1
|
Raczyłło E, Gołowicz D, Skóra T, Kazimierczuk K, Kondrat S. Size Sensitivity of Metabolite Diffusion in Macromolecular Crowds. NANO LETTERS 2024; 24. [PMID: 38607288 PMCID: PMC11057039 DOI: 10.1021/acs.nanolett.3c05100] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/25/2023] [Revised: 04/02/2024] [Accepted: 04/03/2024] [Indexed: 04/13/2024]
Abstract
Metabolites play crucial roles in cellular processes, yet their diffusion in the densely packed interiors of cells remains poorly understood, compounded by conflicting reports in existing studies. Here, we employ pulsed-gradient stimulated-echo NMR and Brownian/Stokesian dynamics simulations to elucidate the behavior of nano- and subnanometer-sized tracers in crowded environments. Using Ficoll as a crowder, we observe a linear decrease in tracer diffusivity with increasing occupied volume fraction, persisting─somewhat surprisingly─up to volume fractions of 30-40%. While simulations suggest a linear correlation between diffusivity slowdown and particle size, experimental findings hint at a more intricate relationship, possibly influenced by Ficoll's porosity. Simulations and numerical calculations of tracer diffusivity in the E. coli cytoplasm show a nonlinear yet monotonic diffusion slowdown with particle size. We discuss our results in the context of nanoviscosity and discrepancies with existing studies.
Collapse
Affiliation(s)
- Edyta Raczyłło
- Institute
of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland
- Department
of Theoretical Chemistry, Institute of Chemical Sciences, Faculty
of Chemistry, Maria Curie-Skłodowska
University in Lublin, 20-031 Lublin, Poland
| | - Dariusz Gołowicz
- Institute
of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland
| | - Tomasz Skóra
- Institute
of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland
- Scientific
Computing and Imaging Institute, University
of Utah, Salt Lake City, Utah 84112, United States
| | | | - Svyatoslav Kondrat
- Institute
of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland
- Institute
for Computational Physics, University of
Stuttgart 70569, Stuttgart, Germany
| |
Collapse
|
2
|
Guin D, Gruebele M. Weak Chemical Interactions That Drive Protein Evolution: Crowding, Sticking, and Quinary Structure in Folding and Function. Chem Rev 2019; 119:10691-10717. [PMID: 31356058 DOI: 10.1021/acs.chemrev.8b00753] [Citation(s) in RCA: 70] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Abstract
In recent years, better instrumentation and greater computing power have enabled the imaging of elusive biomolecule dynamics in cells, driving many advances in understanding the chemical organization of biological systems. The focus of this Review is on interactions in the cell that affect both biomolecular stability and function and modulate them. The same protein or nucleic acid can behave differently depending on the time in the cell cycle, the location in a specific compartment, or the stresses acting on the cell. We describe in detail the crowding, sticking, and quinary structure in the cell and the current methods to quantify them both in vitro and in vivo. Finally, we discuss protein evolution in the cell in light of current biophysical evidence. We describe the factors that drive protein evolution and shape protein interaction networks. These interactions can significantly affect the free energy, ΔG, of marginally stable and low-population proteins and, due to epistasis, direct the evolutionary pathways in an organism. We finally conclude by providing an outlook on experiments to come and the possibility of collaborative evolutionary biology and biophysical efforts.
Collapse
Affiliation(s)
- Drishti Guin
- Department of Chemistry , University of Illinois , Urbana , Illinois 61801 , United States
| | - Martin Gruebele
- Department of Chemistry , University of Illinois , Urbana , Illinois 61801 , United States.,Department of Physics , University of Illinois , Urbana , Illinois 61801 , United States.,Center for Biophysics and Quantitative Biology , University of Illinois , Urbana , Illinois 61801 , United States
| |
Collapse
|
3
|
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.
Collapse
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
| |
Collapse
|
4
|
Shew CY, Oda S, Yoshikawa K. Localization switching of a large object in a crowded cavity: A rigid/soft object prefers surface/inner positioning. J Chem Phys 2018; 147:204901. [PMID: 29195278 DOI: 10.1063/1.5000762] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Abstract
For living cells in the real world, a large organelle is commonly positioned in the inner region away from membranes, such as the nucleus of eukaryotic cells, the nucleolus of nuclei, mitochondria, chloroplast, Golgi body, etc. It contradicts the expectation by the current depletion-force theory in that the larger particle should be excluded from the inner cell space onto cell boundaries in a crowding media. Here we simply model a sizable organelle as a soft-boundary large particle allowing crowders, which are smaller hard spheres in the model, to intrude across its boundary. The results of Monte Carlo simulation indicate that the preferential location of the larger particle switches from the periphery into the inner region of the cavity by increasing its softness. An integral equation theory is further developed to account for the structural features of the model, and the theoretical predictions are found consistent with our simulation results.
