sun in excellent agreement with experiments. In biology, the new theory accounts for crowding in receptor-ligand kinetics and protein aggregation.
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Affiliation(s)
- A Zaccone
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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46
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Seki K, Wojcik M, Tachiya M. Diffusion-mediated geminate reactions under excluded volume interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:011131. [PMID: 22400536 DOI: 10.1103/physreve.85.011131] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2011] [Indexed: 05/31/2023]
Abstract
In this paper, influence of crowding by inert particles on the geminate reaction kinetics is theoretically investigated. Time evolution equations for the survival probability of a geminate pair are derived from the master equation taking into account the correlation among all diffusing particles, and the results are compared with those obtained by Monte Carlo simulations. In general, excluded volume interactions by the inert particles slow down the diffusive motion of reactants. However, when the initial concentration of the inert particles is uniform and high, we show that additional influence of interference between reaction and correlated diffusion accelerates the transient decay of the survival probability in the diffusion-controlled limit. We also study the escape probability for a nonuniform initial distribution of the inert particles by taking the continuous limit in space. We show that reaction yield is increased when the reaction proceeds in the presence of a positive density gradient of the inert particles which inhibits the escape of reactants. The effect can be interpreted as a cage effect.
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Affiliation(s)
- Kazuhiko Seki
- National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba Central 5, Higashi 1-1-1, Tsukuba, Ibaraki, 305-8565 Japan
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Kwon S, Kim Y. Effects of excluded volume interaction on diffusion-reaction processes in crowded environments. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:041103. [PMID: 22181083 DOI: 10.1103/physreve.84.041103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2011] [Indexed: 05/31/2023]
Abstract
In nonequilibrium phase transitions of reaction-diffusion processes, the irrelevance of excluded volume interaction for the critical properties generally has been accepted due to the rare probability of multiple occupancy at criticality. Moreover, this belief is common sense in scale-free (SF) networks, which correspond to infinite dimensional irregular structures. However, the conventional belief is not satisfied in crowded environments in which the total number of particles is preserved in time. In this paper, we show, by investigating a typical process for epidemic spreading in crowded environments, that excluded volume interaction indeed changes critical behaviors in one dimension and surprisingly even mean-field behaviors in SF networks.
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Affiliation(s)
- Sungchul Kwon
- Department of Physics, Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea
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Zaccone A, Dorsaz N, Piazza F, De Michele C, Morbidelli M, Foffi G. Crowding, Intermolecular Interactions, and Shear Flow Effects in the Diffusion Model of Chemical Reactions. J Phys Chem B 2011; 115:7383-96. [DOI: 10.1021/jp200439a] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Alessio Zaccone
- Chemistry and Applied Biosciences, ETH Zurich, CH-8093 Zürich, Switzerland
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Nicolas Dorsaz
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Francesco Piazza
- Centre de Biophysique Moleculaire (CBM-CNRS), Rue Charles Sadron, 45071 Cedex 2 Orleans, France
| | - Cristiano De Michele
- Department of Physics, University of Rome ‘‘La Sapienza’’, Piazzale Aldo Moro 2, I-00185 Roma, Italy
| | - Massimo Morbidelli
- Chemistry and Applied Biosciences, ETH Zurich, CH-8093 Zürich, Switzerland
| | - Giuseppe Foffi
- Institute of Theoretical Physics, Ecole Polytechnique Federale de Lausanne, 1015 Lausanne, Switzerland
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Seki K, Wojcik M, Tachiya M. Effects of excluded volume interaction and dimensionality on diffusion-mediated reactions. J Chem Phys 2011; 134:094506. [DOI: 10.1063/1.3560419] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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