Rosana Collepardo-Guevara

Biomolecular modeling and simulation: a field coming of age

We assess the progress in biomolecular modeling and simulation, focusing on structure prediction and dynamics, by presenting the field’s history, metrics for its rise in popularity, early expressed expectations, and current significant applications. The increases in computational power combined with improvements in algorithms and force fields have led to considerable success, especially in protein folding, specificity of ligand/biomolecule interactions, and interpretation of complex experimental phenomena (e.g. NMR relaxation, protein-folding kinetics and multiple conformational states) through the generation of structural hypotheses and pathway mechanisms. Although far from a general automated tool, structure prediction is notable for proteins and RNA that preceded the experiment, especially by knowledge-based approaches. Thus, despite early unrealistic expectations and the realization that computer technology alone will not quickly bridge the gap between experimental and theoretical time frames, ongoing improvements to enhance the accuracy and scope of modeling and simulation are propelling the field onto a productive trajectory to become full partner with experiment and a field on its own right.

Bimolecular reaction rates from ring polymer molecular dynamics: Application to H + CH4→ H2 + CH3

In a recent paper, we have developed an efficient implementation of the ring polymer molecular dynamics (RPMD) method for calculating bimolecular chemical reaction rates in the gas phase, and illustrated it with applications to some benchmark atom-diatom reactions. In this paper, we show that the same methodology can readily be used to treat more complex polyatomic reactions in their full dimensionality, such as the hydrogen abstraction reaction from methane, H + CH(4) → H(2) + CH(3). The present calculations were carried out using a modified and recalibrated version of the Jordan-Gilbert potential energy surface. The thermal rate coefficients obtained between 200 and 2000 K are presented and compared with previous results for the same potential energy surface. Throughout the temperature range that is available for comparison, the RPMD approximation gives better agreement with accurate quantum mechanical (multiconfigurational time-dependent Hartree) calculations than do either the centroid density version of quantum transition state theory (QTST) or the quantum instanton (QI) model. The RPMD rate coefficients are within a factor of 2 of the exact quantum mechanical rate coefficients at temperatures in the deep tunneling regime. These results indicate that our previous assessment of the accuracy of the RPMD approximation for atom-diatom reactions remains valid for more complex polyatomic reactions. They also suggest that the sensitivity of the QTST and QI rate coefficients to the choice of the transition state dividing surface becomes more of an issue as the dimensionality of the reaction increases.

Bimolecular reaction rates from ring polymer molecular dynamics

We describe an efficient procedure for calculating the rates of bimolecular chemical reactions in the gas phase within the ring polymer molecular dynamics approximation. A key feature of the procedure is that it does not require that one calculate the absolute quantum mechanical partition function of the reactants or the transition state: The rate coefficient only depends on the ratio of these two partition functions which can be obtained from a thermodynamic integration along a suitable reaction coordinate. The procedure is illustrated with applications to the three-dimensional H + H(2), Cl + HCl, and F + H(2) reactions, for which well-converged quantum reactive scattering results are computed for comparison. The ring polymer rate coefficients agree with these exact results at high temperatures and are within a factor of 3 of the exact results at temperatures in the deep quantum tunneling regime, where the classical rate coefficients are too small by several orders of magnitude. This is probably already good enough to encourage future applications of the ring polymer theory to more complex chemical reactions, which it is capable of treating in their full dimensionality. However, there is clearly some scope for improving on the ring polymer approximation at low temperatures, and we end by suggesting a way in which this might be accomplished.

Proton transfer in a polar solvent from ring polymer reaction rate theory

We have used the ring polymer molecular dynamics method to study the Azzouz-Borgis model for proton transfer between phenol (AH) and trimethylamine (B) in liquid methyl chloride. When the A-H distance is used as the reaction coordinate, the ring polymer trajectories are found to exhibit multiple recrossings of the transition state dividing surface and to give a rate coefficient that is smaller than the quantum transition state theory value by an order of magnitude. This is to be expected on kinematic grounds for a heavy-light-heavy reaction when the light atom transfer coordinate is used as the reaction coordinate, and it clearly precludes the use of transition state theory with this reaction coordinate. As has been shown previously for this problem, a solvent polarization coordinate defined in terms of the expectation value of the proton transfer distance in the ground adiabatic quantum state provides a better reaction coordinate with less recrossing. These results are discussed in light of the wide body of earlier theoretical work on the Azzouz-Borgis model and the considerable range of previously reported values for its proton and deuteron transfer rate coefficients.

