1
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Timr S, Melchionna S, Derreumaux P, Sterpone F. Optimized OPEP Force Field for Simulation of Crowded Protein Solutions. J Phys Chem B 2023; 127:3616-3623. [PMID: 37071827 PMCID: PMC10150358 DOI: 10.1021/acs.jpcb.3c00253] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/20/2023]
Abstract
Macromolecular crowding has profound effects on the mobility of proteins, with strong implications on the rates of intracellular processes. To describe the dynamics of crowded environments, detailed molecular models are needed, capturing the structures and interactions arising in the crowded system. In this work, we present OPEPv7, which is a coarse-grained force field at amino-acid resolution, suited for rigid-body simulations of the structure and dynamics of crowded solutions formed by globular proteins. Using the OPEP protein model as a starting point, we have refined the intermolecular interactions to match the experimentally observed dynamical slowdown caused by crowding. The resulting force field successfully reproduces the diffusion slowdown in homogeneous and heterogeneous protein solutions at different crowding conditions. Coupled with the lattice Boltzmann technique, it allows the study of dynamical phenomena in protein assemblies and opens the way for the in silico rheology of protein solutions.
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Affiliation(s)
- Stepan Timr
- Laboratoire de Biochimie Théorique (UPR 9080), CNRS, Université de Paris, 13 rue Pierre et Marie Curie, Paris, 75005, France
- Institut de Biologie Physico-Chimique, Fondation Edmond de Rothschild, PSL Research University, 13 rue Pierre et Marie Curie, Paris, 75005, France
- J. Heyrovský Institute of Physical Chemistry, Czech Academy of Sciences, Dolejškova 3, Prague 8, 18223, Czech Republic
| | - Simone Melchionna
- IAC-CNR, Via dei Taurini 19, 00185, Rome, Italy
- Lexma Technology 1337 Massachusetts Avenue, Arlington, Massachusetts 02476, United States
| | - Philippe Derreumaux
- Laboratoire de Biochimie Théorique (UPR 9080), CNRS, Université de Paris, 13 rue Pierre et Marie Curie, Paris, 75005, France
- Institut de Biologie Physico-Chimique, Fondation Edmond de Rothschild, PSL Research University, 13 rue Pierre et Marie Curie, Paris, 75005, France
- Institut Universitaire de France, 75005 Paris, France
| | - Fabio Sterpone
- Laboratoire de Biochimie Théorique (UPR 9080), CNRS, Université de Paris, 13 rue Pierre et Marie Curie, Paris, 75005, France
- Institut de Biologie Physico-Chimique, Fondation Edmond de Rothschild, PSL Research University, 13 rue Pierre et Marie Curie, Paris, 75005, France
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2
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Bulthuis EP, Dieteren CEJ, Bergmans J, Berkhout J, Wagenaars JA, van de Westerlo EMA, Podhumljak E, Hink MA, Hesp LFB, Rosa HS, Malik AN, Lindert MKT, Willems PHGM, Gardeniers HJGE, den Otter WK, Adjobo-Hermans MJW, Koopman WJH. Stress-dependent macromolecular crowding in the mitochondrial matrix. EMBO J 2023; 42:e108533. [PMID: 36825437 PMCID: PMC10068333 DOI: 10.15252/embj.2021108533] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2021] [Revised: 01/10/2023] [Accepted: 01/19/2023] [Indexed: 02/25/2023] Open
Abstract
Macromolecules of various sizes induce crowding of the cellular environment. This crowding impacts on biochemical reactions by increasing solvent viscosity, decreasing the water-accessible volume and altering protein shape, function, and interactions. Although mitochondria represent highly protein-rich organelles, most of these proteins are somehow immobilized. Therefore, whether the mitochondrial matrix solvent exhibits macromolecular crowding is still unclear. Here, we demonstrate that fluorescent protein fusion peptides (AcGFP1 concatemers) in the mitochondrial matrix of HeLa cells display an elongated molecular structure and that their diffusion constant decreases with increasing molecular weight in a manner typical of macromolecular crowding. Chloramphenicol (CAP) treatment impaired mitochondrial function and reduced the number of cristae without triggering mitochondrial orthodox-to-condensed transition or a mitochondrial unfolded protein response. CAP-treated cells displayed progressive concatemer immobilization with increasing molecular weight and an eightfold matrix viscosity increase, compatible with increased macromolecular crowding. These results establish that the matrix solvent exhibits macromolecular crowding in functional and dysfunctional mitochondria. Therefore, changes in matrix crowding likely affect matrix biochemical reactions in a manner depending on the molecular weight of the involved crowders and reactants.
