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RNA function depends crucially on the details of its dynamics. The simplest RNA dynamical unit is a two-way interhelical junction. Here, for such a unit—the transactivation response RNA element—we present evidence from molecular dynamics simulations, supported by nuclear magnetic resonance relaxation experiments, for a dynamical transition near 230 K. This glass transition arises from the freezing out of collective interhelical motional modes. The motions, resolved with site-specificity, are dynamically heterogeneous and exhibit non-Arrhenius relaxation. The microscopic origin of the glass transition is a low-dimensional, slow manifold consisting largely of the Euler angles describing interhelical reorientation. Principal component analysis over a range of temperatures covering the glass transition shows that the abrupt slowdown of motion finds its explanation in a localization transition that traps probability density into several disconnected conformational pools over the low-dimensional energy landscape. Upon temperature increase, the probability density pools then flood a larger basin, akin to a lakes-to-sea transition. Simulations on transactivation response RNA are also used to backcalculate inelastic neutron scattering data that match previous inelastic neutron scattering measurements on larger and more complex RNA structures and which, upon normalization, give temperature-dependent fluctuation profiles that overlap onto a glass transition curve that is quasi-universal over a range of systems and techniques.

In the bacteriophage ϕ29, DNA is packed into a preassembled capsid from which it ejects under high pressure. A recent cryo-EM reconstruction of ϕ29 revealed a compact toroidal DNA structure (30–40 basepairs) lodged within the exit cavity formed by the connector-lower collar protein complex. Using multiscale models, we compute a detailed structural ensemble of intriguing DNA toroids of various lengths, all highly compatible with experimental observations. In particular, coarse-grained (elastic rod) and atomistic (molecular dynamics) models predict the formation of DNA toroids under significant compression, a largely unexplored state of DNA. Model predictions confirm that a biologically attainable compressive force of 25 pN sustains the toroid and yields DNA electron density maps highly consistent with the experimental reconstruction. The subsequent simulation of dynamic toroid ejection reveals large reactions on the connector that may signal genome release.

The mechanism of DNA compaction by dendrimers is key to the design of nanotechnologies that can deliver genetic material into cells. We present atomistic simulations, mesoscopic modeling and single-molecule pulling experiments describing DNA dendrimer interactions. All-atom molecular dynamics were used to characterize pulling-force-dependent interactions between DNA and generation-3 PAMAM amine-terminated dendrimers, and a free energy profile and mean forces along the interaction coordinate are calculated. The energy, force, and geometry parameters computed at the atomic level are input for a Monte Carlo model yielding mesoscopic force-extension curves. Actual experimental single-molecule curves obtained with optical tweezers are also presented, and they show remarkable agreement with the virtual curves from our model. The calculations reveal the microscopic origin of the hysteresis observed in the phase transition underlying compaction. A broad range of ionic and pulling parameters is sampled, and suggestions for windows of conditions to probe new single-molecule behavior are made.

Thioredoxins (Trx) are a class of enzymes, which catalyze the reduction of disulphide bonds between two cysteine residues, commonly found in proteins. An experimental investigation into the reaction mechanisms employed by various species of Trx was carried out by Perez-Jimenez et al. using single molecule force-clamp spectroscopy. The experiment involved applying a pulling force along the disulfide bond of the protein substrate, and measuring the rate of the Trx-catalyzed reduction as a function of the pulling force. One interesting finding of the experiment was that some forms of thioredoxin exhibit a biphasic relationship for reduction rate as a function of force magnitude. For this project, a mathematical model of this system was created, which employs a Smoluchowski formalism in the vein of Agmon-Hopfied or Sumi-Markus models. The model describes the time evolution of the probability distribution function of the protein's configuration within a space defined as the internal protein coordinate, as it diffuses over a potential which distorts under the applied force, while losing probability density to the Bell model type “sink” term, which is also a function of the applied force, representing reactants going to products (disulphide bond cleavage). By numerically solving the Smoluchowski equation and integrating the resulting surface over both time and the protein coordinate to calculate lifetime for increasing values of applied force, the model successfully reproduced the experimentally observed values for disulphide bond reduction rate as a function of applied force. Parameterizing the Smoluchowski equation to fit the experimentally measured data points provided a means of drawing insights into a physical interpretation of the model including the relationship between degree of biphasic behavior and the distance along the reaction coordinate from the bottom of the reactant well to the top of the transition state.

