Elihu Abrahams
A scaling analysis within a model of hierarchically constrained dynamics is shown to reproduce the main features of non-exponential relaxation observed in kinetic studies of carbonmonoxymyoglobin.
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Relaxation channels for two-vibron bound states in an anharmonic alpha-helix protein are studied. It is pointed out that the relaxation originates in the interaction between the dressed anharmonic vibrons and the remaining phonons. This interaction is responsible for the occurrence of transitions between two-vibron eigenstates mediated by both phonon absorption and phonon emission. At biological temperature, it is shown that the relaxation rate does not significantly depends on the nature of the two-vibron state involved in the process. Therefore, the lifetime for both bound and free states is…
In the present work, we provide a dielectric study on two differently concentrated aqueous lysozyme solutions in the frequency range from 1 MHz to 40 GHz and for temperatures from 275 to 330 K. We analyze the three dispersion regions, commonly found in protein solutions, usually termed beta-, gamma-, and delta-relaxation. The beta-relaxation, occurring in the frequency range around 10 MHz and the gamma-relaxation around 20 GHz (at room temperature) can be attributed to the rotation of the polar protein molecules in their aqueous medium and the reorientational motion of the free water molecules…
Proteins are aminoacid chains that diffusively fold or unfold depending on the thermal and chemical environmental conditions. While sophisticated models account for detailed aspects of real proteins, finding traits that unify protein dynamics to general open chains relaxation is still challenging. The principle of minimal frustration represents a key step towards this goal, revealing a fundamental link between proteins and spin glasses. Here, we search for the emergence of protein-like relaxation in open spin chains by going beyond the validity domain of the minimal frustration principle as to…
Protein binding often involves conformational changes. Important questions are whether a conformational change occurs prior to a binding event ('conformational selection') or after a binding event ('induced fit'), and how conformational transition rates can be obtained from experiments. In this article, we present general results for the chemical relaxation rates of conformational-selection and induced-fit binding processes that hold for all concentrations of proteins and ligands and, thus, go beyond the standard pseudo-first-order approximation of large ligand concentration. These results all…
Glassy, nonexponential relaxations in globular proteins are typically attributed to conformational behaviors that are missing from intrinsically disordered proteins. Yet, we show that single molecules of a disordered-protein construct display two signatures of glassy dynamics, logarithmic relaxations and a Kovacs memory effect, in response to changes in applied tension. We attribute this to the presence of multiple independent local structures in the chain, which we corroborate with a model that correctly predicts the force dependence of the relaxation. The mechanism established here likely ap…
A recent experiment [Sadoon AA, Wang Y. 2018 Phys. Rev. E 98, 042411] has revealed that nucleoid associated proteins (i.e., DNA-binding proteins) exhibit highly heterogeneous diffusion processes in bacteria where not only the diffusion constant but also the anomalous diffusion exponent fluctuates for the various proteins. The distribution of displacements of such proteins is observed to take a q-Gaussian form, which decays as a power law. Here, a statistical model is developed for the diffusive motion of the proteins within the bacterium, based on a superstatistics with two variables. This mod…
The biological properties of proteins are uniquely determined by their structure and dynamics. A protein in solution populates a structural ensemble of metastable configurations around the global fold. From overall rotation to local fluctuations, the dynamics of proteins can cover several orders of magnitude in time scales. We propose a simulation-free coarse-grained approach which utilizes knowledge of the important metastable folded states of the protein to predict the protein dynamics. This approach is based upon the Langevin Equation for Protein Dynamics (LE4PD), a Langevin formalism in th…
Protein collapse can be viewed as a dynamical phase transition, during which new scales and collective variables become excited while the old ones recede and fade away. This causes formidable computational bottle-necks in approaches that are based on atomic scale scrutiny. Here we consider an effective dynamical Landau theory to model the folding process at biologically relevant time and distance scales. We reach both a substantial decrease in the execution time and improvement in the accuracy of the final configuration, in comparison to more conventional approaches. As an example we inspect t…
Diffusion of proteins on length scales of their own diameter in highly concentrated solutions is essential for understanding the cellular machinery of living cells, but its experimental characterization remains a challenge. While X-ray photon correlation spectroscopy (XPCS) is currently the only technique that in principle allows for a measurement of long-time collective diffusion on these length scales for such systems, its application to protein solutions is seriously hampered by radiation damage caused by the highly intense X-ray beams required for such experiments. Here we apply an experim…