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Affiliation(s)
- Elianne P Bulthuis
- Department of Biochemistry, Radboud Institute for Molecular Life Sciences (RIMLS), Radboud Center for Mitochondrial Medicine (RCMM), Radboud University Medical Centre (Radboudumc), Nijmegen, The Netherlands
| | - Cindy E J Dieteren
- Department of Biochemistry, Radboud Institute for Molecular Life Sciences (RIMLS), Radboud Center for Mitochondrial Medicine (RCMM), Radboud University Medical Centre (Radboudumc), Nijmegen, The Netherlands.,Department of Cell Biology and Electron Microscopy Center, Radboudumc, Nijmegen, The Netherlands
| | - Jesper Bergmans
- Department of Pediatrics, Amalia Children's Hospital, Radboud Institute for Molecular Life Sciences (RIMLS), Radboud Center for Mitochondrial Medicine (RCMM), Radboud University Medical Center (Radboudumc), Nijmegen, The Netherlands
| | - Job Berkhout
- Department of Biochemistry, Radboud Institute for Molecular Life Sciences (RIMLS), Radboud Center for Mitochondrial Medicine (RCMM), Radboud University Medical Centre (Radboudumc), Nijmegen, The Netherlands
| | - Jori A Wagenaars
- Department of Biochemistry, Radboud Institute for Molecular Life Sciences (RIMLS), Radboud Center for Mitochondrial Medicine (RCMM), Radboud University Medical Centre (Radboudumc), Nijmegen, The Netherlands
| | - Els M A van de Westerlo
- Department of Biochemistry, Radboud Institute for Molecular Life Sciences (RIMLS), Radboud Center for Mitochondrial Medicine (RCMM), Radboud University Medical Centre (Radboudumc), Nijmegen, The Netherlands
| | - Emina Podhumljak
- Department of Biochemistry, Radboud Institute for Molecular Life Sciences (RIMLS), Radboud Center for Mitochondrial Medicine (RCMM), Radboud University Medical Centre (Radboudumc), Nijmegen, The Netherlands
| | - Mark A Hink
- Swammerdam Institute for Life Sciences, University of Amsterdam, Amsterdam, The Netherlands
| | - Laura F B Hesp
- Department of Biochemistry, Radboud Institute for Molecular Life Sciences (RIMLS), Radboud Center for Mitochondrial Medicine (RCMM), Radboud University Medical Centre (Radboudumc), Nijmegen, The Netherlands
| | - Hannah S Rosa
- Department of Diabetes, King's College London, London, UK
| | - Afshan N Malik
- Department of Diabetes, King's College London, London, UK
| | - Mariska Kea-Te Lindert
- Department of Cell Biology and Electron Microscopy Center, Radboudumc, Nijmegen, The Netherlands
| | - Peter H G M Willems
- Department of Biochemistry, Radboud Institute for Molecular Life Sciences (RIMLS), Radboud Center for Mitochondrial Medicine (RCMM), Radboud University Medical Centre (Radboudumc), Nijmegen, The Netherlands
| | - Han J G E Gardeniers
- Mesoscale Chemical Systems, University of Twente, Enschede, The Netherlands.,MESA+ Institute for Nanotechnology, University of Twente, Enschede, The Netherlands
| | - Wouter K den Otter
