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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.
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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
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2
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Romo‐Uribe A. Extensional flow of stiff‐chain polymer solutions in the semidilute regime. J Appl Polym Sci 2022. [DOI: 10.1002/app.51660] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Angel Romo‐Uribe
- Research & Development, Advanced Science & Technology Division Johnson & Johnson Vision Care Inc Jacksonville Florida USA
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3
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Sadeghi M, Noé F. Hydrodynamic coupling for particle-based solvent-free membrane models. J Chem Phys 2021; 155:114108. [PMID: 34551532 DOI: 10.1063/5.0061623] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
The great challenge with biological membrane systems is the wide range of scales involved, from nanometers and picoseconds for individual lipids to the micrometers and beyond millisecond for cellular signaling processes. While solvent-free coarse-grained membrane models are convenient for large-scale simulations and promising to provide insight into slow processes involving membranes, these models usually have unrealistic kinetics. One major obstacle is the lack of an equally convenient way of introducing hydrodynamic coupling without significantly increasing the computational cost of the model. To address this, we introduce a framework based on anisotropic Langevin dynamics, for which major in-plane and out-of-plane hydrodynamic effects are modeled via friction and diffusion tensors from analytical or semi-analytical solutions to Stokes hydrodynamic equations. Using this framework, in conjunction with our recently developed membrane model, we obtain accurate dispersion relations for planar membrane patches, both free-standing and in the vicinity of a wall. We briefly discuss how non-equilibrium dynamics is affected by hydrodynamic interactions. We also measure the surface viscosity of the model membrane and discuss the affecting dissipative mechanisms.
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Affiliation(s)
- Mohsen Sadeghi
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
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4
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Romo‐Uribe A. Shear rheology and scaling of semiflexible polymers: Effect of polymer‐solvent interactions in the semidilute regime. J Appl Polym Sci 2021. [DOI: 10.1002/app.49712] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Angel Romo‐Uribe
- R&D, Advanced Science & Technology Division Johnson & Johnson Vision Florida USA
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5
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Large-scale simulation of biomembranes incorporating realistic kinetics into coarse-grained models. Nat Commun 2020; 11:2951. [PMID: 32528158 PMCID: PMC7289815 DOI: 10.1038/s41467-020-16424-0] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2019] [Accepted: 04/28/2020] [Indexed: 12/12/2022] Open
Abstract
Biomembranes are two-dimensional assemblies of phospholipids that are only a few nanometres thick, but form micrometre-sized structures vital to cellular function. Explicit molecular modelling of biologically relevant membrane systems is computationally expensive due to the large number of solvent particles and slow membrane kinetics. Coarse-grained solvent-free membrane models offer efficient sampling but sacrifice realistic kinetics, thereby limiting the ability to predict pathways and mechanisms of membrane processes. Here, we present a framework for integrating coarse-grained membrane models with continuum-based hydrodynamics. This framework facilitates efficient simulation of large biomembrane systems with large timesteps, while achieving realistic equilibrium and non-equilibrium kinetics. It helps to bridge between the nanometer/nanosecond spatiotemporal resolutions of coarse-grained models and biologically relevant time- and lengthscales. As a demonstration, we investigate fluctuations of red blood cells, with varying cytoplasmic viscosities, in 150-milliseconds-long trajectories, and compare kinetic properties against single-cell experimental observations.
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6
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Murphy E, Lomboy G, Wang K, Sundararajan S, Subramaniam S. The rheology of slurries of athermal cohesive micro-particles immersed in fluid: A computational and experimental comparison. Chem Eng Sci 2019. [DOI: 10.1016/j.ces.2018.09.010] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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7
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Blanco PM, Garcés JL, Madurga S, Mas F. Macromolecular diffusion in crowded media beyond the hard-sphere model. SOFT MATTER 2018; 14:3105-3114. [PMID: 29620120 DOI: 10.1039/c8sm00201k] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
The effect of macromolecular crowding on diffusion beyond the hard-core sphere model is studied. A new coarse-grained model is presented, the Chain Entanglement Softened Potential (CESP) model, which takes into account the macromolecular flexibility and chain entanglement. The CESP model uses a shoulder-shaped interaction potential that is implemented in the Brownian Dynamics (BD) computations. The interaction potential contains only one parameter associated with the chain entanglement energetic cost (Ur). The hydrodynamic interactions are included in the BD computations via Tokuyama mean-field equations. The model is used to analyze the diffusion of a streptavidin protein among different sized dextran obstacles. For this system, Ur is obtained by fitting the streptavidin experimental long-time diffusion coefficient Dlongversus the macromolecular concentration for D50 (indicating their molecular weight in kg mol-1) dextran obstacles. The obtained Dlong values show better quantitative agreement with experiments than those obtained with hard-core spheres. Moreover, once parametrized, the CESP model is also able to quantitatively predict Dlong and the anomalous exponent (α) for streptavidin diffusion among D10, D400 and D700 dextran obstacles. Dlong, the short-time diffusion coefficient (Dshort) and α are obtained from the BD simulations by using a new empirical expression, able to describe the full temporal evolution of the diffusion coefficient.
