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Attar AG, Paturej J, Banigan EJ, Erbaş A. Chromatin phase separation and nuclear shape fluctuations are correlated in a polymer model of the nucleus. Nucleus 2024; 15:2351957. [PMID: 38753956 DOI: 10.1080/19491034.2024.2351957] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2024] [Accepted: 04/28/2024] [Indexed: 05/18/2024] Open
Abstract
Abnormal cell nuclear shapes are hallmarks of diseases, including progeria, muscular dystrophy, and many cancers. Experiments have shown that disruption of heterochromatin and increases in euchromatin lead to nuclear deformations, such as blebs and ruptures. However, the physical mechanisms through which chromatin governs nuclear shape are poorly understood. To investigate how heterochromatin and euchromatin might govern nuclear morphology, we studied chromatin microphase separation in a composite coarse-grained polymer and elastic shell simulation model. By varying chromatin density, heterochromatin composition, and heterochromatin-lamina interactions, we show how the chromatin phase organization may perturb nuclear shape. Increasing chromatin density stabilizes the lamina against large fluctuations. However, increasing heterochromatin levels or heterochromatin-lamina interactions enhances nuclear shape fluctuations by a "wetting"-like interaction. In contrast, fluctuations are insensitive to heterochromatin's internal structure. Our simulations suggest that peripheral heterochromatin accumulation could perturb nuclear morphology, while nuclear shape stabilization likely occurs through mechanisms other than chromatin microphase organization.
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Affiliation(s)
- Ali Goktug Attar
- UNAM-National Nanotechnology Research Center and Institute of Materials Science & Nanotechnology, Bilkent University, Ankara, Turkey
| | | | - Edward J Banigan
- Institute for Medical Engineering and Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Aykut Erbaş
- UNAM-National Nanotechnology Research Center and Institute of Materials Science & Nanotechnology, Bilkent University, Ankara, Turkey
- Institute of Physics, University of Silesia, Chorzów, Poland
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2
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Rafique M, Erbaş A. Mechanical deformation affects the counterion condensation in highly-swollen polyelectrolyte hydrogels. Soft Matter 2023; 19:7550-7561. [PMID: 37750366 DOI: 10.1039/d3sm00585b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/27/2023]
Abstract
Polyelectrolyte gels can generate electric potentials under mechanical deformation. While the underlying mechanism of such a response is often attributed to changes in counterion-condensation levels or alterations in the ionic conditions in the pervaded volume of the hydrogel, the exact molecular origins are largely unknown. By using all-atom molecular dynamics simulations of a polyacrylic acid hydrogel in explicit water as a model system, we simulate the uniaxial compression and uniaxial stretching of weakly to highly swollen (i.e., between 60-90% solvent content) hydrogel networks and calculate the microscopic condensation levels of counterions around the hydrogel chains. The counterion condensation under deformation is highly non-monotonic. Ionic condensation around the constituting chains of the deformed hydrogel tends to increase as the chains are stretched. This increase reaches a maximum and decreases as the chains are strongly stretched. The condensation around the collapsed chains of the hydrogel is weakly affected by the deformation. As a result, both compressing and stretching the model hydrogel lead to an overall increase in the counterion condensation. The effect vanishes for weakly swollen hydrogels, for which most ions are already condensed. The simulations with single, stretched polyelectrolyte chains show a qualitatively similar response, suggesting the effect of chain elongation on the ionic distribution throughout the hydrogel. Notably, this deformation-induced counterion condensation phenomenon does not occur in a polyelectrolyte solution at its critical concentration, indicating the role of hydrogel topology constraining the chain ends. Our results indicate that counterion condensation in a deforming polyelectrolyte hydrogel can be highly heterogeneous and exhibit a rich behaviour of electrostatic responses.
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Affiliation(s)
- Muzaffar Rafique
- UNAM-Institute of Materials Science and Nanotechnology, Bilkent University, Ankara 06800, Turkey.
| | - Aykut Erbaş
- UNAM-Institute of Materials Science and Nanotechnology, Bilkent University, Ankara 06800, Turkey.