- MESA+ Institute for Nanotechnology, University of Twente, Enschede, The Netherlands.,Thermal and Fluid Engineering, Faculty of Engineering Technology, University of Twente, Enschede, The Netherlands
| | - Merel J W Adjobo-Hermans
- Department of Biochemistry, Radboud Institute for Molecular Life Sciences (RIMLS), Radboud Center for Mitochondrial Medicine (RCMM), Radboud University Medical Centre (Radboudumc), Nijmegen, The Netherlands
| | - Werner J H Koopman
- Department of Pediatrics, Amalia Children's Hospital, Radboud Institute for Molecular Life Sciences (RIMLS), Radboud Center for Mitochondrial Medicine (RCMM), Radboud University Medical Center (Radboudumc), Nijmegen, The Netherlands.,Human and Animal Physiology, Wageningen University, Wageningen, The Netherlands
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3
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Chun BJ, Aryal SP, Varughese P, Sun B, Bruno JA, Richards CI, Bachstetter AD, Kekenes-Huskey PM. Purinoreceptors and ectonucleotidases control ATP-induced calcium waveforms and calcium-dependent responses in microglia: Roles of P2 receptors and CD39 in ATP-stimulated microglia. Front Physiol 2023; 13:1037417. [PMID: 36699679 PMCID: PMC9868579 DOI: 10.3389/fphys.2022.1037417] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2022] [Accepted: 12/12/2022] [Indexed: 01/11/2023] Open
Abstract
Adenosine triphosphate (ATP) and its metabolites drive microglia migration and cytokine production by activating P2X- and P2Y- class purinergic receptors. Purinergic receptor activation gives rise to diverse intracellular calcium (Ca2+ signals, or waveforms, that differ in amplitude, duration, and frequency. Whether and how these characteristics of diverse waveforms influence microglia function is not well-established. We developed a computational model trained with data from published primary murine microglia studies. We simulate how purinoreceptors influence Ca2+ signaling and migration, as well as, how purinoreceptor expression modifies these processes. Our simulation confirmed that P2 receptors encode the amplitude and duration of the ATP-induced Ca2+ waveforms. Our simulations also implicate CD39, an ectonucleotidase that rapidly degrades ATP, as a regulator of purinergic receptor-induced Ca2+ responses. Namely, it was necessary to account for CD39 metabolism of ATP to align the model's predicted purinoreceptor responses with published experimental data. In addition, our modeling results indicate that small Ca2+ transients accompany migration, while large and sustained transients are needed for cytokine responses. Lastly, as a proof-of-principal, we predict Ca2+ transients and cell membrane displacements in a BV2 microglia cell line using published P2 receptor mRNA data to illustrate how our computer model may be extrapolated to other microglia subtypes. These findings provide important insights into how differences in purinergic receptor expression influence microglial responses to ATP.