Molecular dynamics simulations are presented for a Thermus aquaticus (Taq) DNA polymerase I complex (consisting of the protein, the primer-template DNA strands, and the incoming nucleotide) subjected to external forces. The results obtained with a force applied to the DNA template strand provide insights into the effect of the tension on the activity of the enzyme. At forces below 30pN a local model based on the parameters determined from the simulations, including the restricted motion of the DNA bases at the active site, yields a replication rate dependence on force in agreement with experiment. Simulations above 40pN reveal large conformational changes in the enzyme-bound DNA that may have a role in the force-induced exonucleolysis observed experimentally.

Previous studies have shown that an important aspect of designing drugs for RNA drug targets, in particular, the transactivation response element (TAR) from HIV type 1 (HIV-1), is the determination of the thermodynamics and kinetics for WC to HG (Watson-Crick to Hoogsteen) conformation transitions. Previous work by Eunae Kim and Ioan Andricioaei successfully implemented umbrella sampling to produce a two-dimensional free energy surface for WC to HG transitions, where the two independent variables are the “flip-over” angle and “flip-out” angle of the adenine moiety undergoing the transition. The current study builds upon the work of Kim and Andricioaei by exploring the kinetics that arise from the time evolution of the probability density function of configurations, subjected to this potential energy surface. A position-dependent diffusion matrix was first calculated from the umbrella sampling data, in order to accurately describe diffusive motions in this reduced space. Next, a 2D polynomial of order 20 was fit to the energy surface, in order to obtain an analytical expression for the 2D surface. The diffusion matrix and analytical function describing the 2D surface were then used to carry out Langevin dynamics. Numerous Langevin trajectories between states were then analyzed in multiple ways, including calculating first passage time distributions between WC and HG configurations, and determination of regions in configuration space of maximum flux. In order to make the system numerically tractable for a Fokker-Planck approach to diffusion, the energy surface was also fit to a simpler 2D analytical function with a 20 term Fourier series solely in the “flip-over” dimension and a separate harmonic term approximating the “flip-out” dimension. Both approaches were utilized to determine favorable pathways for WC/HG transitions, and their respective time scales.

DNA in cells is often topologically closed, and in some cases, tightly looped by proteins typically associated with transcriptional repression. During transcription initiation, RNA polymerase (RNAP) is challenged to open duplex DNA, wherein RNAP generates torque that consequently overtwists DNA flanking the melted promoter. As initiation proceeds, the transcription bubble expands as RNAP synthesizes downstream RNA while maintaining upstream DNA contacts. We hypothesized that the mechanical strain imparted to DNA during initiation would repress transcription from DNA templates that restrict the relief of torsional stress. To test our hypothesis, we constructed circular DNA templates that are 100 to 108 bp in size (i.e., each initially twisted to various degrees) and quantified transcription initiation by the bacteriophage T7 RNAP. We find that transcriptional repression during initiation is dependent on the sign and magnitude of initial twist within the DNA templates. Surprisingly, however, we observe that for the most overtwisted templates, repression is relieved at positions beyond the promoter that are dependent on the initial DNA twist. To interpret these results, we used elastic rod and molecular dynamics simulations to predict the structures of both the RNAP and the circular DNA template during initiation. Our modeling studies confirm that RNAP is capable of overtwisting the circular DNA template to the point of buckling from a planar into a supercoiled conformation. Further analysis reveals that initial DNA twist determines at what position along the template supercoiling will occur during initiation and that adopting a supercoiled structure substantially relieves the torque encountered by the RNAP. Our results demonstrate that repression of RNAP during initiation is determined not only by the initial mechanics of the DNA template, but also by the torque generated by RNAP itself.

The possibility of using path-integral simulations in a generalized ensemble based on the Tsallis statistics is explored. The primitive model algorithm with the Tsallis ensemble replacing the canonical ensemble converges to the quantum-mechanical result with a smaller number of beads in the isomorphic chain. Examples considered are the harmonic oscillator, two double-well systems and a double-well system immersed in an adiabatic solvent.