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3
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Özkan AU, Tuncel D, Erbaş A. Effect of Charge State on the Equilibrium and Kinetic Properties of Mechanically Interlocked [5]Rotaxane: A Molecular Dynamics Study. J Phys Chem B 2023; 127:1254-1263. [PMID: 36716388 PMCID: PMC9923746 DOI: 10.1021/acs.jpcb.2c07645] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
Rotaxanes can exhibit stimuli-responsive behavior by allowing positional fluctuations of their rota groups in response to physiochemical conditions such as the changes in solution pH. However, ionic strength of the solution also affects the molecular conformation by altering the charge state of the entire molecule, coupling the stimuli-responsiveness of rotaxanes with their conformation. A molecular-scale investigation on a model system can allow the decoupling and identification of various effects and can greatly benefit applications of such molecular switches. By using atomistic molecular dynamics simulations, we study equilibrium and kinetics properties of various charge states of the [5]rotaxane, which is a supramolecular moiety with four rotaxanes bonded to a porphyrin core. We model various physiochemical charge states, each of which can be realized at various solution pH levels as well as several exotic charge distributions. By analyzing molecular configurations, hydrogen bonding, and energetics of single molecules in salt-free water and its polyrotaxanated network at the interface of water and chloroform, we demonstrate that charge-neutral and negatively charged molecules often tend to collapse in a way that they can expose their porphyrin core. Contrarily, positively charged moieties tend to take more extended molecular configurations blocking the core. Further, sudden changes in the charge states emulating the pH alterations in solution conditions lead to rapid, sub-10 ns level, changes in the molecular conformation of [5]rotaxane via shuttling motion of CB6 rings along axles. Finally, simulations of 2D [5]rotaxane network structures support our previous findings on a few nanometer-thick film formation at oil-water interfaces. Overall, our results suggest that rotaxane-based structures can exhibit a rich spectrum of molecular configurations and kinetics depending on the ionic strength of the solution.
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Affiliation(s)
- Ata Utku Özkan
- UNAM-Institute
of Materials Science and Nanotechnology, Bilkent University, Ankara06800, Turkey
| | - Dönüş Tuncel
- UNAM-Institute
of Materials Science and Nanotechnology, Bilkent University, Ankara06800, Turkey,Department
of Chemistry, Bilkent University, Ankara06800, Turkey
| | - Aykut Erbaş
- UNAM-Institute
of Materials Science and Nanotechnology, Bilkent University, Ankara06800, Turkey,E-mail:
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Erbaş A, Inci F. The Role of Ligand Rebinding and Facilitated Dissociation on the Characterization of Dissociation Rates by Surface Plasmon Resonance (SPR) and Benchmarking Performance Metrics. Methods Mol Biol 2022; 2385:237-253. [PMID: 34888723 DOI: 10.1007/978-1-0716-1767-0_11] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Surface plasmon resonance (SPR) is a real-time kinetic measurement principle that can probe the kinetic interactions between ligands and their binding sites, and lies at the backbone of pharmaceutical, biosensing, and biomolecular research. The extraction of dissociation rates from SPR-response signals often relies on several commonly adopted assumptions, one of which is the exponential decay of the dissociation part of the response signal. However, certain conditions, such as high density of binding sites or high concentration fluctuations near the surface as compared to the bulk, can lead to non-exponential decays via ligand rebinding or facilitated dissociation. Consequently, fitting the data with an exponential function can underestimate or overestimate the measured dissociation rates. Here, we describe a set of alternative fit functions that can take such effects into consideration along with plasmonic sensor design principles with key performance metrics, thereby suggesting methods for error-free high-precision extraction of the dissociation rates.
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Affiliation(s)
- Aykut Erbaş
- UNAM-National Nanotechnology Research Center and Institute of Materials Science Nanotechnology, Bilkent University, Ankara, Turkey.
| | - Fatih Inci
- UNAM-National Nanotechnology Research Center and Institute of Materials Science Nanotechnology, Bilkent University, Ankara, Turkey.
