A Continuous Effective Model of the Protein Dynamics
Dmitry Melnikov, Alyson B. F. Neves
备注：
5 pages, 4 figures. This paper contains a discussion of an effective field theory model in application to description of the protein structure. A longer version containing technical details was submitted to the hep-ph archive
The theory of elastic rods can be used to describe certain geometric and topological properties of the DNA molecules. A similar effective field theory approach was previously suggested to describe the conformations and dynamics of proteins. In this letter we report a detailed study of the basic features of a version of the proposed model, which assumes proteins to be very long continuous curves. In the most appealing case, the model is based on a potential with a pair of minima corresponding to helical and strand-like configurations of the curves. It allows to derive several predictions about the geometric features of the molecules, and we show that the predictions are compatible with the phenomenology. While the helices represent the ground state configurations, the abundance of beta strands is controlled by a parameter, which can either completely suppress their presence in a molecule, or make them abundant. The few-parameter model investigated in the letter rather represents a universality class of protein molecules. Generalizations accounting for the discrete nature and inhomogeneity of the molecules presumably allow to model realistic cases.
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…
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 biological function of proteins is encoded in their structure and expressed through the mediation of their dynamics. Local fluctuations are known to initiate biologically relevant pathways as they cooperatively enhance the dynamics in specific regions in the protein. Those biologically active regions provide energetically-comparable conformational states that can be trapped by a reacting partner. We analyze this mechanism as we calculate the dynamics of monomeric and dimerized HIV protease, and free Insulin Growth Factor II Receptor (IGF2R) domain 11 and its IGF2R:IGF2 complex. We adopt a …
Prediction of protein-ligand binding affinity is a major goal in drug discovery. Generally, free energy gap is calculated between two states (e.g., ligand binding and unbinding). The energy gap implicitly includes the effects of changes in protein dynamics induced by the binding ligand. However, the relationship between protein dynamics and binding affinity remains unclear. Here, we propose a novel method that represents protein behavioral change upon ligand binding with a simple feature that can be used to predict protein-ligand affinity. From unbiased molecular simulation data, an unsupervis…
Increased ability to predict protein structures is moving research focus towards understanding protein dynamics. A promising approach is to represent protein dynamics through networks and take advantage of well-developed methods from network science. Most studies build protein dynamics networks from correlation measures, an approach that only works under very specific conditions, instead of the more robust inverse approach. Thus, we apply the inverse approach to the dynamics of protein dihedral angles, a system of internal coordinates, to avoid structural alignment. Using the well-characterize…
Recent advances in protein function prediction exploit graph-based deep learning approaches to correlate the structural and topological features of proteins with their molecular functions. However, proteins in vivo are not static but dynamic molecules that alter conformation for functional purposes. Here we apply normal mode analysis to native protein conformations and augment protein graphs by connecting edges between dynamically correlated residue pairs. In the multilabel function classification task, our method demonstrates a remarkable performance gain based on this dynamics-informed repre…
The growing interest for comparing protein internal dynamics owes much to the realization that protein function can be accompanied or assisted by structural fluctuations and conformational changes. Analogously to the case of functional structural elements, those aspects of protein flexibility and dynamics that are functionally oriented should be subject to evolutionary conservation. Accordingly, dynamics-based protein comparisons or alignments could be used to detect protein relationships that are more elusive to sequence and structural alignments. Here we provide an account of the progress th…
In multi-domain proteins, the domains are connected by a flexible unstructured region called as protein domain linker. The accurate demarcation of these linkers holds a key to understanding of their biochemical and evolutionary attributes. This knowledge helps in designing a suitable linker for engineering stable multi-domain chimeric proteins. Here we propose a novel method for the demarcation of the linker based on a three-dimensional protein structure and a domain definition. The proposed method is based on biological knowledge about structural flexibility of the linkers. We performed struc…
The proper biological functioning of proteins often relies on the occurrence of coordinated fluctuations around their native structure, or of wider and sometimes highly elaborated motions. Coarse-grained elastic-network descriptions are known to capture essential aspects of conformational dynamics in proteins, but have so far remained mostly phenomenological, and unable to account for the chemical specificities of amino acids. Here, we propose a method to derive residue- and distance-specific effective harmonic potentials from the statistical analysis of an extensive dataset of NMR conformatio…
