Department of Physics

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Charge State of the Globular Histone Core Controls Stability of the Nucleosome
Fenley, Andrew T.; Adams, D. A.; Onufriev, Alexey V. (CELL PRESS, 2010-09-01)
Presented here is a quantitative model of the wrapping and unwrapping of the DNA around the histone core of the nucleosome that suggests a mechanism by which this transition can be controlled: alteration of the charge state of the globular histone core. The mechanism is relevant to several classes of posttranslational modifications such as histone acetylation and phosphorylation; several specific scenarios consistent with recent in vivo experiments are considered. The model integrates a description based on an idealized geometry with one based on the atomistic structure of the nucleosome, and the model consistently accounts for both the electrostatic and nonelectrostatic contributions to the nucleosome free energy. Under physiological conditions, isolated nucleosomes are predicted to be very stable (38 +/- 7 kcal/mol). However, a decrease in the charge of the globular histone core by one unit charge, for example due to acetylation of a single lysine residue, can lead to a significant decrease in the strength of association with its DNA. In contrast to the globular histone core, comparable changes in the charge state of the histone tail regions have relatively little effect on the nucleosome's stability. The combination of high stability and sensitivity explains how the nucleosome is able to satisfy the seemingly contradictory requirements for thermodynamic stability while allowing quick access to its DNA informational content when needed by specific cellular processes such as transcription.
Chromosome–nuclear envelope attachments affect interphase chromosome territories and entanglement
Kinney, Nicholas A.; Sharakhov, Igor V.; Onufriev, Alexey V. (2018-01-22)
Background It is well recognized that the interphase chromatin of higher eukaryotes folds into non-random configurations forming territories within the nucleus. Chromosome territories have biologically significant properties, and understanding how these properties change with time during lifetime of the cell is important. Chromosome–nuclear envelope (Chr–NE) interactions play a role in epigenetic regulation of DNA replication, repair, and transcription. However, their role in maintaining chromosome territories remains unclear. Results We use coarse-grained molecular dynamics simulations to study the effects of Chr–NE interactions on the dynamics of chromosomes within a model of the Drosophila melanogaster regular (non-polytene) interphase nucleus, on timescales comparable to the duration of interphase. The model simulates the dynamics of chromosomes bounded by the NE. Initially, the chromosomes in the model are prearranged in fractal-like configurations with physical parameters such as nucleus size and chromosome persistence length taken directly from experiment. Time evolution of several key observables that characterize the chromosomes is quantified during each simulation: chromosome territories, chromosome entanglement, compactness, and presence of the Rabl (polarized) chromosome arrangement. We find that Chr–NE interactions help maintain chromosome territories by slowing down and limiting, but not eliminating, chromosome entanglement on biologically relevant timescales. At the same time, Chr–NE interactions have little effect on the Rabl chromosome arrangement as well as on how chromosome compactness changes with time. These results are rationalized by simple dimensionality arguments, robust to model details. All results are robust to the simulated activity of topoisomerase, which may be present in the interphase cell nucleus. Conclusions Our study demonstrates that Chr–NE attachments may help maintain chromosome territories, while slowing down and limiting chromosome entanglement on biologically relevant timescales. However, Chr–NE attachments have little effect on chromosome compactness or the Rabl chromosome arrangement.
A computational study of nucleosomal DNA flexibility
Ruscio, Jory Z.; Onufriev, Alexey V. (CELL PRESS, 2006-12-01)
Molecular dynamics simulations of the nucleosome core particle and its isolated DNA free in solution are reported. The simulations are based on the implicit solvent methodology and provide insights into the nature of large-scale structural fuctuations and flexibility of the nucleosomal DNA. In addition to the kinked regions previously identified in the x-ray structure of the nucleosome, the simulations support the existence of a biochemically identified distorted region of the DNA. Comparison of computed relative free energies shows that formation of the kinks is associated with little, if any, energy cost relative to a smooth, ideal conformation of the DNA superhelix. Isolated nucleosomal DNA is found to be considerably more flexible than expected for a 147 bp stretch of DNA based on its canonical persistence length of 500 A. Notably, the significant bending of the DNA observed in our simulations occurs without breaking of Watson-Crick bonds. The computed relative stability of bent conformations is sensitive to the ionic strength of the solution in the physiological range; the sensitivity suggests possible experiments that might provide further insights into the structural origins of the unusual flexibility of the DNA.