We use Markov state models (MSMs) to analyze the dynamics of a $β$-hairpin-forming peptide in Monte Carlo (MC) simulations with interacting protein crowders, for two different types of crowder proteins [bovine pancreatic trypsin inhibitor (BPTI) and GB1]. In these systems, at the temperature used, the peptide can be folded or unfolded and bound or unbound to crowder molecules. Four or five major free-energy minima can be identified. To estimate the dominant MC relaxation times of the peptide, we build MSMs using a range of different time resolutions or lag times. We show that stable relaxation…
The processes by which protein sidechains reach equilibrium during a folding reaction are investigated using both lattice and all-atom simulations. We find that rates of sidechain relaxation exhibit a distribution over the protein structure, with the fastest relaxing sidechains being involved in kinetically important positions. Traversal of the major folding transition state corresponds to the freezing of a small number of residues, while the rest of the chain proceeds towards equilibrium via backbone fluctuations around the native fold. The post-nucleation processes by which sidechains relax …
Dynamical Decoherence and Memory Effects in Green Fluorescent Proteins by Dielectric Relaxation
本文利用层级运动方程和德拜介电模型，研究了绿色荧光蛋白发色团在介电环境中的退相干与能量转移，发现介电弛豫产生的强记忆效应可延长相干寿命，且其空腔结构有助于保持二聚体相干性，并揭示了相干能量转移与熵产生之间的动力学关联。
Dependence of energy relaxation and vibrational coherence on the location of light-harvesting chromoproteins in photosynthetic antenna protein complexes
该研究通过二维电子光谱比较藻胆体中不同位置的色素蛋白，发现位置影响能量弛豫与振动相干性，可能是高效单向能量传递的关键机制。
Local molecular motions encode time-resolved infrared spectra of proteins
研究人员结合瞬态红外光谱与非平衡分子动力学模拟，建立实验弛豫时间与局部结构运动的关联，应用于PDZ3、PDZ2蛋白，揭示蛋白质分级弛豫机制，搭建光谱与动力学分子机制的连接框架。
The $β$-relaxation associated with the sub-glass transition temperature ($T_{\text{g},β}$) is attributed to fast, localised molecular motions which can occur below the primary glass transition temperature ($T_{gα}$). Despite $T_{\text{g},β}$ being observed well-below storage temperatures, the $β$-relaxation associated motions have been hypothesised to influence protein stability in the solid state and could thus impact the quality of, e.g. protein powders for inhalation or reconstitution and injection. However, to date, there is no comprehensive explanation in the literature which answers the …
Sequence Complexity and Monomer Rigidity Control the Morphologies and Aging Dynamics of Protein Aggregates
该研究利用最小模型模拟揭示，单体的序列复杂性与弯曲刚性决定蛋白质聚集体形成液滴、向列型纤维或无定形聚集体，并解释其遍历性差异与老化动力学。
Outer hair cells in the inner ear is important for the sensitivity, frequency selectivity, and dynamic range of the mammalian ear. Such a physiological role of outer hair cells is thought to be based an amplifying effect of those cells, which have mechanosensitive their hair bundles and motile cell body embedding prestin, a membrane protein with electromechanical coupling at high density. Mechanical power production by outer hair cells were previously evaluated based on an assumption that the intrinsic transition rates of this motile protein is faster than the operating frequency. This report …
Networks of filamentous actin (F-actin) are important for the mechanics of most animal cells. These cytoskeletal networks are highly dynamic, with a variety of actin-associated proteins that control cross-linking, polymerization and force generation in the cytoskeleton. Inspired by recent rheological experiments on reconstituted solutions of dynamic actin filaments, we report a theoretical model that describes stress relaxation behavior of these solutions in the presence of severing proteins. We show that depending on the kinetic rates of assembly, disassembly, and severing, one can observe bo…
Fluorescence-detected Wavepacket Interferometry reveals time-varying Exciton Relaxation Pathways in single Light-Harvesting Complexes
本文利用双锁相超短脉冲在单个光合色素-蛋白质复合物中产生激子波包干涉，通过荧光探测揭示了能量弛豫路径在数十秒尺度上的波动，并指出该波动源于电子激发与低频振动模式耦合的时间变化。
Coherent X-ray Scattering Reveals Nanoscale Fluctuations in Hydrated Proteins
本文利用X射线光子关联光谱研究水合溶菌酶在深度过冷区的纳米尺度应力弛豫，发现弛豫时间遵循Arrhenius温度依赖，并在T=227 K处出现KWW指数最小值，揭示了动力学异质性与时空涨落增强的关联机制。
How type 2 Topoisomerase (TopoII) proteins relax and simplify the topology of DNA molecules is one of the most intriguing open questions in biophysics. Most of the existing models neglect the dynamics of TopoII which is characteristics for proteins searching their targets via facilitated diffusion. Here, we show that dynamic binding of TopoII speeds up the topological relaxation of knotted substrates by enhancing the search of the knotted arc. Intriguingly, this in turn implies that the timescale of topological relaxation is virtually independent of the substrate length. We then discover that …
Multivalent associative proteins with strong complementary interactions play a crucial role in phase separation of intracellular liquid condensates. We study the internal dynamics of such "bond-network" condensates comprised of two complementary proteins via scaling analysis and molecular dynamics. We find that when stoichiometry is balanced, relaxation slows down dramatically due to a scarcity of alternative partners following a bond break. This microscopic slow-down strongly affects the bulk diffusivity, viscosity and mixing, which provides a means to experimentally test our predictions.
