arXiv subjects

Nikolay V. Dokholyan

Publications and source records attributed to Nikolay V. Dokholyan.

18 recordsLinked to original sources

arXiv2023

Differentiable Rotamer Sampling with Molecular Force Fields

Molecular dynamics is the primary computational method by which modern structural biology explores macromolecule structure and function. Boltzmann generators have been proposed as an alternative to molecular dynamics, by replacing the integration of molecular systems over time with the training of generative neural networks. This neural network approach to MD samples rare events at a higher rate than traditional MD, however critical gaps in the theory and computational feasibility of Boltzmann generators significantly reduce their usability. Here, we develop a mathematical foundation to overcome these barriers; we demonstrate that the Boltzmann generator approach is sufficiently rapid to replace traditional MD for complex macromolecules, such as proteins in specific applications, and we provide a comprehensive toolkit for the exploration of molecular energy landscapes with neural networks.

physics.comp-ph↗

arXiv2021

Drug Discovery Approaches using Quantum Machine Learning

Traditional drug discovery pipeline takes several years and cost billions of dollars. Deep generative and predictive models are widely adopted to assist in drug development. Classical machines cannot efficiently produce atypical patterns of quantum computers which might improve the training quality of learning tasks. We propose a suite of quantum machine learning techniques e.g., generative adversarial network (GAN), convolutional neural network (CNN) and variational auto-encoder (VAE) to generate small drug molecules, classify binding pockets in proteins, and generate large drug molecules, respectively.

cs.ET↗

arXiv2004

The architecture of the protein domain universe

Understanding the design of the universe of protein structures may provide insights into protein evolution. We study the architecture of the protein domain universe, which has been found to poses peculiar scale-free properties (Dokholyan et al., Proc. Natl. Acad. Sci. USA 99: 14132-14136 (2002)). We examine the origin of these scale-free properties of the graph of protein domain structures (PDUG) and determine that that the PDUG is not modular, i.e. it does not consist of modules with uniform properties. Instead, we find the PDUG to be self-similar at all scales. We further characterize the PDUG architecture by studying the properties of the hub nodes that are responsible for the scale-free connectivity of the PDUG. We introduce a measure of the betweenness centrality of protein domains in the PDUG and find a power-law distribution of the betweenness centrality values. The scale-free distribution of hubs in the protein universe suggests that a set of specific statistical mechanics models, such as the self-organized criticality model, can potentially identify the principal driving forces of molecular evolution. We also find a gatekeeper protein domain, removal of which partitions the largest cluster into two large sub-clusters. We suggest that the loss of such gatekeeper protein domains in the course of evolution is responsible for the creation of new fold families.

q-bio.MN↗

arXiv2004

Folding Trp-cage to NMR resolution native structure using a coarse-grained model

We develop a coarse-grained protein model with a simplified amino acid interaction potential. We perform discrete molecular dynamics folding simulations of a small 20 residue protein - Trp-cage - from a fully extended conformation. We demonstrate the ability of the Trp-cage model to consistently reach conformations within 2angstrom backbone root-mean-square distance (RMSD) from the corresponding NMR structures. The minimum RMSD of Trp-cage conformations in the simulation can be smaller than 1.00angstrom. Our findings suggest that, at least for the case of Trp-cage, a detailed all-atom protein model with a physical molecular mechanics force field is not necessary to reach the native state of a protein. Our results also suggest that the success folding Trp-cage in our simulations and in the reported all-atom molecular mechanics simulations studies may be mainly due to the special stabilizing features specific to this miniprotein.

physics.bio-ph↗

arXiv2004

Can contact potentials reliably predict stability of proteins?

The simplest approximation of interaction potential between amino-acids in proteins is the contact potential, which defines the effective free energy of a protein conformation by a set of amino acid contacts formed in this conformation. Finding a contact potential capable of predicting free energies of protein states across a variety of protein families will aid protein folding and engineering in silico on a computationally tractable time-scale. We test the ability of contact potentials to accurately and transferably (across various protein families) predict stability changes of proteins upon mutations. We develop a new methodology to determine the contact potentials in proteins from experimental measurements of changes in protein thermodynamic stabilities (ddG) upon mutations. We apply our methodology to derive sets of contact interaction parameters for a hierarchy of interaction models including solvation and multi-body contact parameters. We test how well our models reproduce experimental measurements by statistical tests. We evaluate the maximum accuracy of predictions obtained by using contact potentials and the correlation between parameters derived from different data-sets of experimental ddG values. We argue that it is impossible to reach experimental accuracy and derive fully transferable contact parameters using the contact models of potentials. However, contact parameters can yield reliable predictions of ddG for datasets of mutations confined to specific amino-acid positions in the sequence of a single protein.

q-bio.BM↗

arXiv2003

Folding of Cu, Zn superoxide dismutase and Familial Amyotrophic Lateral Sclerosis