In this study, we introduced a new unit, named "protein token", as a dynamic protein structural unit for protein-protein interactions. Unlike the conventional structural units, protein token is not based on the sequential or spatial arrangement of residues, but comprises remote residues involved in cooperative conformational changes during protein interactions. Application of protein token on Ras GTPases revealed various tokens present in the superfamily. Distinct token combinations were found in H-Ras interacting with its various regulators and effectors, directing to a possible clue for the …
We present a thermodynamically consistent mesoscopic model of protein adsorption at liquid-solid interfaces. First describing the equilibrium state under varying protein concentration of the solution and binding conditions, we predict a non-trivial (non- monotonic) dependence of the experimentally observable properties of the adsorbed layer (such as the surface density and surface coverage) on these parameters. We subsequently proceed to develop a dynamical model consistent with the equilibrium description, which qualitatively reproduces known experimental phenomena and offers a promising way …
We present a theoretical model for the description of the adsorption kinetics of globular proteins onto charged core-shell microgel particles based on Dynamic Density Functional Theory (DDFT). This model builds on a previous description of protein adsorption thermodynamics [Yigit \textit{et al}, Langmuir 28 (2012)], shown to well interpret the available calorimetric experimental data of binding isotherms. In practice, a spatially-dependent free-energy functional including the same physical interactions is built, and used to study the kinetics via a generalised diffusion equation. To test this …
Previous studies of the flexibilities of ancestral proteins suggests that proteins evolve their function by altering their native state ensemble. Here we propose a more direct method of visualizing this by measuring the changes in the vibrational density of states (VDOS) of proteins as they evolve. Through analysis of VDOS profiles of ancestral and extant proteins we observe that $β$-lactamase and thioredoxins evolve by altering their density of states in the terahertz region. Particularly, the shift in VDOS profiles between ancestral and extant proteins suggests that nature utilize dynamic al…
We provide evidence that the energy landscapes of folded proteins do not shift with temperature, but the onset of functional dynamics is associated with its effective sampling. The motion of the backbone is described by three distinct regimes. One is associated with slow time scales of the activity along the envelope of the energy surface defining the folded protein. Another, with fast time scales, is due to activity along the pockets decorating the folded-state envelope. The intermediate regime emerges at temperatures where jumps between the pockets become possible, leading to an active prote…
The effect of interactions on dynamics of coupled motor proteins is investigated theoretically. A simple stochastic discrete model, that allows to calculate explicitly the dynamic properties of the system, is developed. It is shown that there are two dynamic regimes, depending on the interaction between the particles. For strong interactions the motor proteins move as one tight cluster, while for weak interactions there is no correlation in the motion of the proteins, and the particle separation increases steadily with time. The boundary between two dynamic phases is specified by a critical in…
Motivated by single-molecule experiments on synaptic membrane protein domains, we use a stochastic lattice model to study protein reaction and diffusion processes in crowded membranes. We find that the stochastic reaction-diffusion dynamics of synaptic proteins provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the single-molecule trajectories observed for synaptic proteins, and spatially inhomogeneous protein lifetimes at the cell membrane. Our results suggest that central aspects of the sin…
A novel combination of discontinuous molecular dynamics and the Langevin equation, together with an intermediate-resolution model, are used to carry out long (several $μ$s) simulation and study folding transition and transport of proteins in slit nanopores. Both attractive ($U^+$) and repulsive ($U^-$) interaction potentials between the proteins and the pore walls are considered. Near the folding temperature $T_f$ and in the presence of $U^+$ the proteins undergo a repeating sequence of folding/partially-folding/ unfolding transitions, while $T_f$ decreases with decreasing pore sizes. The oppo…
Using an Ising-like model of protein mechanical unfolding, we introduce a diffusive dynamics on its exactly known free energy profile, reducing the nonequilibrium dynamics of the model to a biased random walk. As an illustration, the model is then applied to the protein translocation phenomenon, taking inspiration from a recent experiment on the green fluorescent protein pulled by a molecular motor. The average translocation time is evaluated exactly, and the analysis of single trajectories shows that translocation proceeds through an intermediate state, similar to that observed in the experim…
The principles underlying protein folding remains one of Nature's puzzles with important practical consequences for Life. An approach that has gathered momentum since the late 1990's, looks at protein hetero-polymers and their folding process through the lens of complex network analysis. Consequently, there is now a body of empirical studies describing topological characteristics of protein macro-molecules through their contact networks and linking these topological characteristics to protein folding. The present paper is primarily a review of this rich area. But it delves deeper into certain …