Modeling studies of chromatin fiber structure as a function of DNA linker length.

Chromatin fibers encountered in various species and tissues are characterized by different nucleosome repeat lengths (NRLs) of the linker DNA connecting the nucleosomes. While single cellular organisms and rapidly growing cells with high protein production have short NRL ranging from 160 to 189xa0bp, mature cells usually have longer NRLs ranging between 190 and 220xa0bp. Recently, various experimental studies have examined the effect of NRL on the internal organization of chromatin fiber. Here, we investigate by mesoscale modeling of oligonucleosomes the folding patterns for different NRL, with and without linker histone (LH), under typical monovalent salt conditions using both one-start solenoid and two-start zigzag starting configurations. We find that short to medium NRL chromatin fibers (173 to 209xa0bp) with LH condense into zigzag structures and that solenoid-like features are viable only for longer NRLs (226xa0bp). We suggest that medium NRLs are more advantageous for packing and various levels of chromatin compaction throughout the cell cycle than their shortest and longest brethren; the former (short NRLs) fold into narrow fibers, while the latter (long NRLs) arrays do not easily lead to high packing ratios due to possible linker DNA bending. Moreover, we show that the LH has a small effect on the condensation of short-NRL arrays but has an important condensation effect on medium-NRL arrays, which have linker lengths similar to the LH lengths. Finally, we suggest that the medium-NRL species, with densely packed fiber arrangements, may be advantageous for epigenetic control because their histone tail modifications can have a greater effect compared to other fibers due to their more extensive nucleosome interaction network.

Chromatin fiber polymorphism triggered by variations of DNA linker lengths

Significance The structure of the chromatin fiber remains one of the most fundamental open biological questions because structure dictates many template-directed processes. We use coarse-grained modeling to investigate systematically how variations in the linker DNA length that arise naturally for chromatin in different tissues, species, and cell cycle stages affect fiber architecture. We unravel a natural source of fiber polymorphism, in which irregular interdigitated 10-nm and compact 30-nm fibers coexist. These results suggest how structural diversity can be advantageous for gene regulation activity. Interesting DNA design applications also arise. Deciphering the factors that control chromatin fiber structure is key to understanding fundamental chromosomal processes. Although details remain unknown, it is becoming clear that chromatin is polymorphic depending on internal and external factors. In particular, different lengths of the linker DNAs joining successive nucleosomes (measured in nucleosome-repeat lengths or NRLs) that characterize different cell types and cell cycle stages produce different structures. NRL is also nonuniform within single fibers, but how this diversity affects chromatin fiber structure is not clear. Here we perform Monte Carlo simulations of a coarse-grained oligonucleosome model to help interpret fiber structure subject to intrafiber NRL variations, as relevant to proliferating cells of interphase chromatin, fibers subject to remodeling factors, and regulatory DNA sequences. We find that intrafiber NRL variations have a profound impact on chromatin structure, with a wide range of different architectures emerging (highly bent narrow forms, canonical and irregular zigzag fibers, and polymorphic conformations), depending on the NRLs mixed. This stabilization of a wide range of fiber forms might allow NRL variations to regulate both fiber compaction and selective DNA exposure. The polymorphic forms spanning canonical to sharply bent structures, like hairpins and loops, arise from large NRL variations and are surprisingly more compact than uniform NRL structures. They are distinguished by tail-mediated far-nucleosome interactions, in addition to the near-nucleosome interactions of canonical 30-nm fibers. Polymorphism is consistent with chromatin’s diverse biological functions and heterogeneous constituents. Intrafiber NRL variations, in particular, may contribute to fiber bending and looping and thus to distant communication in associated regulatory processes.

Chromatin Unfolding by Epigenetic Modifications Explained by Dramatic Impairment of Internucleosome Interactions: A Multiscale Computational Study