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Affiliation(s)
- Byeong J. Chun
- Department of Cell and Molecular Physiology, Loyola University Chicago, Chicago, IL, United States,*Correspondence: Byeong J. Chun, ; Peter M. Kekenes-Huskey,
| | - Surya P. Aryal
- Department of Chemistry, University of Kentucky, Lexington, KY, United States
| | - Peter Varughese
- Department of Cell and Molecular Physiology, Loyola University Chicago, Chicago, IL, United States
| | - Bin Sun
- Department of Cell and Molecular Physiology, Loyola University Chicago, Chicago, IL, United States
| | - Joshua A. Bruno
- Department of Physics, Loyola University Chicago, Chicago, IL, United States
| | - Chris I. Richards
- Department of Chemistry, University of Kentucky, Lexington, KY, United States
| | | | - Peter M. Kekenes-Huskey
- Department of Cell and Molecular Physiology, Loyola University Chicago, Chicago, IL, United States,*Correspondence: Byeong J. Chun, ; Peter M. Kekenes-Huskey,
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4
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Dey D, Nunes-Alves A, Wade RC, Schreiber G. Diffusion of small molecule drugs is affected by surface interactions and crowder proteins. iScience 2022; 25:105088. [PMID: 36157590 PMCID: PMC9490042 DOI: 10.1016/j.isci.2022.105088] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2022] [Revised: 08/04/2022] [Accepted: 08/31/2022] [Indexed: 11/30/2022] Open
Abstract
Crowded environments are known to affect the diffusion of macromolecules, but their effects on the diffusion of small molecules are largely uncharacterized. We investigate how three protein crowders, bovine serum albumin (BSA), hen egg-white lysozyme, and myoglobin, influence the diffusion rates and interactions of four small molecules: fluorescein, and three drugs, doxorubicin, glycogen synthase kinase-3 inhibitor SB216763, and quinacrine. Using Line-FRAP measurements, Brownian dynamics simulations, and molecular docking, we find that the diffusion rates of the small molecules are highly affected by self-aggregation, interactions with the proteins, and surface adsorption. The diffusion of fluorescein is decreased because of its interactions with the protein crowders and their surface adsorption. Protein crowders increase the diffusion rates of doxorubicin and SB216763 by reducing surface interactions and self-aggregation, respectively. Quinacrine diffusion was not affected by protein crowders. The mechanistic insights gained here may assist in optimization of compounds for higher mobility in complex macromolecular environments.
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Affiliation(s)
- Debabrata Dey
- Department of Biomolecular Sciences, Weizmann Institute of Science, Israel
| | - Ariane Nunes-Alves
- Molecular and Cellular Modeling Group, Heidelberg Institute for Theoretical Studies, Schloss-Wolfsbrunnenweg 35, 69118 Heidelberg, Germany.,Center for Molecular Biology (ZMBH), DKFZ-ZMBH Alliance, Heidelberg University, Im Neuenheimer Feld 282, 69120 Heidelberg, Germany
| | - Rebecca C Wade
- Molecular and Cellular Modeling Group, Heidelberg Institute for Theoretical Studies, Schloss-Wolfsbrunnenweg 35, 69118 Heidelberg, Germany.,Center for Molecular Biology (ZMBH), DKFZ-ZMBH Alliance, Heidelberg University, Im Neuenheimer Feld 282, 69120 Heidelberg, Germany.,Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Im Neuenheimer Feld 205, Heidelberg, Germany
| | - Gideon Schreiber
- Department of Biomolecular Sciences, Weizmann Institute of Science, Israel
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5
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Rahmaninejad H, Pace T, Chun BJ, Kekenes-Huskey PM. Crowding within synaptic junctions influences the degradation of nucleotides by CD39 and CD73 ectonucleotidases. Biophys J 2022; 121:309-318. [PMID: 34922916 PMCID: PMC8790186 DOI: 10.1016/j.bpj.2021.12.013] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2021] [Revised: 11/01/2021] [Accepted: 12/07/2021] [Indexed: 01/21/2023] Open
Abstract
Synapsed cells can communicate using exocytosed nucleotides like adenosine triphosphate (ATP). Ectonucleotidases localized to synaptic junctions degrade nucleotides into metabolites like adenosine monophosphate (AMP) or adenosine. Oftentimes nucleotide degradation occurs in a sequential manner, of which ATP degradation by CD39 and CD73 is a representative example. Here, CD39 first converts ATP and adenosine diphosphate (ADP) into AMP, after which AMP is dephosphorylated into adenosine by CD73. Hence, the concerted activity of CD39 and CD73 can help shape cellular responses to extracellular ATP. In a previous study, we demonstrated that coupled CD39 and CD73 activity within synapse-like junctions is strongly controlled by the enzymes' co-localization, their surface charge densities, and the electrostatic potential of the surrounding cell membranes. In this study, we demonstrate that crowders within synaptic junctions, which can include globular proteins like cytokines and membrane-bound proteins, impact coupled CD39 and CD73 ectonucleotidase activity and, in turn, the availability of intrasynapse ATP. Specifically, we developed a spatially explicit, reaction-diffusion model for the coupled conversion of ATP → AMP and AMP → adenosine in a model synaptic junction with crowders that is solved via the finite element method. Our modeling results suggest that the association rate for ATP to CD39 is strongly influenced by the density of intrasynaptic protein crowders, as increasing crowder density generally suppressed ATP association kinetics. Much of this suppression can be rationalized based on a loss of configurational entropy. The surface charges of crowders can further influence the association rate, with the surprising result that favorable crowder-nucleotide electrostatic interactions can yield CD39 association rates that are faster than crowder-free configurations. However, attractive crowder-nucleotide interactions decrease the rate and efficiency of adenosine production, which in turn increases the availability of ATP and AMP within the synapse relative to crowder-free configurations. These findings highlight how CD39 and CD73 ectonucleotidase activity, electrostatics, and crowding within synapses influence the availability of nucleotides for intercellular communication.
