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Zheng X, Wang J. Universal statistical fluctuations in thermodynamics and kinetics of single molecular recognition. Phys Chem Chem Phys 2016; 18:8570-8. [PMID: 26947972 DOI: 10.1039/c5cp06416c] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We investigated the main universal statistical distributions of single molecular recognition. The distributions of the single molecule binding free energy spectrum or density of states were characterized in the ligand-receptor binding energy landscape. The analytical results are consistent with the microscopic molecular simulations. The free energy distribution of different binding modes or states for a single molecule ligand receptor pair is approximately Gaussian near the mean and exponential at the tail. The equilibrium constant of single molecule binding is log-normal distributed near the mean and power law distributed near the tail. Additionally, we found that the kinetics distribution of single molecule ligand binding can be characterized by log-normal around the mean and power law distribution near the tail. This distribution is caused by exploration of the underlying inhomogeneous free energy landscape. Different ligand-receptor binding complexes have the same universal form of distribution but differ in parameters.
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Affiliation(s)
- Xiliang Zheng
- State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, China
| | - Jin Wang
- State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, China and Department of Chemistry and Physics, State University of New York at Stony Brook, Stony Brook, NY 11794-3400, USA.
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Danielsson J, Meuwly M. Atomistic Simulation of Adiabatic Reactive Processes Based on Multi-State Potential Energy Surfaces. J Chem Theory Comput 2015; 4:1083-93. [PMID: 26636362 DOI: 10.1021/ct800066q] [Citation(s) in RCA: 64] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
The adiabatic reactive molecular dynamics (ARMD) method provides a framework to study chemical reactions using molecular dynamics simulations with minimal computational overhead. Here, ARMD is generalized to an arbitrary reactive process between two states in which reactants and products can be treated by an atomistic force field. The implementation is described, and the method is applied to two systems: the kinetics of NO rebinding to myoglobin (Mb) as a validation system and the conformational transition in neuroglobin (Ngb) which explores the full functionality of ARMD. For MbNO, the nonexponential kinetics observed both in experiment and earlier ARMD studies is reproduced. Furthermore, the sensitivity of the results with respect to the asymptotic separation between the two potential energy surfaces (NO bound and unbound) is studied.
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Affiliation(s)
- Jonas Danielsson
- Chemistry Department, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| | - Markus Meuwly
- Chemistry Department, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
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Fatmi MQ, Chang CEA. The role of oligomerization and cooperative regulation in protein function: the case of tryptophan synthase. PLoS Comput Biol 2010; 6:e1000994. [PMID: 21085641 PMCID: PMC2978696 DOI: 10.1371/journal.pcbi.1000994] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2010] [Accepted: 10/08/2010] [Indexed: 11/25/2022] Open
Abstract
The oligomerization/co-localization of protein complexes and their cooperative regulation in protein function is a key feature in many biological systems. The synergistic regulation in different subunits often enhances the functional properties of the multi-enzyme complex. The present study used molecular dynamics and Brownian dynamics simulations to study the effects of allostery, oligomerization and intermediate channeling on enhancing the protein function of tryptophan synthase (TRPS). TRPS uses a set of α/β–dimeric units to catalyze the last two steps of L-tryptophan biosynthesis, and the rate is remarkably slower in the isolated monomers. Our work shows that without their binding partner, the isolated monomers are stable and more rigid. The substrates can form fairly stable interactions with the protein in both forms when the protein reaches the final ligand–bound conformations. Our simulations also revealed that the α/β–dimeric unit stabilizes the substrate–protein conformation in the ligand binding process, which lowers the conformation transition barrier and helps the protein conformations shift from an open/inactive form to a closed/active form. Brownian dynamics simulations with a coarse-grained model illustrate how protein conformations affect substrate channeling. The results highlight the complex roles of protein oligomerization and the fine balance between rigidity and dynamics in protein function. Conformational changes of enzymes are often related to regulating and creating an optimal environment for efficient chemistry. An increasing number of evidences also indicate that oligomerization/co-localization of proteins contributes to the efficiency of metabolic pathways. Although static structures have been available for many multi-enzyme complexes, their efficiency is also governed by the synergistic regulation between the multi-units. Our study applies molecular dynamics and Brownian dynamics simulations to the model system, the tryptophan synthase complex. The multi-enzyme complex is a bienzyme nanomachine and its catalytic activity is intimately related to the allosteric signaling and the metabolite transfer between its α– and β–subunits connected by a 25-Å long channel. Our studies suggest that the binding partner is crucial for the ligand binding processes. Although the isolated monomers are stable in the ligand–free state and can form stable interaction if the substrate is in the final bound conformation, it has higher energy barrier when ligand binds to the active site. We also show that the channel does not always exist, but it may be blocked before the enzyme reaches its final bound conformation. The results highlight the importance of forming protein complexes and the cooperative changes during different states.