Exploring optimization strategies for improving explicit water models: Rigid n-point model and polarizable model based on Drude oscillator
Xiong, Yeyue; Onufriev, Alexey V. (PLOS, 2019-11-14)
Rigid n-point water models are widely used in atomistic simulations, but have known accuracy drawbacks. Increasing the number of point charges, as well as adding electronic polarizability, are two common strategies for accuracy improvements. Both strategies come at considerable computational cost, which weighs heavily against modest possible accuracy improvements in practical simulations. In an effort to provide guidance for model development, here we have explored the limiting accuracy of “electrostatically globally optimal” npoint water models in terms of their ability to reproduce properties of water dimer—a mimic of the condensed state of water. For a given n, each model is built upon a set of reference multipole moments (e.g. ab initio) and then optimized to reproduce water dimer total dipole moment. The models are then evaluated with respect to the accuracy of reproducing the geometry of the water dimer. We find that global optimization of the charge distribution alone can deliver high accuracy of the water model: for n = 4 or n = 5, the geometry of the resulting water dimer can be almost within 50 of the ab initio reference, which is half that of the experimental error margin. Thus, global optimization of the charge distribution of classical n-point water models can lead to high accuracy models. We also find that while the accuracy improvement in going from n = 3 to n = 4 is substantial, the additional accuracy increase in going from n = 4 to n = 5 is marginal. Next, we have explored accuracy limitations of the standard practice of adding electronic polarizability (via a Drude particle) to a “rigid base”—pre-optimization rigid n-point water model. The resulting model (n = 3) shows a relatively small improvement in accuracy, suggesting that the strategy of merely adding the polarizability to an inferior accuracy water model used as the base cannot fix the defects of the latter. An alternative strategy in which the parameters of the rigid base model are globally optimized along with the polarizability parameter is much more promising: the resulting 3-point polarizable model out-performs even the 5-point optimal rigid model by a large margin. We suggest that future development efforts consider 3- and 4-point polarizable models where global optimization of the “rigid base” is coupled to optimization of the polarizability to deliver globally optimal solutions.
H++3.0: automating pK prediction and the preparation of biomolecular structures for atomistic molecular modeling and simulations
Anandakrishnan, Ramu; Aguilar, Boris; Onufriev, Alexey V. (2012-07)
The accuracy of atomistic biomolecular modeling and simulation studies depend on the accuracy of the input structures. Preparing these structures for an atomistic modeling task, such as molecular dynamics (MD) simulation, can involve the use of a variety of different tools for: correcting errors, adding missing atoms, filling valences with hydrogens, predicting pK values for titratable amino acids, assigning predefined partial charges and radii to all atoms, and generating force field parameter/topology files for MD. Identifying, installing and effectively using the appropriate tools for each of these tasks can be difficult for novice and time-consuming for experienced users. H++ (http://biophysics.cs.vt.edu/) is a free open-source web server that automates the above key steps in the preparation of biomolecular structures for molecular modeling and simulations. H++ also performs extensive error and consistency checking, providing error/warning messages together with the suggested corrections. In addition to numerous minor improvements, the latest version of H++ includes several new capabilities and options: fix erroneous (flipped) side chain conformations for HIS, GLN and ASN, include a ligand in the input structure, process nucleic acid structures and generate a solvent box with specified number of common ions for explicit solvent MD.
Heat conductivity of the DNA double helix
Savin, A. V.; Mazo, M. A.; Kikot, I. P.; Manevitch, L. I.; Onufriev, Alexey V. (American Physical Society, 2011-06-20)
Thermal conductivity of isolated single molecule DNA fragments is of importance for nanotechnology, but has not yet been measured experimentally. Theoretical estimates based on simplified (1D) models predict anomalously high thermal conductivity. To investigate thermal properties of single molecule DNA we have developed a 3D coarse-grained (CG) model that retains the realism of the full all-atom description, but is significantly more efficient. Within the proposed model each nucleotide is represented by six particles or grains; the grains interact via effective potentials inferred from classical molecular dynamics (MD) trajectories based on a well-established all-atom potential function. Comparisons of 10 ns long MD trajectories between the CG and the corresponding all-atom model show similar root-mean-square deviations from the canonical B-form DNA, and similar structural fluctuations. At the same time, the CG model is 10 to 100 times faster depending on the length of the DNA fragment in the simulation. Analysis of dispersion curves derived from the CG model yields longitudinal sound velocity and torsional stiffness in close agreement with existing experiments. The computational efficiency of the CG model makes it possible to calculate thermal conductivity of a single DNA molecule not yet available experimentally. For homogeneous (polyG-polyC) DNA, the estimated conductivity coefficient is 0.3 W/mK which is half the value of thermal conductivity for water. This result is in stark contrast with estimates of thermal conductivity for simplified, effectively 1D chains ("beads on a spring") that predict anomalous (infinite) thermal conductivity. Thus, the full 3D character of DNA double-helix retained in the proposed model appears to be essential for describing thermal properties of DNA at a single molecule level.