Cu,Zn superoxide dismutase (SOD1) has been implicated in the familial form of the neurodegenerative disease Amyotrophic Lateral Sclerosis (ALS). It has been suggested that mutant mediated SOD1 misfolding/aggregation is an integral part of the pathology of ALS. We study the folding thermodynamics and kinetics of SOD1 using a hybrid molecular dynamics approach. We reproduce the experimentally observed SOD1 folding thermodynamics and find that the residues which contribute the most to SOD1 thermal stability are also crucial for apparent two-state folding kinetics. Surprisingly, we find that these residues are located on the surface of the protein and not in the hydrophobic core. Mutations in some of the identified residues are found in patients with the disease. We argue that the identified residues may play an important role in aggregation. To further characterize the folding of SOD1, we study the role of cysteine residues in folding and find that non-native disulfide bond formation may significantly alter SOD1 folding dynamics and aggregation propensity.

physics.bio-ph↗

arXiv2003

A possible mechanism for cold denaturation of proteins at high pressure

We study cold denaturation of proteins at high pressures. Using multicanonical Monte Carlo simulations of a model protein in a water bath, we investigate the effect of water density fluctuations on protein stability. We find that above the pressure where water freezes to the dense ice phase ($\approx2$ kbar), the mechanism for cold denaturation with decreasing temperature is the loss of local low-density water structure. We find our results in agreement with data of bovine pancreatic ribonuclease A.

cond-mat.soft↗

arXiv2003

Protein Evolution within a Structural Space

Understanding of the evolutionary origins of protein structures represents a key component of the understanding of molecular evolution as a whole. Here we seek to elucidate how the features of an underlying protein structural "space" might impact protein structural evolution. We approach this question using lattice polymers as a completely characterized model of this space. We develop a measure of structural comparison of lattice structures that is analgous to the one used to understand structural similarities between real proteins. We use this measure of structural relatedness to create a graph of lattice structures and compare this graph (in which nodes are lattice structures and edges are defined using structural similarity) to the graph obtained for real protein structures. We find that the graph obtained from all compact lattice structures exhibits a distribution of structural neighbors per node consistent with a random graph. We also find that subgraphs of 3500 nodes chosen either at random or according to physical constraints also represent random graphs. We develop a divergent evolution model based on the lattice space which produces graphs that, within certain parameter regimes, recapitulate the scale-free behavior observed in similar graphs of real protein structures.

cond-mat.soft↗

arXiv2001

Glassy behavior of a homopolymer from molecular dynamics simulations

We study at- and out-of-equilibrium dynamics of a single homopolymer chain at low temperature using molecular dynamics simulations. The main quantities of interest are the average root mean square displacement of the monomers below the theta point, and the structure factor, as a function of time. The observation of these quantities show a close resemblance to those measured in structural glasses and suggest that the polymer chain in its low temperature phase is in a glassy phase, with its dynamics dominated by traps. In equilibrium, at low temperature, we observe the trapping of the monomers and a slowing down of the overall motion of the polymer as well as non-exponential relaxation of the structure factor. In out-of-equilibrium, at low temperatures, we compute the two-time quantities and observe breaking of ergodicity in a range of waiting times, with the onset of aging.

cond-mat.soft↗

arXiv2001

Understanding hierarchical protein evolution from first principles

We propose a model that explains the hierarchical organization of proteins in fold families. The model, which is based on the evolutionary selection of proteins by their native state stability, reproduces patterns of amino acids conserved across protein families. Due to its dynamic nature, the model sheds light on the evolutionary time scales. By studying the relaxation of the correlation function between consecutive mutations at a given position in proteins, we observe separation of the evolutionary time scales: at the short time intervals families of proteins with similar sequences and structures are formed, while at long time intervals the families of structurally similar proteins that have low sequence similarity are formed. We discuss the evolutionary implications of our model. We provide a ``profile'' solution to our model and find agreement between predicted patterns of conserved amino acids and those actually observed in nature.

cond-mat.stat-mech↗

arXiv2000

Thermodynamically Important Contacts in Folding of Model Proteins

We introduce a quantity, the entropic susceptibility, that measures the thermodynamic importance-for the folding transition-of the contacts between amino acids in model proteins. Using this quantity, we find that only one equilibrium run of a computer simulation of a model protein is sufficient to select a subset of contacts that give rise to the peak in the specific heat observed at the folding transition. To illustrate the method, we identify thermodynamically important contacts in a model 46-mer. We show that only about 50% of all contacts present in the protein native state are responsible for the sharp peak in the specific heat at the folding transition temperature, while the remaining 50% of contacts do not affect the specific heat.