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Affiliation(s)
- Pablo M Blanco
- Department of Material Science and Physical Chemistry, Barcelona University, 08028 Barcelona, Spain. and Institute of Theoretical and Computational Chemistry (IQTC), Barcelona University, 08028 Barcelona, Spain
| | - Josep Lluís Garcés
- Department of Chemistry, University of Lleida (UdL), 25003 Lleida, Spain.
| | - Sergio Madurga
- Department of Material Science and Physical Chemistry, Barcelona University, 08028 Barcelona, Spain. and Institute of Theoretical and Computational Chemistry (IQTC), Barcelona University, 08028 Barcelona, Spain
| | - Francesc Mas
- Department of Material Science and Physical Chemistry, Barcelona University, 08028 Barcelona, Spain. and Institute of Theoretical and Computational Chemistry (IQTC), Barcelona University, 08028 Barcelona, Spain
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8
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Brownian Dynamics Computational Model of Protein Diffusion in Crowded Media with Dextran Macromolecules as Obstacles. ENTROPY 2017. [DOI: 10.3390/e19030105] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
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10
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Skolnick J. Perspective: On the importance of hydrodynamic interactions in the subcellular dynamics of macromolecules. J Chem Phys 2016; 145:100901. [PMID: 27634243 PMCID: PMC5018002 DOI: 10.1063/1.4962258] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2016] [Accepted: 08/01/2016] [Indexed: 12/30/2022] Open
Abstract
An outstanding challenge in computational biophysics is the simulation of a living cell at molecular detail. Over the past several years, using Stokesian dynamics, progress has been made in simulating coarse grained molecular models of the cytoplasm. Since macromolecules comprise 20%-40% of the volume of a cell, one would expect that steric interactions dominate macromolecular diffusion. However, the reduction in cellular diffusion rates relative to infinite dilution is due, roughly equally, to steric and hydrodynamic interactions, HI, with nonspecific attractive interactions likely playing rather a minor role. HI not only serve to slow down long time diffusion rates but also cause a considerable reduction in the magnitude of the short time diffusion coefficient relative to that at infinite dilution. More importantly, the long range contribution of the Rotne-Prager-Yamakawa diffusion tensor results in temporal and spatial correlations that persist up to microseconds and for intermolecular distances on the order of protein radii. While HI slow down the bimolecular association rate in the early stages of lipid bilayer formation, they accelerate the rate of large scale assembly of lipid aggregates. This is suggestive of an important role for HI in the self-assembly kinetics of large macromolecular complexes such as tubulin. Since HI are important, questions as to whether continuum models of HI are adequate as well as improved simulation methodologies that will make simulations of more complex cellular processes practical need to be addressed. Nevertheless, the stage is set for the molecular simulations of ever more complex subcellular processes.
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Affiliation(s)
- Jeffrey Skolnick
- Center for the Study of Systems Biology, School of Biology, Georgia Institute of Technology, 950 Atlantic Dr., NW, Atlanta, Georgia 30332, USA
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11
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Delmotte B, Keaveny EE. Simulating Brownian suspensions with fluctuating hydrodynamics. J Chem Phys 2015; 143:244109. [DOI: 10.1063/1.4938173] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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12
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Sedeh RS, Pan K, Adendorff MR, Hallatschek O, Bathe KJ, Bathe M. Computing Nonequilibrium Conformational Dynamics of Structured Nucleic Acid Assemblies. J Chem Theory Comput 2015; 12:261-73. [PMID: 26636351 DOI: 10.1021/acs.jctc.5b00965] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Synthetic nucleic acids can be programmed to form precise three-dimensional structures on the nanometer-scale. These thermodynamically stable complexes can serve as structural scaffolds to spatially organize functional molecules including multiple enzymes, chromophores, and force-sensing elements with internal dynamics that include substrate reaction-diffusion, excitonic energy transfer, and force-displacement response that often depend critically on both the local and global conformational dynamics of the nucleic acid assembly. However, high molecular weight assemblies exhibit long time-scale and large length-scale motions that cannot easily be sampled using all-atom computational procedures such as molecular dynamics. As an alternative, here we present a computational framework to compute the overdamped conformational dynamics of structured nucleic acid assemblies and apply it to a DNA-based tweezer, a nine-layer DNA origami ring, and a pointer-shaped DNA origami object, which consist of 204, 3,600, and over 7,000 basepairs, respectively. The framework employs a mechanical finite element model for the DNA nanostructure combined with an implicit solvent model to either simulate the Brownian dynamics of the assembly or alternatively compute its Brownian modes. Computational results are compared with an all-atom molecular dynamics simulation of the DNA-based tweezer. Several hundred microseconds of Brownian dynamics are simulated for the nine-layer ring origami object to reveal its long time-scale conformational dynamics, and the first ten Brownian modes of the pointer-shaped structure are predicted.