Investigation of the Chromosome Regions with Significant Affinity for the Nuclear Envelope in Fruit Fly - A Model Based Approach
Kinney, Nicholas A.; Sharakhov, Igor V.; Onufriev, Alexey V. (PLOS, 2014-03-20)
Three dimensional nuclear architecture is important for genome function, but is still poorly understood. In particular, little is known about the role of the ‘‘boundary conditions’’ – points of attachment between chromosomes and the nuclear envelope. We describe a method for modeling the 3D organization of the interphase nucleus, and its application to analysis of chromosome-nuclear envelope (Chr-NE) attachments of polytene (giant) chromosomes in Drosophila melanogaster salivary glands. The model represents chromosomes as self-avoiding polymer chains confined within the nucleus; parameters of the model are taken directly from experiment, no fitting parameters are introduced. Methods are developed to objectively quantify chromosome territories and intertwining, which are discussed in the context of corresponding experimental observations. In particular, a mathematically rigorous definition of a territory based on convex hull is proposed. The self-avoiding polymer model is used to re-analyze previous experimental data; the analysis suggests 33 additional Chr-NE attachments in addition to the 15 already explored Chr-NE attachments. Most of these new Chr-NE attachments correspond to intercalary heterochromatin – gene poor, dark staining, late replicating regions of the genome; however, three correspond to euchromatin – gene rich, light staining, early replicating regions of the genome. The analysis also suggests 5 regions of anti-contact, characterized by aversion for the NE, only two of these correspond to euchromatin. This composition of chromatin suggests that heterochromatin may not be necessary or sufficient for the formation of a Chr- NE attachment. To the extent that the proposed model represents reality, the confinement of the polytene chromosomes in a spherical nucleus alone does not favor the positioning of specific chromosome regions at the NE as seen in experiment; consequently, the 15 experimentally known Chr-NE attachment positions do not appear to arise due to non-specific (entropic) forces. Robustness of the key conclusions to model assumptions is thoroughly checked.
Statistics and Physical Origins of pK and Ionization State Changes upon Protein-Ligand Binding
Aguilar, Boris; Anandakrishnan, Ramu; Ruscio, Jory Z.; Onufriev, Alexey V. (CELL PRESS, 2010-03-01)
This work investigates statistical prevalence and overall physical origins of changes in charge states of receptor proteins upon ligand binding. These changes are explored as a function of the ligand type (small molecule, protein, and nucleic acid), and distance from the binding region. Standard continuum solvent methodology is used to compute, on an equal footing, pK changes upon ligand binding for a total of 5899 ionizable residues in 20 protein-protein, 20 protein-small molecule, and 20 protein-nucleic acid high-resolution complexes. The size of the data set combined with an extensive error and sensitivity analysis allows us to make statistically justified and conservative conclusions: in 60% of all protein-small molecule, 90% of all protein-protein, and 85% of all protein-nucleic acid complexes there exists at least one ionizable residue that changes its charge state upon ligand binding at physiological conditions (pH = 6.5). Considering the most biologically relevant pH range of 4-8, the number of ionizable residues that experience substantial pK changes (Delta pK > 1.0) due to ligand binding is appreciable: on average, 6% of all ionizable residues in protein-small molecule complexes, 9% in protein-protein, and 12% in protein-nucleic acid complexes experience a substantial pK change upon ligand binding. These changes are safely above the statistical false-positive noise level. Most of the changes occur in the immediate binding interface region, where approximately one out of five ionizable residues experiences substantial pK change regardless of the ligand type. However, the physical origins of the change differ between the types: in protein-nucleic acid complexes, the pK values of interface residues are predominantly affected by electrostatic effects, whereas in protein-protein and protein-small molecule complexes, structural changes due to the induced-fit effect play an equally important role. In protein-protein and protein-nucleic acid complexes, there is a statistically significant number of substantial pK perturbations, mostly due to the induced-fit structural changes, in regions far from the binding interface.