Log-periodic oscillations as real-time signatures of hierarchical dynamics in proteins
本研究发现蛋白质层级动力学因离散尺度不变性而产生对数间隔时间尺度，通过引入一维反应坐标揭示自由能景观的阶梯形状导致系统随时间演化呈现对数周期振荡。
Enlightening the blind spot of the Michaelis-Menten rate law: The role of relaxation dynamics in molecular complex formation
本文系统扩展有效时滞方案，研究分子复合物形成中弛豫动力学的作用，发现其不仅引入时间延迟，还降低复合物浓度振荡幅度，二者共同塑造昼夜节律等时间变化生物分子过程。
Target search on networks-within-networks with applications to protein-DNA interactions
本研究提出一个三层多路复用网络框架，用于理解层级网络中的目标搜索，推导出稳态通量的闭式解，揭示搜索效率与网络参数的普遍关系，并应用于蛋白质-DNA相互作用等场景。
Roles of individual pigments in ultrafast excitation dynamics of light-harvesting phycobiliproteins revealed by recombinant techniques and two-dimensional electronic spectroscopy
通过重组蛋白工程和二维电子光谱，研究了色素排列和色素-蛋白质相互作用对藻胆蛋白超快能量弛豫和相干动力学的影响，发现β153色素在超快弛豫中作用次要，而色素-蛋白质相互作用是APC与CPC差异的关键。
The low-frequency collective vibrational modes in proteins as well as the protein-water interface have been suggested as dominant factors controlling the efficiency of biochemical reactions and biological energy transport. It is thus crucial to uncover the mystery of hydration structure and dynamics as well as their coupling to collective motions of proteins in aqueous solutions. Here we report dielectric properties of aqueous bovine serum albumin protein solutions as a model system using an extremely sensitive dielectric spectrometer with frequencies spanning from megahertz to terahertz. The …
The dynamics of two 12-monomer heteropolymers on the square lattice is studied exactly within the master equation approach. The time evolution of the occupancy of the native state is determined. At low temperatures, the median folding time follows the Arrhenius law and is governed by the longest relaxation time. For good folders, significant kinetic traps appear in the folding funnel whereas for bad folders, the traps also occur in non-native energy valleys.
Nitrogen-Vacancy Magnetic Relaxometry of Nanoclustered Cytochrome C Proteins
本文利用氮-空位磁弛豫测量检测细胞色素C纳米簇，通过T1变化揭示Fe3+顺磁信号，实现蛋白质顺磁中心的高灵敏检测。
This study explores, both theoretically and experimentally, the photochemically induced dynamic nuclear polarization (photo-CIDNP) of 19F nuclei, the associated spin relaxation, cross-relaxation and cross-correlation effects, as well as potential applications of 19F CIDNP to protein structure and folding problems. Keywords: CIDNP, relaxation, fluorine, NMR, NOE, TR-CIDNP, tc5b, Trp-cage, GFP
The understanding of dynamics and functioning of biological membranes and in particular of membrane embedded proteins is one of the most fundamental problems and challenges in modern biology and biophysics. In particular the impact of membrane composition and properties and of structure and dynamics of the surrounding hydration water on protein function is an upcoming hot topic, which can be addressed by modern experimental and computational techniques. Correlated molecular motions might play a crucial role for the understanding of, for instance, transport processes and elastic properties, and…
Mossbauer spectroscopy and neutron scattering measurements on proteins embedded in solvents including water and aqueous mixtures have emphasized the observation of the distinctive temperature dependence of the atomic mean square displacements, <u2>, commonly referred to as the dynamic transition at some temperature Td. At low temperatures, <u2> increases slowly, but it assume stronger temperature dependence after crossing Td, which depends on the time/frequency resolution of the spectrometer. Various authors have made connection of the dynamics of solvated proteins including the dynamic transi…
A Markov state model of the dynamics of a protein-like chain immersed in an implicit hard sphere solvent is derived from first principles for a system of monomers that interact via discontinuous potentials designed to account for local structure and bonding in a coarse-grained sense. The model is based on the assumption that the implicit solvent interacts on a fast time scale with the monomers of the chain compared to the time scale for structural rearrangements of the chain and provides sufficient friction so that the motion of monomers is governed by the Smoluchowski equation. A microscopic …