Collapse
Affiliation(s)
- Chwen-Yang Shew
- Ph.D. Program in Chemistry, The Graduate Center of the City University of New York, New York, New York 10016, USA and Department of Chemistry, College of Staten Island, Staten Island, New York 10314, USA
| | - Soutaro Oda
- Faculty of Life and Medical Sciences, Doshisha University, Kyotanabe 610-0394, Japan
| | - Kenichi Yoshikawa
- Faculty of Life and Medical Sciences, Doshisha University, Kyotanabe 610-0394, Japan
| |
Collapse
|
5
|
Nandigrami P, Grove B, Konya A, Selinger RLB. Gradient-driven diffusion and pattern formation in crowded mixtures. Phys Rev E 2017; 95:022107. [PMID: 28297895 DOI: 10.1103/physreve.95.022107] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2016] [Indexed: 11/07/2022]
Abstract
Gradient-driven diffusion in crowded, multicomponent mixtures is a topic of high interest because of its role in biological processes such as transport in cell membranes. In partially phase-separated solutions, gradient-driven diffusion affects microstructure, which in turn affects diffusivity; a key question is how this complex coupling controls both transport and pattern formation. To examine these mechanisms, we study a two-dimensional multicomponent lattice gas model, where "tracer" molecules diffuse between a source and a sink separated by a solution of sticky "crowder" molecules that cluster to form dynamically evolving obstacles. In the high-temperature limit, crowders and tracers are miscible, and transport may be predicted analytically. At intermediate temperatures, crowders phase separate into clusters that drift toward the tracer sink. As a result, steady-state tracer diffusivity depends nonmonotonically on both temperature and crowder density, and we observe a variety of complex microstructures. In the low-temperature limit, crowders rapidly aggregate to form obstacles that are kinetically arrested; if crowder density is near the percolation threshold, resulting tracer diffusivity shows scaling behavior with the same scaling exponent as the random resistor network model. Though highly idealized, this simple model reveals fundamental mechanisms governing coupled gradient-driven diffusion, phase separation, and microstructural evolution in crowded mixtures.
Collapse
Affiliation(s)
| | - Brandy Grove
- Department of Macromolecular Science and Engineering, Case Western Reserve University, Cleveland, Ohio 44106, USA
| | - Andrew Konya
- Liquid Crystal Institute, Kent State University, Kent, Ohio 44242, USA
| | | |
Collapse
|
6
|
Mura F, Zaccone A. Effects of shear flow on phase nucleation and crystallization. Phys Rev E 2016; 93:042803. [PMID: 27176370 DOI: 10.1103/physreve.93.042803] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2016] [Indexed: 05/28/2023]
Abstract
Classical nucleation theory offers a good framework for understanding the common features of new phase formation processes in metastable homogeneous media at rest. However, nucleation processes in liquids are ubiquitously affected by hydrodynamic flow, and there is no satisfactory understanding of whether shear promotes or slows down the nucleation process. We developed a classical nucleation theory for sheared systems starting from the molecular level of the Becker-Doering master kinetic equation and we analytically derived a closed-form expression for the nucleation rate. The theory accounts for the effect of flow-mediated transport of molecules to the nucleus of the new phase, as well as for the mechanical deformation imparted to the nucleus by the flow field. The competition between flow-induced molecular transport, which accelerates nucleation, and flow-induced nucleus straining, which lowers the nucleation rate by increasing the nucleation energy barrier, gives rise to a marked nonmonotonic dependence of the nucleation rate on the shear rate. The theory predicts an optimal shear rate at which the nucleation rate is one order of magnitude larger than in the absence of flow.