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Affiliation(s)
| | | | | | - Oskar Hallatschek
- Department of Physics, University of California, Berkeley , Berkeley, California 94720, United States
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Dell ZE, Tsang B, Jiang L, Granick S, Schweizer KS. Correlated two-particle diffusion in dense colloidal suspensions at early times: Theory and comparison to experiment. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052304. [PMID: 26651692 DOI: 10.1103/physreve.92.052304] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2015] [Indexed: 06/05/2023]
Abstract
The spatially resolved diffusive dynamic cross correlations of a pair of colloids in dense quasi-two-dimensional monolayers of identical particles are studied experimentally and theoretically at early times where motion is Fickian. In very dense systems where strong oscillatory equilibrium packing correlations are present, we find an exponential decay of the dynamic cross correlations on small and intermediate length scales. At large separations where structure becomes random, an apparent power law decay with an exponent of approximately -2.2 is observed. For a moderately dense suspension where local structural correlations are essentially absent, this same apparent power law decay is observed over all probed interparticle separations. A microscopic nonhydrodynamic theory is constructed for the dynamic cross correlations which is based on interparticle frictional effects and effective structural forces. Hydrodynamics enters only via setting the very short-time single-particle self-diffusion constant. No-adjustable-parameter quantitative predictions of the theory for the dynamic cross correlations are in good agreement with experiment over all length scales. The origin of the long-range apparent power law is the influence of the constraint of fixed interparticle separation on the amplitude of the mean square force exerted on the two tagged particles by the surrounding fluid. The theory is extended to study high-packing-fraction 3D hard sphere fluids. The same pattern of an oscillatory exponential form of the dynamic cross correlation function is predicted in the structural regime, but the long-range tail decays faster than in monolayers with an exponent of -3.
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Affiliation(s)
- Zachary E Dell
- Department of Physics, University of Illinois, Urbana, Illinois 61801, USA
| | - Boyce Tsang
- Department of Physics, University of Illinois, Urbana, Illinois 61801, USA
| | - Lingxiang Jiang
- Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
| | - Steve Granick
- Department of Physics, University of Illinois, Urbana, Illinois 61801, USA
- Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
- Department of Materials Science, University of Illinois, Urbana, Illinois 61801, USA
- IBS Center for Soft and Living Matter, Ulsan National Institute of Science and Technology, Ulju-gun 689-789, South Korea
| | - Kenneth S Schweizer
- Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
- Department of Materials Science, University of Illinois, Urbana, Illinois 61801, USA
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Sterpone F, Derreumaux P, Melchionna S. Protein Simulations in Fluids: Coupling the OPEP Coarse-Grained Force Field with Hydrodynamics. J Chem Theory Comput 2015; 11:1843-53. [PMID: 26574390 PMCID: PMC5242371 DOI: 10.1021/ct501015h] [Citation(s) in RCA: 53] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
A novel simulation framework that integrates the OPEP coarse-grained (CG) model for proteins with the Lattice Boltzmann (LB) methodology to account for the fluid solvent at mesoscale level is presented. OPEP is a very efficient, water-free and electrostatic-free force field that reproduces at quasi-atomistic detail processes like peptide folding, structural rearrangements, and aggregation dynamics. The LB method is based on the kinetic description of the solvent in order to solve the fluid mechanics under a wide range of conditions, with the further advantage of being highly scalable on parallel architectures. The capabilities of the approach are presented, and it is shown that the strategy is effective in exploring the role of hydrodynamics on protein relaxation and peptide aggregation. The end result is a strategy for modeling systems of thousands of proteins, such as in the case of dense protein suspensions. The future perspectives of the multiscale approach are also discussed.