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Affiliation(s)
- Hadi Rahmaninejad
- Department of Physics, Virginia Tech, Blacksburg,Corresponding author
| | - Tom Pace
- Department of Cell & Molecular Physiology, Loyola University Chicago, Chicago,Corresponding author
| | - Byeong Jae Chun
- Department of Cell & Molecular Physiology, Loyola University Chicago, Chicago
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6
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KhudaBukhsh WR, Kang HW, Kenah E, Rempała GA. Incorporating age and delay into models for biophysical systems. Phys Biol 2021; 18:015002. [PMID: 33075757 DOI: 10.1088/1478-3975/abc2ab] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
In many biological systems, chemical reactions or changes in a physical state are assumed to occur instantaneously. For describing the dynamics of those systems, Markov models that require exponentially distributed inter-event times have been used widely. However, some biophysical processes such as gene transcription and translation are known to have a significant gap between the initiation and the completion of the processes, which renders the usual assumption of exponential distribution untenable. In this paper, we consider relaxing this assumption by incorporating age-dependent random time delays (distributed according to a given probability distribution) into the system dynamics. We do so by constructing a measure-valued Markov process on a more abstract state space, which allows us to keep track of the 'ages' of molecules participating in a chemical reaction. We study the large-volume limit of such age-structured systems. We show that, when appropriately scaled, the stochastic system can be approximated by a system of partial differential equations (PDEs) in the large-volume limit, as opposed to ordinary differential equations (ODEs) in the classical theory. We show how the limiting PDE system can be used for the purpose of further model reductions and for devising efficient simulation algorithms. In order to describe the ideas, we use a simple transcription process as a running example. We, however, note that the methods developed in this paper apply to a wide class of biophysical systems.