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Affiliation(s)
- M. Qaiser Fatmi
- Department of Chemistry, University of California, Riverside, Riverside, California, United States of America
| | - Chia-en A. Chang
- Department of Chemistry, University of California, Riverside, Riverside, California, United States of America
- * E-mail:
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Born B, Kim SJ, Ebbinghaus S, Gruebele M, Havenith M. The terahertz dance of water with the proteins: the effect of protein flexibility on the dynamical hydration shell of ubiquitin. Faraday Discuss 2009; 141:161-73; discussion 175-207. [DOI: 10.1039/b804734k] [Citation(s) in RCA: 160] [Impact Index Per Article: 10.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
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Wang J, Xu L, Xue K, Wang E. Exploring the origin of power law distribution in single-molecule conformation dynamics: Energy landscape perspectives. Chem Phys Lett 2008. [DOI: 10.1016/j.cplett.2008.08.081] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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6
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Diffusional channeling in the sulfate-activating complex: combined continuum modeling and coarse-grained brownian dynamics studies. Biophys J 2008; 95:4659-67. [PMID: 18689458 PMCID: PMC2576392 DOI: 10.1529/biophysj.108.140038] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Enzymes required for sulfur metabolism have been suggested to gain efficiency by restricted diffusion (i.e., channeling) of an intermediate APS(2-) between active sites. This article describes modeling of the whole channeling process by numerical solution of the Smoluchowski diffusion equation, as well as by coarse-grained Brownian dynamics. The results suggest that electrostatics plays an essential role in the APS(2-) channeling. Furthermore, with coarse-grained Brownian dynamics, the substrate channeling process has been studied with reactions in multiple active sites. Our simulations provide a bridge for numerical modeling with Brownian dynamics to simulate the complicated reaction and diffusion and raise important questions relating to the electrostatically mediated substrate channeling in vitro, in situ, and in vivo.
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Wang J, Huang W, Lu H, Wang E. Downhill kinetics of biomolecular interface binding: globally connected scenario. Biophys J 2005; 87:2187-94. [PMID: 15454421 PMCID: PMC1304644 DOI: 10.1529/biophysj.104.042747] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We study the kinetics of the biomolecular binding process at the interface using energy landscape theory. The global kinetic connectivity case is considered for a downhill funneled energy landscape. By solving the kinetic master equation, the kinetic time for binding is obtained and shown to have a U-shape curve-dependence on the temperature. The kinetic minimum of the binding time monotonically decreases when the ratio of the underlying energy gap between native state and average non-native states versus the roughness or the fluctuations of the landscape increases. At intermediate temperatures, fluctuations measured by the higher moments of the binding time lead to non-Poissonian, non-exponential kinetics. At both high and very low temperatures, the kinetics is nearly Poissonian and exponential.
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Affiliation(s)
- Jin Wang
- State Key Laboratory of Electro-analytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, People's Republic of China.
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Barzykin AV, Seki K, Tachiya M. Kinetics of diffusion-assisted reactions in microheterogeneous systems. Adv Colloid Interface Sci 2001; 89-90:47-140. [PMID: 11215811 DOI: 10.1016/s0001-8686(00)00053-1] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Abstract
This review is focused on the basic theory of diffusion-assisted reactions in microheterogeneous systems, from porous solids to self-organized colloids and biomolecules. Rich kinetic behaviors observed experimentally are explained in a unified fashion using simple concepts of competing distance and time scales of the reaction and the embedding structure. We mainly consider pseudo-first-order reactions, such as luminescence quenching, described by the Smoluchowski type of equation for the reactant pair distribution function with a sink term defined by the reaction mechanism. Microheterogeneity can affect the microscopic rate constant. It also enters the evolution equation through various spatial constraints leading to complicated boundary conditions and, possibly, to the reduction of dimensionality of the diffusion space. The reaction coordinate and diffusive motion along this coordinate are understood in a general way, depending on the problem at hand. Thus, the evolution operator can describe translational and rotational diffusion of molecules in a usual sense, it can be a discrete random walk operator when dealing with hopping of adsorbates in solids, or it can correspond to conformational fluctuations in proteins. Mathematical formulation is universal but physical consequences can be different. Understanding the principal features of reaction kinetics in microheterogeneous systems enables one to extract important structural and dynamical information about the host environments by analyzing suitably designed experiments, it helps building effective strategies for computer simulations, and ultimately opens possibilities for designing systems with controllable reactivity properties.
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Affiliation(s)
- A V Barzykin
- National Institute of Materials and Chemical Research, Tsukuba, Ibaraki, Japan.