Molecular motors involved in the packaging of DNA in tailed viruses are among the strongest known. The mechanism by which the motors operate has long been speculated to involve a coupling between rotation of the portal pore (the gate through which DNA passes upon its packaging or ejection), and translation of DNA. Recent experimental evidence rules out portal rotation with a substantial degree of certainty. We have created an atomistic model for the interaction between DNA and the portal of the bacteriophage SPP1, on the basis of cryo-electron microscopy images and of a recently solved crystal structure. A free energy surface describing the interaction is calculated using molecular dynamics simulations, and found to be inconsistent with a mechanism in which portal rotation drives DNA import. The low-energy pathways on the surface are used to advance a hypothesis on DNA import compatible with all available experiments. Additionally, temperature-dependent kinetic data are used to validate computed barriers to DNA ejection.

A new Monte Carlo algorithm which provides enhanced sampling in the calculation of equilibrium thermodynamic properties of spin systems is presented. The algorithm proposed performs trial moves based on the generalized statistical distributions derived from a modification of the Gibbs-Shannon entropy by Tsallis. Results for a two-dimensional Ising model demonstrate that the algorithm leads to a greatly enhanced rate of barrier crossing and convergence in the calculation of equilibrium thermodynamic averages. Comparison is made with standard Metropolis Monte Carlo.

The conformations that DNA takes are often vital in many biological processes. The physical effects Hoogsteen conformation base pairs have on the full strand of DNA are still being determined. Through molecular dynamics simulations in CHARMM, the effect Hoogsteen conformation has on the entropy of the strand can be examined. The absolute entropy of both Hoogsteen and Watson-Crick conformations can be calculated with the use of a quasi-harmonic approximation using the trajectories of each simulation. Using this method, the entropy contribution of varying amounts of neighboring base pairs can be estimated. This work can be compared with experimental entropy values for entire double-strands. Our calculations show how a localized conformational change can affect the entropy in neighboring site and over longer-range base pairs.

In cells, DNA is subjected to substantial contortions. Here, we investigate the difference in structure, dynamics and flexibility between two topological states of short (∼100 bp) DNA sequencea in linear form and covalently closed, tightly curved circular DNA form. By employing a combination of all-atom molecular dynamics (MD) simulations and elastic rod modeling of DNA, which allows capturing microscopic details while monitoring the global dynamics, we demonstrate that in the highly curved regime the microscopic flexibility of the DNA drastically increases due to the local mobility of the duplex. By analyzing vibrational entropy and Lipari-Szabo NMR order parameters from the simulation data, we propose a novel model for the thermodynamic stability of high-curvature DNA states based on vibrational untightening of the duplex. This novel view of DNA bending provides a fundamental explanation that bridges the gap between classical models of DNA and experimental studies on DNA cyclization, which so far have been in substantial disagreement.Using MD, we also compute free energy profiles for the initial unzipping of the first base pair of DNA at blunt ends, and reveal the role of entropy in modulating the kinetic barrier to initial unzipping, making connections to possible experiments and existing theories based on the Peyrard-Bishop model.

DNA topoisomerases are enzymes that can change the topological state of DNA without changing its primary structure by changing the linking number of the molecule. Topoisomerases are able to solve all the topological problems of DNA that arise during such processes as replication, transcription, recombination or chromosome separation. In our study, S. cerevisiae topoII structure is used to investigate structural and energetic changes of the protein from initial state to final state ( our final state is the DNA-TopoII complex when the protein binds to DNA and the stage just before the DNA cleavage by TopoII). The second goal is to investigate conformational changes of cleavage dependent DNA-gate and C-gate mechanisms of the protein after the protein captures the DNA. Lastly, we aim to get the transition rate constants from free energy profile by employing umbrella sampling method after defining the reaction pathway. In order to investigate the conformational changes during DNA-gate and C-gate opening and/or closing processes, small perturbations are introduced by using HQBMD (Half Quadratic Biased MD) and TMD (Targeted MD) methods by performing a version of CHARMM (Chemistry at HARvard Macromolecular Mechanics).