Protein functions in cells may be activated or modified by the attachment of several kinds of chemical groups. While protein phosphorylation, i.e. the attachment of a phosphoryl (PO$_3^-$) group, is the most studied form of protein modification, and is known to regulate the functions of many proteins, protein behavior can also be modified by nitrosylation, acetylation, methylation, etc. A protein can have multiple modification sites, and display some form of transition only when enough sites are modified. In a previous paper we have modeled the generic equilibrium properties of multisite prote…
It is not merely the position of residues that are of utmost importance in protein function and stability, but the interactions between them. We illustrate, by using a network construction on a set of 595 non-homologous proteins, that regular packing is preserved in short-range interactions, but short average path lengths are achieved through some long-range contacts. Thus, lying between the two extremes of regularity and randomness, residues in folded proteins are distributed according to a "small-world" topology. Using this topology, we show that the core residues have the same local packing…
Urea at sufficiently high concentration unfolds the secondary structure of proteins leading to denaturation. In contrast, Choline Chloride (ChCl) and urea, in 1:2 molar ratio form a deep eutectic mixture, a liquid at room temperature and protect proteins from denaturation. In order to get a microscopic picture of this phenomenon, we perform extensive all-atom molecular dynamics simulations on a model protein HP-36. Based on our calculation of Kirkwood-Buff integrals, we analyze the relative accumulation of these osmolytes around the protein. Additional insights are drawn from the analyses of t…
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.
Solvation is essential for protein activities. To study internal solvation of protein, site-directed mutagenesis is applied. Intrinsic fluorescent probe, tryptophan, is inserted into desired position inside protein molecule for ultrafast spectroscopic study. Here we review this unique method for protein dynamics researches. We introduce the frontiers of protein solvation, site-directed mutagenesis, protein stability and characteristics, and the spectroscopic methods. Then we present time-resolved spectroscopic dynamics of solvation dynamics inside caves of active sites. The studies are carried…
Protein folding produces characteristic and functional three-dimensional structures from unfolded polypeptides or disordered coils. The emergence of extraordinary complexity in the protein folding process poses astonishing challenges to theoretical modeling and computer simulations. The present work introduces molecular nonlinear dynamics (MND), or molecular chaotic dynamics, as a theoretical framework for describing and analyzing protein folding. We unveil the existence of intrinsically low dimensional manifolds (ILDMs) in the chaotic dynamics of folded proteins. Additionally, we reveal that …
We use plasmon rulers to follow the conformational dynamics of a single protein for up to 24 h at a video rate. The plasmon ruler consists of two gold nanospheres connected by a single protein linker. In our experiment, we follow the dynamics of the molecular chaperone heat shock protein 90, which is known to show open and closed conformations. Our measurements confirm the previously known conformational dynamics with transition times in the second to minute time scale and reveals new dynamics on the time scale of minutes to hours. Plasmon rulers thus extend the observation bandwidth 3/4 order…
Prion diseases cover a large range of neurodegenerative diseases in humans and animals, which are invariably fatal and highly infectious. By now there have not been some effective therapeutic approaches or medications to treat all prion diseases. Fortunately, numerous experimental experiences have showed that rabbits are resistant to infection from prion diseases isolated from other species, and recently the molecular structures of rabbit prion protein and its mutants were released into protein data bank. Prion diseases are "protein structural conformational" diseases. Thus, in order to reveal…
We describe a combination of all-atom simulations with CABS, a well-established coarse-grained protein modeling tool, into a single multiscale protocol. The simulation method has been tested on the C-terminal beta hairpin of protein G, a model system of protein folding. After reconstructing atomistic details, conformations derived from the CABS simulation were subjected to replica-exchange molecular dynamics simulations with OPLS-AA and AMBER99sb force fields in explicit solvent. Such a combination accelerates system convergence several times in comparison with all-atom simulations starting fr…
We propose a dynamical model depicting the interactions between DNA and a specific binding protein involving long range transmissions. The dynamics rely on the coupling between Hydrogen bonds formed between DNA and protein and between the base pairs because they account for site specificity of the binding. We adopt the Morse potential with coupling terms to construct the Hamiltonian. This model gives rise to a breather excitation, corresponding to the DNA bubble formation, which propagates as the carrier of genetic information. We examine the various kind of possible coupling dynamics and sugg…
Quantum mechanical calculations are performed on 116 conformers of the protein ubiquitin (Lange et al., Science 2008, 320, 1471-1475). The results indicate that the heat of formation (HOF), dipole moment, energy of the frontier orbitals HOMO and LUMO, and HOMO-LUMO gap fluctuate within their corresponding ranges. This study thus provides a link between the conformational dynamics of a protein and its electronic structure.