Strongly Bent Double-Stranded DNA: Reconciling Theory and Experiment
Drozdetski, Aleksander V.; Mukhopadhyay, Abhishek; Onufriev, Alexey V. (2019-11-29)
The strong bending of polymers is poorly understood. We propose a general quantitative framework of polymer bending that includes both the weak and strong bending regimes on the same footing, based on a single general physical principle. As the bending deformation increases beyond a certain (polymer-specific) point, the change in the convexity properties of the effective bending energy of the polymer makes the harmonic deformation energetically unfavorable: in this strong bending regime the energy of the polymer varies linearly with the average bending angle as the system follows the convex hull of the deformation energy function. For double-stranded DNA, the effective bending deformation energy becomes non-convex for bends greater than similar to 2 degrees per base-pair, equivalent to the curvature of a closed circular loop of similar to 160 base pairs. A simple equation is derived for the polymer loop energy that covers both the weak and strong bending regimes. The theory shows quantitative agreement with recent DNA cyclization experiments on short DNA fragments, while maintaining the expected agreement with experiment in the weak bending regime. Counter-intuitively, cyclization probability (j-factor) of very short DNA loops is predicted to increase with decreasing loop length; the j-factor reaches its minimum for loops of similar or equal to 45 base pairs. Atomistic simulations reveal that the attractive component of the short-range Lennard-Jones interaction between the backbone atoms can explain the underlying non-convexity of the DNA effective bending energy, leading to the linear bending regime. Applicability of the theory to protein-DNA complexes, including the nucleosome, is discussed.
Systematic Reverse Engineering of Network Topologies: A Case Study of Resettable Bistable Cellular Responses
Mondal, Debasish; Dougherty, Edward T.; Mukhopadhyay, Abhishek; Carbo, Adria; Yao, Guang; Xing, Jianhua (Public Library of Science, 2014-08-29)
A focused theme in systems biology is to uncover design principles of biological networks, that is, how specific network structures yield specific systems properties. For this purpose, we have previously developed a reverse engineering procedure to identify network topologies with high likelihood in generating desired systems properties. Our method searches the continuous parameter space of an assembly of network topologies, without enumerating individual network topologies separately as traditionally done in other reverse engineering procedures. Here we tested this CPSS (continuous parameter space search) method on a previously studied problem: the resettable bistability of an Rb-E2F gene network in regulating the quiescence-to-proliferation transition of mammalian cells. From a simplified Rb-E2F gene network, we identified network topologies responsible for generating resettable bistability. The CPSS-identified topologies are consistent with those reported in the previous study based on individual topology search (ITS), demonstrating the effectiveness of the CPSS approach. Since the CPSS and ITS searches are based on different mathematical formulations and different algorithms, the consistency of the results also helps cross-validate both approaches. A unique advantage of the CPSS approach lies in its applicability to biological networks with large numbers of nodes. To aid the application of the CPSS approach to the study of other biological systems, we have developed a computer package that is available in Information S1.
Why double-stranded RNA resists condensation
Tolokh, Igor S.; Pabit, Suzette A.; Katz, Andrea M.; Chen, Yujie; Drozdetski, Aleksander V.; Baker, Nathan; Pollack, Lois; Onufriev, Alexey V. (2014-09-15)
The addition of small amounts of multivalent cations to solutions containing double-stranded DNA leads to inter-DNA attraction and eventual condensation. Surprisingly, the condensation is suppressed in double-stranded RNA, which carries the same negative charge as DNA, but assumes a different double helical form. Here, we combine experiment and atomistic simulations to propose a mechanism that explains the variations in condensation of short (25 base-pairs) nucleic acid (NA) duplexes, from B-like form of homopolymeric DNA, to mixed sequence DNA, to DNA: RNA hybrid, to A-like RNA. Circular dichroism measurements suggest that duplex helical geometry is not the fundamental property that ultimately determines the observed differences in condensation. Instead, these differences are governed by the spatial variation of cobalt hexammine (CoHex) binding to NA. There are two major NA-CoHex binding modes-internal and external-distinguished by the proximity of bound CoHex to the helical axis. We find a significant difference, up to 5-fold, in the fraction of ions bound to the external surfaces of the different NA constructs studied. NA condensation propensity is determined by the fraction of CoHex ions in the external binding mode.

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