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Erbaş A, Marko JF. How do DNA-bound proteins leave their binding sites? The role of facilitated dissociation. Curr Opin Chem Biol 2019; 53:118-124. [PMID: 31586479 PMCID: PMC6926143 DOI: 10.1016/j.cbpa.2019.08.007] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2019] [Revised: 07/11/2019] [Accepted: 08/24/2019] [Indexed: 10/25/2022]
Abstract
Dissociation of a protein from DNA is often assumed to be described by an off rate that is independent of other molecules in solution. Recent experiments and computational analyses have challenged this view by showing that unbinding rates (residence times) of DNA-bound proteins can depend on concentrations of nearby molecules that are competing for binding. This 'facilitated dissociation' (FD) process can occur at the single-binding site level via formation of a ternary complex, and can dominate over 'spontaneous dissociation' at low (submicromolar) concentrations. In the crowded intracellular environment FD introduces new regulatory possibilities at the level of individual biomolecule interactions.
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Affiliation(s)
- Aykut Erbaş
- UNAM-National Nanotechnology Research Center and Institute of Materials Science & Nanotechnology, Bilkent University, Ankara 06800, Turkey
| | - John F Marko
- Department of Molecular Biosciences, Northwestern University, Evanston, IL 60208, USA; Department of Physics & Astronomy, Northwestern University, Evanston, IL 60208, USA
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Erbaş A, Olvera de la Cruz M, Marko JF. Receptor-Ligand Rebinding Kinetics in Confinement. Biophys J 2019; 116:1609-1624. [PMID: 31029377 PMCID: PMC6506716 DOI: 10.1016/j.bpj.2019.02.033] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2018] [Revised: 02/05/2019] [Accepted: 02/19/2019] [Indexed: 10/27/2022] Open
Abstract
Rebinding kinetics of molecular ligands plays a key role in the operation of biomachinery, from regulatory networks to protein transcription, and is also a key factor in design of drugs and high-precision biosensors. In this study, we investigate initial release and rebinding of ligands to their binding sites grafted on a planar surface, a situation commonly observed in single-molecule experiments and that occurs in vivo, e.g., during exocytosis. Via scaling arguments and molecular dynamic simulations, we analyze the dependence of nonequilibrium rebinding kinetics on two intrinsic length scales: the average separation distance between the binding sites and the total diffusible volume (i.e., height of the experimental reservoir in which diffusion takes place or average distance between receptor-bearing surfaces). We obtain time-dependent scaling laws for on rates and for the cumulative number of rebinding events. For diffusion-limited binding, the (rebinding) on rate decreases with time via multiple power-law regimes before the terminal steady-state (constant on-rate) regime. At intermediate times, when particle density has not yet become uniform throughout the diffusible volume, the cumulative number of rebindings exhibits a novel, to our knowledge, plateau behavior because of the three-dimensional escape process of ligands from binding sites. The duration of the plateau regime depends on the average separation distance between binding sites. After the three-dimensional diffusive escape process, a one-dimensional diffusive regime describes on rates. In the reaction-limited scenario, ligands with higher affinity to their binding sites (e.g., longer residence times) delay entry to the power-law regimes. Our results will be useful for extracting hidden timescales in experiments such as kinetic rate measurements for ligand-receptor interactions in microchannels, as well as for cell signaling via diffusing molecules.
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Affiliation(s)
- Aykut Erbaş
- UNAM-National Nanotechnology Research Center and Institute of Materials Science & Nanotechnology, Bilkent University, Ankara, Turkey.
| | - Monica Olvera de la Cruz
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois; Department of Physics and Astronomy, Northwestern University, Evanston, Illinois; Department of Chemistry, Northwestern University, Evanston, Illinois
| | - John F Marko
- Department of Physics and Astronomy, Northwestern University, Evanston, Illinois; Department of Molecular Biosciences, Northwestern University, Evanston, Illinois.