Current all-atom potential based molecular dynamics (MD) allow the identification of a protein's functional motions on a wide-range of time-scales, up to few tens of ns. However, functional large scale motions of proteins may occur on a time-scale currently not accessible by all-atom potential based molecular dynamics. To avoid the massive computational effort required by this approach several simplified schemes have been introduced. One of the most satisfactory is the Gaussian Network approach based on the energy expansion in terms of the deviation of the protein backbone from its native conf…
Many aspects of the study of protein folding and dynamics have been affected by the recent advances in machine learning. Methods for the prediction of protein structures from their sequences are now heavily based on machine learning tools. The way simulations are performed to explore the energy landscape of protein systems is also changing as force-fields are started to be designed by means of machine learning methods. These methods are also used to extract the essential information from large simulation datasets and to enhance the sampling of rare events such as folding/unfolding transitions.…
We propose to develop mean field theory in combination with Glauber algorithm, to model and interpret protein dynamics and structure formation in small to wide angle x-ray scattering (S/WAXS) experiments. We develop the methodology by analysing the Engrailed homeodomain protein as an example. We demonstrate how to interpret S/WAXS data with a good precision and over an extended temperature range. We explain experimentally observed phenomena in terms of protein phase structure, and we make predictions for future experiments how the scattering data behaves at different ambient temperature values…
The network paradigm is increasingly used to describe the topology and dynamics of complex systems. Here we review the results of the topological analysis of protein structures as molecular networks describing their small-world character, and the role of hubs and central network elements in governing enzyme activity, allosteric regulation, protein motor function, signal transduction and protein stability. We summarize available data how central network elements are enriched in active centers and ligand binding sites directing the dynamics of the entire protein. We assess the feasibility of con…
Network theory-based approaches provide valuable insights into the variations in global structural connectivity between differing dynamical states of proteins. Our objective is to review network-based analyses to elucidate such variations, especially in the context of subtle conformational changes. We present technical details of the construction and analyses of protein structure networks, encompassing both the non-covalent connectivity and dynamics. We examine the selection of optimal criteria for connectivity based on the physical concept of percolation. We highlight the advantages of using …
De novo prediction of protein structures, the prediction of structures from amino-acid sequences which are not similar to those of hitherto resolved structures, has been one of the major challenges in molecular biophysics. In this paper, we develop a new method of de novo prediction, which combines the fragment assembly method and the simulation of physical folding process: Structures which have consistently assembled fragments are dynamically searched by Langevin molecular dynamics of conformational change. The benchmarking test shows that the prediction is improved when the candidate structu…
Protein Folding with Neural Ordinary Differential Equations
University of Chicago, Department of Computer Science（芝加哥大学计算机科学系）；Technical University of Munich, School of CIT, Department of Computer Science（慕尼黑技术大学 CIT 学院计算机科学系）；TUM Institute for Advanced Study, Lichtenbergstraße 2a（慕尼黑技术大学高级研究学院）
We study the dynamics of protein folding via statistical energy-landscape theory. In particular, we concentrate on the local-connectivity case with the folding progress described by the fraction of native conformations. We obtain information for the first passage-time (FPT) distribution and its moments. The results show a dynamic transition temperature below which the FPT distribution develops a power-law tail, a signature of the intermittency phenomena of the folding dynamics. We also discuss the possible application of the results to single-molecule dynamics experiments.