Cytoskeletal networks of biopolymers are cross-linked by a variety of proteins. Experiments have shown that dynamic cross-linking with physiological linker proteins leads to complex stress relaxation and enables network flow at long times. We present a model for the mechanical properties of transient networks. By a combination of simulations and analytical techniques we show that a single microscopic timescale for cross-linker unbinding leads to a broad spectrum of macroscopic relaxation times, resulting in a weak power-law dependence of the shear modulus on frequency. By performing rheologica…
A modeling framework for the internal conformational dynamics and external mechanical movement of single biological macromolecules in aqueous solution at constant temperature is developed. Both the internal dynamics and external movement are stochastic; the former is represented by a master equation for a set of discrete states, and the latter is described by a continuous Smoluchowski equation. Combining these two equations into one, a comprehensive theory for the Brownian dynamics and statistical thermodynamics of single macromolecules arises. This approach is shown to have wide applications.…
The bioprotective nature of disaccharides is hypothesized to derive from the modification of the hydrogen bonding network of water which protects biomolecules through lowered water activity at the protein interface. Using ultrafast fluorescence spectroscopy we measured the relaxation of bulk water dynamics around the induced dipole moment of two fluorescent probes (Lucifer Yellow Ethylenediamine and Tryptophan). Our results indicate a reduction in bulk water reorganization rate of approximately of 30%. We observe this retardation in the low concentration regime measured at 0.1M and 0.25 M, far…
We discuss theoretical models for the cooperative binding dynamics of ligands to substrates, such as dimeric motor proteins to microtubules or more extended macromolecules like tropomyosin to actin filaments. We study the effects of steric constraints, size of ligands, binding rates and interaction between neighboring proteins on the binding dynamics and binding stoichiometry. Starting from an empty lattice the binding dynamics goes, quite generally, through several stages. The first stage represents fast initial binding closely resembling the physics of random sequential adsorption processes.…
Relaxation and first passage processes are the pillars of kinetics in condensed matter, polymeric and single-molecule systems. Yet, an explicit connection between relaxation and first passage time-scales so far remained elusive. Here we prove a duality between them in the form of an interlacing of spectra. In the basic form the duality holds for reversible Markov processes to effectively one-dimensional targets. The exploration of a triple-well potential is analyzed to demonstrate how the duality allows for an intuitive understanding of first passage trajectories in terms of relaxational eigen…
Energy transfer (relaxation) phenomena are ubiquitous in nature. At a macroscopic level, the phenomenological theory of heat (Fourier law) successfully describes heat transfer and energy flow. However, its microscopic origin is still under debate. This is because the phenomena can contain many-body, multi-scale, nonequilibrium, and even quantum mechanical aspects, which present significant challenges to theories addressing energy transfer phenomena in physics, chemistry and biology. In this paper, we describe our recent theoretical attempts to treat vibrational energy relaxation (VER) in biomo…
Modulating lipid membrane morphology by dynamic DNA origami networks
本研究提出可锚定巨型单层囊泡的DNA折纸十字结构，其能聚合为可重构的一维或二维网络，通过DNA燃料切换左右手构象以调控膜曲率，为合成细胞的可编程调控提供新方法。
Emergent memory in cell signaling: Persistent adaptive dynamics in cascades can arise from the diversity of relaxation time-scales
本文通过计算模型揭示MAPK信号级联因组分弛豫速率差异而在刺激撤除后产生持续尖峰和回响，表现出细胞短期记忆，无需反馈或串扰。
The eye lens is the most characteristic example of mammalian tissues exhibiting complex colloidal behaviour. In this paper we briefly describe how dynamics in colloidal suspensions can help addressing selected aspects of lens cataract which is ultimately related to the protein self-assembly under pathological conditions. Results from dynamic light scattering of eye lens homogenates over a wide protein concentration were analyzed and the various relaxation modes were identified in terms of collective and self-diffusion processes. Using this information as an input, the complex relaxation patter…
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