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Abstract
We study unbinding of multivalent cationic ligands from oppositely charged polymeric binding sites sparsely grafted on a flat neutral substrate. Our molecular dynamics simulations are suggested by single-molecule studies of protein-DNA interactions. We consider univalent salt concentrations spanning roughly a 1000-fold range, together with various concentrations of excess ligands in solution. To reveal the ionic effects on unbinding kinetics of spontaneous and facilitated dissociation mechanisms, we treat electrostatic interactions both at a Debye-Hückel (DH) (or implicit ions, i.e., use of an electrostatic potential with a prescribed decay length) level and by the more precise approach of considering all ionic species explicitly in the simulations. We find that the DH approach systematically overestimates unbinding rates, relative to the calculations where all ion pairs are present explicitly in solution, although many aspects of the two types of calculation are qualitatively similar. For facilitated dissociation (FD) (acceleration of unbinding by free ligands in solution) explicit-ion simulations lead to unbinding at lower free-ligand concentrations. Our simulations predict a variety of FD regimes as a function of free-ligand and ion concentrations; a particularly interesting regime is at intermediate concentrations of ligands where nonelectrostatic binding strength controls FD. We conclude that explicit-ion electrostatic modeling is an essential component to quantitatively tackle problems in molecular ligand dissociation, including nucleic-acid-binding proteins.
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Affiliation(s)
- Aykut Erbaş
- Department of Materials Science and Engineering, Department of Molecular Biosciences, and Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
| | - Monica Olvera de la Cruz
- Department of Materials Science and Engineering, Department of Chemistry, Department of Chemical and Biological Engineering, and Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
| | - John F Marko
- Department of Molecular Biosciences and Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
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Affiliation(s)
- Aykut Erbaş
- Department
of Materials Science and Engineering and ‡Department of Chemistry, Department
of Chemical and Biological Engineering, and Department of Physics, Northwestern University, Evanston, Illinois 60208, United States
| | - Monica Olvera de la Cruz
- Department
of Materials Science and Engineering and ‡Department of Chemistry, Department
of Chemical and Biological Engineering, and Department of Physics, Northwestern University, Evanston, Illinois 60208, United States
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Affiliation(s)
| | | | - Jos Zwanikken
- Department
of Physics and Applied Physics, University of Massachusetts Lowell, Lowell, Massachusetts 01854, United States
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10
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Abstract
The size polarity and tail stiffness of amphiphilic ionic liquid molecules can be tailored to obtain 3D continuous ionic channels possessing isotropic conductivities.
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Affiliation(s)
- Aykut Erbaş
- Department of Materials Science and Engineering
- Northwestern University
- Evanston
- USA
| | - Monica Olvera de la Cruz
- Department of Materials Science and Engineering
- Northwestern University
- Evanston
- USA
- Department of Chemistry
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Abstract
Friction between ring polymer brush bilayers sliding past each other at melt densities is studied using extensive coarse-grained molecular dynamics simulations and scaling arguments, and the results are compared to the friction between bilayers of linear polymer brushes. We show that for a velocity range spanning over three decades, the frictional forces measured for ring polymer brushes are half of the corresponding friction in the case of linear brushes. In the linear-force regime, the weak inter-digitation between ring brush layers as compared to linear brushes leads also to a lower number of binary collisions between the monomers from opposing brushes. At high velocities, where the thickness of the inter-digitation between bilayers is on the order of monomer size regardless of brush topology, stretched segments of ring polymers adopt the double-stranded conformation. As a result, monomers of the double-stranded segments collide on average less with the monomers of the opposing ring brush even though a similar number of monomers occupies the inter-digitation layer for ring and linear brush bilayers. The numerical data obtained from our simulations are consistent with the proposed scaling analysis. Conformation-dependent friction reduction observed in ring brushes can have important consequences in non-equilibrium bulk systems.
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Affiliation(s)
- Aykut Erbaş
- Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60208, USA.