Large protein assemblies, such as virus capsids, may be coarse-grained as a set of rigid domains linked by generalized (rotational and stretching) harmonic springs. We present a method to obtain the elastic parameters and overdamped dynamics for these springs from all-atom molecular dynamics simulations of one pair of domains at a time. The computed relaxation times of this pair give a consistency check for the simulation, and (using a fluctuation-dissipation relationship) we find the corrective force needed to null systematic drifts. As a first application we predict the stiffness of an HIV c…
A molecular understanding of how protein function is related to protein structure will require an ability to understand large conformational changes between multiple states. Unfortunately these states are often separated by high free energy barriers and within a complex energy landscape. This makes it very difficult to reliably connect, for example by all-atom molecular dynamics calculations, the states, their energies and the pathways between them. A major issue needed to improve sampling on the intermediate states is an order parameter -- a reduced descriptor for the major subset of degrees …
Allostery is an intrinsic spatiotemporal property of all proteins, resulting from long range correlations in the order of several nanometers and time scales of nanoseconds. Information is carried asymmetrically from one part to another by entropy transfer. Here, we present a master equation model of allosteric communication in proteins based on the transfer entropy concept of Schreiber (PRL, 85, 465, 2000). We show how the model relates the path and velocity of asymmetric entropy transfer to conformational transitions over the rugged energy surface of proteins and how this relates to function.
The molecular mechanism of the solvent motion that is required to instigate the protein structural relaxation above a critical hydration level or transition temperature has yet to be determined. In this work we use quasi-elastic neutron scattering (QENS) and molecular dynamics simulation to investigate hydration water dynamics near a greatly simplified protein surface. We consider the hydration water dynamics near the completely deuterated N-acetyl-leucine-methylamide (NALMA) solute, a hydrophobic amino acid side chain attached to a polar blocked polypeptide backbone, as a function of concentr…
Normal mode analysis is a widely used technique for reconstructing conformational changes of proteins from the knowledge of native structures. In this Letter, we investigate to what extent normal modes capture the salient features of the dynamics over a range of temperatures from close to T = 0 to above unfolding. We show that on the one hand, the use of normal modes at physiological temperatures is justified provided proteins are cooperative. On the other hand, it is imperative to consider several modes in order to eliminate the unpredictable temperature dependence of single- mode contributio…
School of Computer Science and Technology, East China Normal University（东华师范大学计算机科学与技术学院）；College of Foreign Languages and Literatures, Fudan University（复旦大学外国语言文学学院）；Institute of Artificial Intelligence (TeleAI), China Telecom（中国电信人工智能研究所）
In this conceptual paper we propose to explore the analogy between ontic/epistemic description of quantum phenomena and interrelation between dynamics of conformational and functional states of proteins. Another new idea is to apply theory of automata to model the latter dynamics. In our model protein's behavior is modeled with the aid of two dynamical systems, ontic and epistemic, which describe evolution of conformational and functional states of proteins, respectively. The epistemic automaton is constructed from the ontic automaton on the basis of functional (observational) equivalence rela…
We investigate dynamical coupling between water and amino acid side-chain residues in solvation dynamics by selecting residues often used as natural probes, namely tryptophan, tyrosine and histidine, located at different positions on protein surface and having various degrees of solvent exposure. Such differently placed residues are found to exhibit different timescales of relaxation. The total solvation response, as measured by the probe is decomposed in terms of its interactions with (i) protein core, (ii) side-chain atoms and (iii) water molecules. Significant anti cross-correlations among …
We study the size fluctuations of a local denaturation zone in a DNA molecule in the presence of proteins that selectively bind to single-stranded DNA, based on a (2+1)-dimensional master equation. By tuning the physical parameters we can drive the system from undisturbed bubble fluctuations to full, binding protein-induced denaturation. We determine the effective free energy landscape of the DNA-bubble and explore its relaxation modes.
This chapter reviews how molecular dynamics simulations, experimental data, and Markov state models can synergize to map-out the mechanism of protein-protein association and dissociation.
A simple and surprisingly accurate description of spectral diffusion in deeply frozen globular proteins is constructed directly using the concept of ultrametricity of protein dynamics. Earlier the similar concept has been used for successful description of ligand-rebinding kinetics of myoglobin at temperatures about of 200 K. Hence the ultrametricity offers a universal background for the protein dynamics in a wide range of scales of protein motions.
Emergence of new protein structures has proved difficult to trace in nature and engineer in the laboratory. However, one aspect of structure evolution has proved immensely helpful for determining the three-dimensional structure of proteins from their sequences: in the vast majority of cases, proteins that share more than 30% sequence identity have similar structures. Below this mark is the "twilight zone" where proteins may have identical or very different structures. These observations form the foundational intuition behind structure homology modeling. Despite their importance, however, they …