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Affiliation(s)
- Wasiur R KhudaBukhsh
- Mathematical Biosciences Institute and the College of Public Health, The Ohio State University, 1735 Neil Avenue, Columbus OH 43210, United States of America
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7
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Rahmaninejad H, Pace T, Bhatt S, Sun B, Kekenes-Huskey P. Co-localization and confinement of ecto-nucleotidases modulate extracellular adenosine nucleotide distributions. PLoS Comput Biol 2020; 16:e1007903. [PMID: 32584811 PMCID: PMC7316229 DOI: 10.1371/journal.pcbi.1007903] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2019] [Accepted: 04/22/2020] [Indexed: 12/30/2022] Open
Abstract
Nucleotides comprise small molecules that perform critical signaling roles in biological systems. Adenosine-based nucleotides, including adenosine tri-, di-, and mono-phosphate, are controlled through their rapid degradation by diphosphohydrolases and ecto-nucleotidases (NDAs). The interplay between nucleotide signaling and degradation is especially important in synapses formed between cells, which create signaling 'nanodomains'. Within these 'nanodomains', charged nucleotides interact with densely-packed membranes and biomolecules. While the contributions of electrostatic and steric interactions within such nanodomains are known to shape diffusion-limited reaction rates, less is understood about how these factors control the kinetics of nucleotidase activity. To quantify these factors, we utilized reaction-diffusion numerical simulations of 1) adenosine triphosphate (ATP) hydrolysis into adenosine monophosphate (AMP) and 2) AMP into adenosine (Ado) via two representative nucleotidases, CD39 and CD73. We evaluate these sequentially-coupled reactions in nanodomain geometries representative of extracellular synapses, within which we localize the nucleotidases. With this model, we find that 1) nucleotidase confinement reduces reaction rates relative to an open (bulk) system, 2) the rates of AMP and ADO formation are accelerated by restricting the diffusion of substrates away from the enzymes, and 3) nucleotidase co-localization and the presence of complementary (positive) charges to ATP enhance reaction rates, though the impact of these contributions on nucleotide pools depends on the degree to which the membrane competes for substrates. As a result, these contributions integratively control the relative concentrations and distributions of ATP and its metabolites within the junctional space. Altogether, our studies suggest that CD39 and CD73 nucleotidase activity within junctional spaces can exploit their confinement and favorable electrostatic interactions to finely control nucleotide signaling.
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Affiliation(s)
- Hadi Rahmaninejad
- Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky, United States of America
| | - Tom Pace
- Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky, United States of America
| | - Shashank Bhatt
- Paul Laurence Dunbar High School, Lexington, Kentucky, United States of America
| | - Bin Sun
- Department of Chemistry, University of Kentucky, Lexington, Kentucky, United States of America
| | - Peter Kekenes-Huskey
- Department of Cell & Molecular Physiology, Loyola University Chicago, Chicago, Illinois, United States of America
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8
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von Bülow S, Siggel M, Linke M, Hummer G. Dynamic cluster formation determines viscosity and diffusion in dense protein solutions. Proc Natl Acad Sci U S A 2019; 116:9843-9852. [PMID: 31036655 PMCID: PMC6525548 DOI: 10.1073/pnas.1817564116] [Citation(s) in RCA: 107] [Impact Index Per Article: 21.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Abstract
We develop a detailed description of protein translational and rotational diffusion in concentrated solution on the basis of all-atom molecular dynamics simulations in explicit solvent. Our systems contain up to 540 fully flexible proteins with 3.6 million atoms. In concentrated protein solutions (100 mg/mL and higher), the proteins ubiquitin and lysozyme, as well as the protein domains third IgG-binding domain of protein G and villin headpiece, diffuse not as isolated particles, but as members of transient clusters between which they constantly exchange. A dynamic cluster model nearly quantitatively explains the increase in viscosity and the decrease in protein diffusivity with protein volume fraction, which both exceed the predictions from widely used colloid models. The Stokes-Einstein relations for translational and rotational diffusion remain valid, but the effective hydrodynamic radius grows linearly with protein volume fraction. This increase follows the observed increase in cluster size and explains the more dramatic slowdown of protein rotation compared with translation. Baxter's sticky-sphere model of colloidal suspensions captures the concentration dependence of cluster size, viscosity, and rotational and translational diffusion. The consistency between simulations and experiments for a diverse set of soluble globular proteins indicates that the cluster model applies broadly to concentrated protein solutions, with equilibrium dissociation constants for nonspecific protein-protein binding in the Kd ≈ 10-mM regime.