Collapse
Affiliation(s)
- Federica Mura
- Department of Physics, Ludwig-Maximilians-University Munich, Theresienstrasse 37, 80333 Munich, Germany
| | - Alessio Zaccone
- Statistical Physics Group, Department of Chemical Engineering and Biotechnology, University of Cambridge, New Museums Site, Pembroke Street, CB2 3RA Cambridge, United Kingdom
| |
Collapse
|
7
|
Shendruk TN, Bertrand M, de Haan HW, Harden JL, Slater GW. Simulating the entropic collapse of coarse-grained chromosomes. Biophys J 2015; 108:810-820. [PMID: 25692586 PMCID: PMC4336370 DOI: 10.1016/j.bpj.2014.11.3487] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2014] [Revised: 10/31/2014] [Accepted: 11/14/2014] [Indexed: 10/24/2022] Open
Abstract
Depletion forces play a role in the compaction and decompaction of chromosomal material in simple cells, but it has remained debatable whether they are sufficient to account for chromosomal collapse. We present coarse-grained molecular dynamics simulations, which reveal that depletion-induced attraction is sufficient to cause the collapse of a flexible chain of large structural monomers immersed in a bath of smaller depletants. These simulations use an explicit coarse-grained computational model that treats both the supercoiled DNA structural monomers and the smaller protein crowding agents as combinatorial, truncated Lennard-Jones spheres. By presenting a simple theoretical model, we quantitatively cast the action of depletants on supercoiled bacterial DNA as an effective solvent quality. The rapid collapse of the simulated flexible chromosome at the predicted volume fraction of depletants is a continuous phase transition. Additional physical effects to such simple chromosome models, such as enthalpic interactions between structural monomers or chain rigidity, are required if the collapse is to be a first-order phase transition.
Collapse
Affiliation(s)
- Tyler N Shendruk
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, Theoretical Physics, University of Oxford, Oxford, United Kingdom.
| | - Martin Bertrand
- Department of Physics, University of Ottawa, Ottawa, Ontario, Canada
| | - Hendrick W de Haan
- Faculty of Science, University of Ontario Institute of Technology, Oshawa, Ontario, Canada
| | - James L Harden
- Department of Physics, University of Ottawa, Ottawa, Ontario, Canada
| | - Gary W Slater
- Department of Physics, University of Ottawa, Ottawa, Ontario, Canada.
| |
Collapse
|
8
|
Shendruk TN, Bertrand M, Harden JL, Slater GW, de Haan HW. Coarse-grained molecular dynamics simulations of depletion-induced interactions for soft matter systems. J Chem Phys 2014; 141:244910. [DOI: 10.1063/1.4903992] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Tyler N. Shendruk
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom
| | - Martin Bertrand
- Department of Physics, University of Ottawa, 150 Louis-Pasteur, Ottawa, Ontario K1N 6N5, Canada
| | - James L. Harden
- Department of Physics, University of Ottawa, 150 Louis-Pasteur, Ottawa, Ontario K1N 6N5, Canada
| | - Gary W. Slater
- Department of Physics, University of Ottawa, 150 Louis-Pasteur, Ottawa, Ontario K1N 6N5, Canada
| | - Hendrick W. de Haan
- Faculty of Science, University of Ontario Institute of Technology, 2000 Simcoe St. North, Oshawa, Ontario L1H 7K4, Canada
| |
Collapse
|
9
|
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.
Collapse
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
| |
Collapse
|
10
|
Ratcheted diffusion transport through crowded nanochannels. Sci Rep 2013; 3:3103. [PMID: 24173137 PMCID: PMC3813928 DOI: 10.1038/srep03103] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2013] [Accepted: 10/16/2013] [Indexed: 01/18/2023] Open
Abstract
The problem of transport through nanochannels is one of the major questions in cell biology, with a wide range of applications. In this paper we discuss the process of spontaneous translocation of molecules (Brownian particles) by ratcheted diffusion: a problem relevant for protein translocation along bacterial flagella or injectosome complex, or DNA translocation by bacteriophages. We use molecular dynamics simulations and statistical theory to identify two regimes of transport: at low rate of particle injection into the channel the process is controlled by the individual diffusion towards the open end (the first passage problem), while at a higher rate of injection the crowded regime sets in. In this regime the particle density in the channel reaches a constant saturation level and the resistance force increases substantially, due to the osmotic pressure build-up. To achieve a steady-state transport, the apparatus that injects new particles into a crowded channel has to operate with an increasing power consumption, proportional to the length of the channel and the required rate of transport. The analysis of resistance force, and accordingly – the power required to inject the particles into a crowded channel to overcome its clogging, is also relevant for many microfluidics applications.
Collapse
|
11
|
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.
Collapse
Affiliation(s)
- Francesco Piazza
- Centre de Biophysique Moléculaire, CNRS-UPR 4301, Université d'Orléans, Orléans, France.
| | | | | |
Collapse
|
12
|
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
|