Histone tails and their epigenetic modifications play crucial roles in gene expression regulation by altering the architecture of chromatin. However, the structural mechanisms by which histone tails influence the interconversion between active and inactive chromatin remain unknown. Given the technical challenges in obtaining detailed experimental characterizations of the structure of chromatin, multiscale computations offer a promising alternative to model the effect of histone tails on chromatin folding. Here we combine multimicrosecond atomistic molecular dynamics simulations of dinucleosomes and histone tails in explicit solvent and ions, performed with three different state-of-the-art force fields and validated by experimental NMR measurements, with coarse-grained Monte Carlo simulations of 24-nucleosome arrays to describe the conformational landscape of histone tails, their roles in chromatin compaction, and the impact of lysine acetylation, a widespread epigenetic change, on both. We find that while the wild-type tails are highly flexible and disordered, the dramatic increase of secondary-structure order by lysine acetylation unfolds chromatin by decreasing tail availability for crucial fiber-compacting internucleosome interactions. This molecular level description of the effect of histone tails and their charge modifications on chromatin folding explains the sequence sensitivity and underscores the delicate connection between local and global structural and functional effects. Our approach also opens new avenues for multiscale processes of biomolecular complexes.

Dynamic condensation of linker histone C-terminal domain regulates chromatin structure

The basic and intrinsically disordered C-terminal domain (CTD) of the linker histone (LH) is essential for chromatin compaction. However, its conformation upon nucleosome binding and its impact on chromatin organization remain unknown. Our mesoscale chromatin model with a flexible LH CTD captures a dynamic, salt-dependent condensation mechanism driven by charge neutralization between the LH and linker DNA. Namely, at low salt concentration, CTD condenses, but LH only interacts with the nucleosome and one linker DNA, resulting in a semi-open nucleosome configuration; at higher salt, LH interacts with the nucleosome and two linker DNAs, promoting stem formation and chromatin compaction. CTD charge reduction unfolds the domain and decondenses chromatin, a mechanism in consonance with reduced counterion screening in vitro and phosphorylated LH in vivo. Divalent ions counteract this decondensation effect by maintaining nucleosome stems and expelling the CTDs to the fiber exterior. Additionally, we explain that the CTD folding depends on the chromatin fiber size, and we show that the asymmetric structure of the LH globular head is responsible for the uneven interaction observed between the LH and the linker DNAs. All these mechanisms may impact epigenetic regulation and higher levels of chromatin folding.

Crucial role of dynamic linker histone binding and divalent ions for DNA accessibility and gene regulation revealed by mesoscale modeling of oligonucleosomes

Monte Carlo simulations of a mesoscale model of oligonucleosomes are analyzed to examine the role of dynamic-linker histone (LH) binding/unbinding in high monovalent salt with divalent ions, and to further interpret noted chromatin fiber softening by dynamic LH in monovalent salt conditions. We find that divalent ions produce a fiber stiffening effect that competes with, but does not overshadow, the dramatic softening triggered by dynamic-LH behavior. Indeed, we find that in typical in vivo conditions, dynamic-LH binding/unbinding reduces fiber stiffening dramatically (by a factor of almost 5, as measured by the elasticity modulus) compared with rigidly fixed LH, and also the force needed to initiate chromatin unfolding, making it consistent with those of molecular motors. Our data also show that, during unfolding, divalent ions together with LHs induce linker-DNA bending and DNA–DNA repulsion screening, which guarantee formation of heteromorphic superbeads-on-a-string structures that combine regions of loose and compact fiber independently of the characteristics of the LH–core bond. These structures might be important for gene regulation as they expose regions of the DNA selectively. Dynamic control of LH binding/unbinding, either globally or locally, in the presence of divalent ions, might constitute a mechanism for regulation of gene expression.

Energy landscapes, folding mechanisms, and kinetics of RNA tetraloop hairpins.

RNA hairpins play a pivotal role in a diverse range of cellular functions, and are integral components of ribozymes, mRNA, and riboswitches. However, the mechanistic and kinetic details of RNA hairpin folding, which are key determinants of most of its biological functions, are poorly understood. In this work, we use the discrete path sampling (DPS) approach to explore the energy landscapes of two RNA tetraloop hairpins, and provide insights into their folding mechanisms and kinetics in atomistic detail. Our results show that the potential energy landscapes have a distinct funnel-like bias toward the folded hairpin state, consistent with efficient structure-seeking properties. Mechanistic and kinetic information is analyzed in terms of kinetic transition networks. We find microsecond folding times, consistent with temperature jump experiments, for hairpin folding initiated from relatively compact unfolded states. This process is essentially driven by an initial collapse, followed by rapid zippering of the helix stem in the final phase. Much lower folding rates are predicted when the folding is initiated from extended chains, which undergo longer excursions on the energy landscape before nucleation events can occur. Our work therefore explains recent experiments and coarse-grained simulations, where the folding kinetics exhibit precisely this dependency on the initial conditions.