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Affiliation(s)
- Sören von Bülow
- Department of Theoretical Biophysics, Max Planck Institute of Biophysics, 60438 Frankfurt am Main, Germany
| | - Marc Siggel
- Department of Theoretical Biophysics, Max Planck Institute of Biophysics, 60438 Frankfurt am Main, Germany
| | - Max Linke
- Department of Theoretical Biophysics, Max Planck Institute of Biophysics, 60438 Frankfurt am Main, Germany
| | - Gerhard Hummer
- Department of Theoretical Biophysics, Max Planck Institute of Biophysics, 60438 Frankfurt am Main, Germany;
- Department of Physics, Goethe University Frankfurt, 60438 Frankfurt am Main, Germany
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9
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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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10
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Kekenes-Huskey PM, Scott CE, Atalay S. Quantifying the Influence of the Crowded Cytoplasm on Small Molecule Diffusion. J Phys Chem B 2016; 120:8696-706. [PMID: 27327486 DOI: 10.1021/acs.jpcb.6b03887] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Cytosolic crowding can influence the thermodynamics and kinetics of in vivo chemical reactions. Most significantly, proteins and nucleic acid crowders reduce the accessible volume fraction, ϕ, available to a diffusing substrate, thereby reducing its effective diffusion rate, Deff, relative to its rate in bulk solution. However, Deff can be further hindered or even enhanced, when long-range crowder/diffuser interactions are significant. To probe these effects, we numerically estimated Deff values for small, charged molecules in representative, cytosolic protein lattices up to 0.1 × 0.1 × 0.1 μm(3) in volume via the homogenized Smoluchowski electro-diffusion equation. We further validated our predictions against Deff estimates from ϕ-dependent analytical relationships, such as the Maxwell-Garnett (MG) bound, as well as explicit solutions of the time-dependent electro-diffusion equation. We find that in typical, moderately crowded cell cytoplasm (ϕ ≈ 0.8), Deff is primarily determined by ϕ; in other words, diverse protein shapes and heterogeneous distributions only modestly impact Deff. However, electrostatic interactions between diffusers and crowders, particularly at low electrolyte ionic strengths, can substantially modulate Deff. These findings help delineate the extent that cytoplasmic crowders influence small molecule diffusion, which ultimately may shape the efficiency and timing of intracellular signaling pathways. More generally, the quantitative agreement between computationally expensive solutions of the time-dependent electro-diffusion equation and its comparatively cheaper homogenized form suggest that the latter is a broadly effective model for diffusion in wide-ranging, crowded biological media.
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Affiliation(s)
- Peter M Kekenes-Huskey
- Department of Chemistry, University of Kentucky , Lexington, Kentucky 40506, United States
| | - Caitlin E Scott
- Department of Chemistry, University of Kentucky , Lexington, Kentucky 40506, United States
| | - Selcuk Atalay
- Department of Chemistry, University of Kentucky , Lexington, Kentucky 40506, United States
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11
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Signon L, Nowakowski B, Lemarchand A. Modeling somite scaling in small embryos in the framework of Turing patterns. Phys Rev E 2016; 93:042402. [PMID: 27176324 DOI: 10.1103/physreve.93.042402] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2015] [Indexed: 11/07/2022]
Abstract
The adaptation of prevertebra size to embryo size is investigated in the framework of a reaction-diffusion model involving a Turing pattern. The reaction scheme and Fick's first law of diffusion are modified in order to take into account the departure from dilute conditions induced by confinement in smaller embryos. In agreement with the experimental observations of scaling in somitogenesis, our model predicts the formation of smaller prevertebrae or somites in smaller embryos. These results suggest that models based on Turing patterns cannot be automatically disregarded by invoking the question of maintaining proportions in embryonic development. Our approach highlights the nontrivial role that the solvent can play in biology.
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Affiliation(s)
- Laurence Signon
- Institut de Génétique et Microbiologie, Université Paris-Sud, CNRS UMR No. 8621, 15 Rue Georges Clémenceau, 91405 Orsay Cedex, France
| | - Bogdan Nowakowski
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland.,SGGW, Warsaw University of Life Sciences, Nowoursynowska 159, 02-776 Warsaw, Poland
| | - Annie Lemarchand
- Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie, Sorbonne Universités, CNRS UMR No. 7600, 4 Place Jussieu, Case Courrier 121, 75252 Paris Cedex 05, France
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