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Affiliation(s)
- Jianshu Cao
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
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Hornbach MJ, Dakhnovskii Y. Electron transfer in a slow relaxation bath: Coherence and nonexponential kinetics. J Chem Phys 1999. [DOI: 10.1063/1.479763] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Ormos P, Száraz S, Cupane A, Nienhaus GU. Structural factors controlling ligand binding to myoglobin: a kinetic hole-burning study. Proc Natl Acad Sci U S A 1998; 95:6762-7. [PMID: 9618486 PMCID: PMC22626 DOI: 10.1073/pnas.95.12.6762] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Abstract
Using temperature-derivative spectroscopy in the temperature range below 100 K, we have studied the dependence of the Soret band on the recombination barrier in sperm whale carbonmonoxy myoglobin (MbCO) after photodissociation at 12 K. The spectra were separated into contributions from the photodissociated species, Mb*CO, and CO-bound myoglobin. The line shapes of the Soret bands of both photolyzed and liganded myoglobin were analyzed with a model that takes into account the homogeneous bandwidth, coupling of the electronic transition to vibrational modes, and static conformational heterogeneity. The analysis yields correlations between the activation enthalpy for rebinding and the model parameters that characterize the homogeneous subensembles within the conformationally heterogeneous ensemble. Such couplings between spectral and functional parameters arise when they both originate from a common structural coordinate. This effect is frequently denoted as "kinetic hole burning." The study of these correlations gives direct insights into the structure-function relationship in proteins. On the basis of earlier work that assigned spectral parameters to geometric properties of the heme, the connections with the heme geometry are discussed. We show that two separate structural coordinates influence the Soret line shape, but only one of the two is coupled to the enthalpy barrier for rebinding. We give evidence that this coordinate, contrary to widespread belief, is not the iron displacement from the mean heme plane.
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Affiliation(s)
- P Ormos
- Institute of Biophysics, Biological Research Centre of the Hungarian Academy of Sciences, P.O. Box 521 H-6701 Szeged, Hungary.
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McMahon BH, Müller JD, Wraight CA, Nienhaus GU. Electron transfer and protein dynamics in the photosynthetic reaction center. Biophys J 1998; 74:2567-87. [PMID: 9591682 PMCID: PMC1299598 DOI: 10.1016/s0006-3495(98)77964-0] [Citation(s) in RCA: 180] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Abstract
We have measured the kinetics of electron transfer (ET) from the primary quinone (Q(A)) to the special pair (P) of the reaction center (RC) complex from Rhodobacter sphaeroides as a function of temperature (5-300 K), illumination protocol (cooled in the dark and under illumination from 110, 160, 180, and 280 K), and warming rate (1.3 and 13 mK/s). The nonexponential kinetics are interpreted with a quantum-mechanical ET model (Fermi's golden rule and the spin-boson model), in which heterogeneity of the protein ensemble, relaxations, and fluctuations are cast into a single coordinate that relaxes monotonically and is sensitive to all types of relaxations caused by ET. Our analysis shows that the structural changes that occur in response to ET decrease the free energy gap between donor and acceptor states by 120 meV and decrease the electronic coupling between donor and acceptor states from 2.7 x 10(-4) cm(-1) to 1.8 x 10(-4) cm(-1). At cryogenic temperatures, conformational changes can be slowed or completely arrested, allowing us to monitor relaxations on the annealing time scale (approximately 10(3)-10(4) s) as well as the time scale of ET (approximately 100 ms). The relaxations occur within four broad tiers of conformational substates with average apparent Arrhenius activation enthalpies of 17, 50, 78, and 110 kJ/mol and preexponential factors of 10(13), 10(15), 10(21), and 10(25) s(-1), respectively. The parameterization provides a prediction of the time course of relaxations at all temperatures. At 300 K, relaxations are expected to occur from 1 ps to 1 ms, whereas at lower temperatures, even broader distributions of relaxation times are expected. The weak dependence of the ET rate on both temperature and protein conformation, together with the possibility of modeling heterogeneity and dynamics with a single conformational coordinate, make RC a useful model system for probing the dynamics of conformational changes in proteins.
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Affiliation(s)
- B H McMahon
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana 61801, USA
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Denisov VP, Peters J, Hörlein HD, Halle B. Using buried water molecules to explore the energy landscape of proteins. NATURE STRUCTURAL BIOLOGY 1996; 3:505-9. [PMID: 8646535 DOI: 10.1038/nsb0696-505] [Citation(s) in RCA: 112] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
Buried water molecules constitute a highly conserved, integral part of nearly all known protein structures. Such water molecules exchange with external solvent as a result of protein conformational fluctuations. We report here the results of water (17)O and (2)H magnetic relaxation dispersion measurements on wild-type and mutant bovine pancreatic trypsin inhibitor in aqueous solution at 4-80 degrees C. These data lead to the first determination of the exchange rate of a water molecule buried in a protein. The strong temperature dependence of this rate is ascribed to large-scale conformational fluctuations in an energy landscape with a statistical ruggedness of approximately 10 kJ mol(-1).
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Affiliation(s)
- V P Denisov
- Condensed Matter Magnetic Resonance Group, Department of Chemistry, Lund University, Lund, Sweden
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