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12
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Abstract
Friction within globular proteins or between adhering macromolecules crucially determines the kinetics of protein folding, the formation, and the relaxation of self-assembled molecular systems. One fundamental question is how these friction effects depend on the local environment and in particular on the presence of water. In this model study, we use fully atomistic MD simulations with explicit water to obtain friction forces as a single polyglycine peptide chain is pulled out of a bundle of k adhering parallel polyglycine peptide chains. The whole system is periodically replicated along the peptide axes, so a stationary state at prescribed mean sliding velocity V is achieved. The aggregation number is varied between k = 2 (two peptide chains adhering to each other with plenty of water present at the adhesion sites) and k = 7 (one peptide chain pulled out from a close-packed cylindrical array of six neighboring peptide chains with no water inside the bundle). The friction coefficient per hydrogen bond, extrapolated to the viscous limit of vanishing pulling velocity V → 0, exhibits an increase by five orders of magnitude when going from k = 2 to k = 7. This dramatic confinement-induced friction enhancement we argue to be due to a combination of water depletion and increased hydrogen-bond cooperativity.
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Affiliation(s)
- Aykut Erbaş
- Free University of Berlin, Fachbereich Physik, Berlin, Germany.
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13
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Affiliation(s)
- Aykut Erbaş
- Physik Department, Technische Universität München, 85748
Garching, Germany,
- Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | - Dominik Horinek
- Institut
für Physikalische
und Theoretische Chemie, Universität Regensburg, 93040 Regensburg, Germany
| | - Roland R. Netz
- Physik Department, Technische Universität München, 85748
Garching, Germany,
- Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
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Erbaş A, Podgornik R, Netz RR. Viscous compressible hydrodynamics at planes, spheres and cylinders with finite surface slip. Eur Phys J E Soft Matter 2010; 32:147-164. [PMID: 20632199 DOI: 10.1140/epje/i2010-10610-7] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/27/2009] [Accepted: 06/02/2010] [Indexed: 05/29/2023]
Abstract
We consider the linearized time-dependent Navier-Stokes equation including finite compressibility and viscosity. We first constitute the Green's function, from which we derive the flow profiles and response functions for a plane, a sphere and a cylinder for arbitrary surface slip length. For high driving frequency the flow pattern is dominated by the diffusion of vorticity and compression, for low frequency compression propagates in the form of sound waves which are exponentially damped at a screening length larger than the sound wave length. The crossover between the diffusive and propagative compression regimes occurs at the fluid's intrinsic frequency omega approximately c2rho0/eta, with c the speed of sound, rho0 the fluid density and eta the viscosity. In the propagative regime the hydrodynamic response function of spheres and cylinders exhibits a high-frequency resonance when the particle size is of the order of the sound wave length. A distinct low-frequency resonance occurs at the boundary between the propagative and diffusive regimes. Those resonant features should be detectable experimentally by tracking the diffusion of particles, as well as by measuring the fluctuation spectrum or the response spectrum of trapped particles. Since the response function depends sensitively on the slip length, in principle the slip length can be deduced from an experimentally measured response function.
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Affiliation(s)
- A Erbaş
- Physics Department, Technical University Munich, Garching, Germany.
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Erbaş A, Tuncer A, Yücesoy B, Berker AN. Phase diagrams and crossover in spatially anisotropic d = 3 Ising, XY magnetic, and percolation systems: exact renormalization-group solutions of hierarchical models. Phys Rev E Stat Nonlin Soft Matter Phys 2005; 72:026129. [PMID: 16196666 DOI: 10.1103/physreve.72.026129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2005] [Indexed: 05/04/2023]
Abstract
Hierarchical lattices that constitute spatially anisotropic systems are introduced. These lattices provide exact solutions for hierarchical models and, simultaneously, approximate solutions for uniaxially or fully anisotropic d = 3 physical models. The global phase diagrams, with d = 2 and d = 1 to d = 3 crossovers, are obtained for Ising and XY magnetic models and percolation systems, including crossovers from algebraic order to true long-range order.
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Affiliation(s)
- Aykut Erbaş
- Department of Physics, Istanbul Technical University, Maslak 34469, Istanbul, Turkey
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