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Affiliation(s)
- Fabio Sterpone
- Laboratoire de Biochimie Théorique, IBPC, CNRS UPR9080, Univ. Paris Diderot, Sorbonne Paris Cité, 13 rue Pierre et Marie Curie, 75005, Paris, France
| | - Philippe Derreumaux
- Laboratoire de Biochimie Théorique, IBPC, CNRS UPR9080, Univ. Paris Diderot, Sorbonne Paris Cité, 13 rue Pierre et Marie Curie, 75005, Paris, France
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15
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Shin J, Cherstvy AG, Metzler R. Kinetics of polymer looping with macromolecular crowding: effects of volume fraction and crowder size. SOFT MATTER 2015; 11:472-88. [PMID: 25413029 DOI: 10.1039/c4sm02007c] [Citation(s) in RCA: 70] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
The looping of polymers such as DNA is a fundamental process in the molecular biology of living cells, whose interior is characterised by a high degree of molecular crowding. We here investigate in detail the looping dynamics of flexible polymer chains in the presence of different degrees of crowding. From the analysis of the looping-unlooping rates and the looping probabilities of the chain ends we show that the presence of small crowders typically slows down the chain dynamics but larger crowders may in fact facilitate the looping. We rationalise these non-trivial and often counterintuitive effects of the crowder size on the looping kinetics in terms of an effective solution viscosity and standard excluded volume. It is shown that for small crowders the effect of an increased viscosity dominates, while for big crowders we argue that confinement effects (caging) prevail. The tradeoff between both trends can thus result in the impediment or facilitation of polymer looping, depending on the crowder size. We also examine how the crowding volume fraction, chain length, and the attraction strength of the contact groups of the polymer chain affect the looping kinetics and hairpin formation dynamics. Our results are relevant for DNA looping in the absence and presence of protein mediation, DNA hairpin formation, RNA folding, and the folding of polypeptide chains under biologically relevant high-crowding conditions.
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Affiliation(s)
- Jaeoh Shin
- Institute for Physics & Astronomy, University of Potsdam, D-14476 Potsdam-Golm, Germany.
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Hasnain S, McClendon CL, Hsu MT, Jacobson MP, Bandyopadhyay P. A new coarse-grained model for E. coli cytoplasm: accurate calculation of the diffusion coefficient of proteins and observation of anomalous diffusion. PLoS One 2014; 9:e106466. [PMID: 25180859 PMCID: PMC4152264 DOI: 10.1371/journal.pone.0106466] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2014] [Accepted: 07/30/2014] [Indexed: 01/07/2023] Open
Abstract
A new coarse-grained model of the E. coli cytoplasm is developed by describing the proteins of the cytoplasm as flexible units consisting of one or more spheres that follow Brownian dynamics (BD), with hydrodynamic interactions (HI) accounted for by a mean-field approach. Extensive BD simulations were performed to calculate the diffusion coefficients of three different proteins in the cellular environment. The results are in close agreement with experimental or previously simulated values, where available. Control simulations without HI showed that use of HI is essential to obtain accurate diffusion coefficients. Anomalous diffusion inside the crowded cellular medium was investigated with Fractional Brownian motion analysis, and found to be present in this model. By running a series of control simulations in which various forces were removed systematically, it was found that repulsive interactions (volume exclusion) are the main cause for anomalous diffusion, with a secondary contribution from HI.
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Affiliation(s)
- Sabeeha Hasnain
- School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi, India
| | - Christopher L. McClendon
- Skaggs School of Pharmacy and Pharmaceutical Sciences, University of California San Diego, San Diego, California, United States of America
| | - Monica T. Hsu
- Graduate Group in Biophysics, University of California San Francisco, San Francisco, California, United States of America
| | - Matthew P. Jacobson
- Department of Pharmaceutical Chemistry, University of California San Francisco, San Francisco, California, United States of America
| | - Pradipta Bandyopadhyay
- School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi, India
- * E-mail:
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17
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Gruebele M, Thirumalai D. Perspective: Reaches of chemical physics in biology. J Chem Phys 2013; 139:121701. [PMID: 24089712 PMCID: PMC5942441 DOI: 10.1063/1.4820139] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2013] [Accepted: 08/20/2013] [Indexed: 01/09/2023] Open
Abstract
Chemical physics as a discipline contributes many experimental tools, algorithms, and fundamental theoretical models that can be applied to biological problems. This is especially true now as the molecular level and the systems level descriptions begin to connect, and multi-scale approaches are being developed to solve cutting edge problems in biology. In some cases, the concepts and tools got their start in non-biological fields, and migrated over, such as the idea of glassy landscapes, fluorescence spectroscopy, or master equation approaches. In other cases, the tools were specifically developed with biological physics applications in mind, such as modeling of single molecule trajectories or super-resolution laser techniques. In this introduction to the special topic section on chemical physics of biological systems, we consider a wide range of contributions, all the way from the molecular level, to molecular assemblies, chemical physics of the cell, and finally systems-level approaches, based on the contributions to this special issue. Chemical physicists can look forward to an exciting future where computational tools, analytical models, and new instrumentation will push the boundaries of biological inquiry.
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Affiliation(s)
- Martin Gruebele
- Departments of Chemistry and Physics, and Center for Biophysics and Computational Biology, University of Illinois, Urbana, Illinois 61801, USA
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