Many cellular processes involving DNA, including replication and transcription, result in significant superhelical stresses. During transcription, for example, RNA polymerase locally untwists about a helical turn of the DNA double helix. Then to elongate the RNA transcript, it proceeds along the template strand of the DNA and thereby induces supercoiling. DNA topoisomerases play an important role in relieving these stresses. Here we focus on understanding the action of human DNA topoisomerase I (Topo1) which operates in three basic steps: (i) cleaving a single strand of the DNA double helix, (ii) allowing the DNA superhelical stresses to relax, and (iii) religating the DNA. Recently, the Dekker lab, at Delft University of Technology, performed single molecule experiments to probe the relaxation of supercoils by topo1. A significant molecular dynamics (MD) effort (>100 cpu years) by the Andricioaei lab, at the University of California Irvine, characterized the energetics and topological changes of topo1 in complex with only a short fragment of DNA (∼20 bp). Including a longer length of DNA to represent a biologically relevant length-scale (greater than a persistence length), is computationally prohibitive for MD and was necessarily neglected. Here we introduce an elasto-dynamic rod model as a first approximation to provide a dynamic description of the DNA as it relaxes. The rod model describes bending and torsion of the DNA helical axis, electrostatic and self-contact interactions, and approximates the hydrodynamic drag on the molecule. For our simulations, we provide as initial conditions, a plectomemic supercoil. The MD simulations serve to provide boundary conditions to the rod model by characterizing the torque applied to the DNA by topo1 as it rotates. Here we present preliminary results for the relaxation rates of supercoils.

Force-pulling experiments on the unfolding of mechanical and non-mechanical protein domains have greatly increased our understanding of the structural stability of proteins. Because these experiments are done on the single molecule level, they also enable experimentalists to observe differences in the unfolding behavior of individual molecules. However, it is difficult to determine the source of unfolding heterogeneity through experiments alone. We present here evidence from experiments and simulations that the s domain of Streptokinase, a non-mechanical protein, unfolds under force via three distinct pathways. High temperature SMD simulations were used to determine the source of the velocity-dependent heterogeneity observed in AFM force puling experiments. We show that hydrophobic interactions in the core of the protein underlie the differences observed in experiments and contribute significantly to the structural stability of the protein under force. Using an expansion of the Jarzynski equality12, we calculate free energy surfaces to describe the energetics of the different pathways.1 C. Jarzynski, PRL 78, 2690-2693 (1997)2 D. Minh, J. Phys. Chem. B. 111, 4137-4140 (2007)

Mitochondrial import machinery catalyses unfolding of the native precursor proteins by trapping some faster local unfolding fluctuations due to specific secondary structural element adjacent to the targeting sequence. On the rupture of the first resistant structure, the rest of the protein unfolds rapidly by cooperative unfolding during import into the mitochondrial matrix. The process of circular permutation on the protein chain can give important information about the connectivity, structure and folding or unfolding kinetics which guides its translocation and subsequent function in the cell. To study the process of co-translocational unfolding and its dependence on the secondary structure at the N-terminus of the protein imported, we conduct a comparative molecular dynamics study of circular permutants of Dihydrofolate reductase(DHFR) using atomistic model in CHARMM. Six Circular Permutants - CP25, CP38, CP78, CP97, CP108, CP133 - are generated such that the new N-terminus leads either to an alpha helix or a beta-strand. using Steered Molecular Dynamics we compute the work distributions for the forced unfolding of each of the CP's and native DHFR using two processes - unfolding through the geometrical constriction of the model pore as in mitochondrial translocation and mechanical unfolding with the C-terminus fixed. In both cases the unfolding force is applied at the N-terminus. A comparison of the free energy profile along the reaction coordinate for each circular permutant can lead to identification of different unfolding pathways and hence import efficiency based on first resistant structure adjacent to the targeting sequence.