cond-mat.stat-mech↗

arXiv2000

Understanding conserved amino acids in proteins

It has been conjectured that evolution exerted pressure to preserve amino acids bearing thermodynamic, kinetic, and functional roles. In this letter we show that the physical requirement to maintain protein stability gives rise to a sequence conservatism pattern that is in remarkable agreement with that found in natural proteins. Based on the physical properties of amino acids, we propose a model of evolution that explains conserved amino acids across protein families sharing the same fold.

cond-mat.stat-mech↗

arXiv2000

Flow Between Two Sites on a Percolation Cluster

We study the flow of fluid in porous media in dimensions $d=2$ and 3. The medium is modeled by bond percolation on a lattice of $L^d$ sites, while the flow front is modeled by tracer particles driven by a pressure difference between two fixed sites (``wells'') separated by Euclidean distance $r$. We investigate the distribution function of the shortest path connecting the two sites, and propose a scaling {\it Ansatz} that accounts for the dependence of this distribution (i) on the size of the system, $L$, and (ii) on the bond occupancy probability, $p$. We confirm by extensive simulations that the {\it Ansatz} holds for $d=2$ and 3, and calculate the relevant scaling parameters. We also study two dynamical quantities: the minimal traveling time of a tracer particle between the wells and the length of the path corresponding to the minimal traveling time ``fastest path'', which is not identical to the shortest path. A scaling {\it Ansatz} for these dynamical quantities also includes the effect of finite system size $L$ and off-critical bond occupation probability $p$. We find that the scaling form for the distribution functions for these dynamical quantities for $d=2$ and 3 is similar to that for the shortest path but with different critical exponents. The scaling form is represented as the product of a power law and three exponential cutoff functions. We summarize our results in a table which contains estimates for all parameters which characterize the scaling form for the shortest path and the minimal traveling time in 2 and 3 dimensions; these parameters are the fractal dimension, the power law exponent, and the constants and exponents that characterize the exponential cutoff functions.

cond-mat.stat-mech↗

arXiv1999

Dependence of Conductance on Percolation Backbone Mass

On two-dimensional percolation clusters at the percolation threshold, we study $<σ(M_B,r)>$, the average conductance of the backbone, defined by two points separated by Euclidean distance $r$, of mass $M_B$. We find that with increasing $M_B$ and for fixed r, $<σ(M_B,r)>$ asymptotically {\it decreases} to a constant, in contrast with the behavior of homogeneous sytems and non-random fractals (such as the Sierpinski gasket) in which conductance increases with increasing $M_B$. We explain this behavior by studying the distribution of shortest paths between the two points on clusters with a given $M_B$. We also study the dependence of conductance on $M_B$ slightly above the percolation threshold.

cond-mat.stat-mech↗

arXiv1999

Scaling of the distribution of shortest paths in percolation

We present a scaling hypothesis for the distribution function of the shortest paths connecting any two points on a percolating cluster which accounts for {\it (i)} the effect of the finite size of the system, and {\it (ii)} the dependence of this distribution on the site occupancy probability $p$. We test the hypothesis for the case of two-dimensional percolation.

cond-mat.stat-mech↗

arXiv1999

Traveling time and traveling length for flow in porous media

We study traveling time and traveling length for tracer dispersion in porous media. We model porous media by two-dimensional bond percolation, and we model flow by tracer particles driven by a pressure difference between two points separated by Euclidean distance $r$. We find that the minimal traveling time $t_{min}$ scales as $t_{min} \sim r^{1.40}$, which is different from the scaling of the most probable traveling time, ${\tilde t} \sim r^{1.64}$. We also calculate the length of the path corresponding to the minimal traveling time and find $\ell_{min} \sim r^{1.13}$ and that the most probable traveling length scales as ${\tilde \ell} \sim r^{1.21}$. We present the relevant distribution functions and scaling relations.

cond-mat.stat-mech↗

arXiv1998

Identifying the protein folding nucleus using molecular dynamics

Molecular dynamics simulations of folding in an off-lattice protein model reveal a nucleation scenario, in which a few well-defined contacts are formed with high probability in the transition state ensemble of conformations. Their appearance determines folding cooperativity and drives the model protein into its folded conformation.

cond-mat.stat-mech↗

arXiv1998

Discrete molecular dynamics studies of the folding of a protein-like model

Background: Many attempts have been made to resolve in time the folding of model proteins in computer simulations. Different computational approaches have emerged. Some of these approaches suffer from the insensitivity to the geometrical properties of the proteins (lattice models), while others are computationally heavy (traditional MD). Results: We use a recently-proposed approach of Zhou and Karplus to study the folding of the protein model based on the discrete time molecular dynamics algorithm. We show that this algorithm resolves with respect to time the folding --- unfolding transition. In addition, we demonstrate the ability to study the coreof the model protein. Conclusion: The algorithm along with the model of inter-residue interactions can serve as a tool to study the thermodynamics and kinetics of protein models.

cond-mat.stat-mech↗