Tailed bacteriophages are highly efficient machines for infecting a host cell. A single virion must attach to the host surface, penetrate the cell wall, then release its double-stranded DNA genome. In these remarkable DNA delivery machines, controlling how and when the genome is released is a task of paramount importance. Recently, a three-dimensional cryo-electron microscopy (cryo-EM) reconstruction of mature bacteriophage φ29 revealed an intriguing toroidal DNA structure contained in a small cavity below the viral capsid. This highly bent toroidal DNA supercoil is thought to be 30-40 basepairs of dsDNA and its function remains unknown.In this study, we employ an elastic rod model to simulate highly strained DNA as it is compressed within the protein cavity. The model provides estimates of force and energy required to form the toroid as well as its equilibrium conformation. Results reveal that a toroid can indeed form under the biologically relevant forces for the viral packing motor (up to 100 pN). To understand the effects of the highly stressed toroid on DNA structure, we then employ molecular dynamics (MD) simulations starting with the rod model-computed equilibrium as the initial condition. Following equilibration in MD, we construct an approximate density map using the final predicted toroid to compare with the recently published cryo-EM data. The computed density map correctly predicts the major dimensions of the toroid as well as regions of high and low density. Finally, we simulate the start of the ejection process by integrating the rod model forward in time upon sudden removal of the protein “tail knob.” The resulting fast dynamic collapse of the toroid suggests that its function could be to prime the ejection of the remaining viral genome.

Water is essential to nearly all biological reactions, and yet the role of solvent is often overlooked in studying such interactions. In particular, the ability of highly charged molecules to orient the dipole moments of water molecules has not been thoroughly explored. While short-range solvent ordering effects have been previously investigated, we report evidence of the existence of ordered waters between charged molecules at large distances and characterize the free energy contributions of this solvent ordering to the interaction. We present evidence from molecular dynamics simulations that the hydrogen bonding network in ordered waters between a strand of DNA and a highly charged nanoparticle, a generation 3 polyamidoamine (PAMAM) dendrimer, contribute significantly to the free energy and extend the interaction beyond the electrostatic range of the molecules. Such long-range water effects could potentially be of great importance to many biological systems, in which molecules appear to be able to recognize each other across significant distances, or for which the kinetic rates are too fast to be due to pure diffusion. Our results are in good agreement with experiments on the role of solvent in DNA condensation by multivalent cations.

I will present molecular dynamics simulations of several examples of conformational transitions that nucleic acids and their complexes undergo upon the application of external forces and/or torques:(1) DNA supercoil relaxation by topoisomerases,(2) the condensation of DNA by dendrimers and,(3) RNA unfolding.Then I will showcase the use of the formalism of stochastic path integrals to deduce the kinetics of these transitions, from simulation trajectories or experimental single molecule recordings of the transition, under other conditions that those that are actually simulated or recorded.

While the typical viral genome is several kilobases long, it is packed to near crystalline density within a viral capsid only tens of nanometers in diameter. In the case of bacteriophage φ29, this enormous compaction results from strong molecular motors that generate forces of approximately 100 pN. Recently, a three-dimensional cryo-electron microscopy reconstruction of mature φ29 was published. An intriguing feature in the reconstruction is a 60A diameter toroidal DNA supercoil, estimated to be only 30-40 base pairs in length, within the cavity formed by the connector and the lower collar. The function of this highly-bent DNA, remains unknown. In this study, we use an elastic rod model to simulate the DNA inside the cavity. We learn that as more DNA is pushed into the capsid, compressive forces build until a critical load is reached and the DNA ‘buckles’ to fill the cavity thereby forming the toroidal supercoil observed in the reconstruction. We estimate the energy, forces, and torques required to form this toroidal DNA inside the cavity. Based on these results, we propose possible biological functions of this intriguing structure.

In recent years, nonlinear multidimensional optical spectroscopy has been used as a highly sensitive probe of molecular dynamics in the condensed phase. Multidimensional optical spectroscopy builds upon the methodology of two-dimensional nuclear magnetic resonance spectroscopy and applies the same principles to vibrational and electronic resonances such that these techniques may be used as an ultrafast probe of molecular dynamics. In particular, these techniques have been used to study the thermal unfolding of proteins following a nanosecond temperature jump. In this study, we examine the multidimensional optical spectra of several biological systems of interest out of thermal equilibrium by using molecular dynamics to develop snapshots of the systems and the SPECTRON software package to calculate the spectroscopic signals. In order to enhance conformational sampling, an artificial temperature is used; the exact correlation functions of the system contributing to the material response are recovered using an action-reweighting scheme based on a stochastic path-integral formalism. The calculated spectra provide information on the states sampled by the system during the course of thermal unfolding.