For simulating proteins at work in millisecond time scale or longer, we develop a coarse-grained (CG) molecular dynamics (MD) method and software, CafeMol. At the resolution of one-particle-per-residue, CafeMol equips four structure-based protein models: (1) the off-lattice Go model, (2) the atomic interaction based CG model for native state and folding dynamics, (3) the multiple-basin model for conformational change dynamics, and (4) the elastic network model for quasiharmonic fluctuations around the native structure. Ligands can be treated either explicitly or implicitly. For mimicking functional motions of proteins driven by some external force, CafeMol has various and flexible means to "switch" the energy functions that induce active motions of the proteins. CafeMol can do parallel computation with modest sized PC clusters. We describe CafeMol methods and illustrate it with several examples, such as rotary motions of F1-ATPase and drug exports from a transporter. The CafeMol source code is available at www.cafemol.org .

We develop a robust coarse-grained model for single- and double-stranded DNA by representing each nucleotide by three interaction sites (TIS) located at the centers of mass of sugar, phosphate, and base. The resulting TIS model includes base-stacking, hydrogen bond, and electrostatic interactions as well as bond-stretching and bond angle potentials that account for the polymeric nature of DNA. The choices of force constants for stretching and the bending potentials were guided by a Boltzmann inversion procedure using a large representative set of DNA structures extracted from the Protein Data Bank. Some of the parameters in the stacking interactions were calculated using a learning procedure, which ensured that the experimentally measured melting temperatures of dimers are faithfully reproduced. Without any further adjustments, the calculations based on the TIS model reproduce the experimentally measured salt and sequence-dependence of the size of single-stranded DNA (ssDNA), as well as the persistence lengths of poly(dA) and poly(dT) chains. Interestingly, upon application of mechanical force, the extension of poly(dA) exhibits a plateau, which we trace to the formation of stacked helical domains. In contrast, the force-extension curve (FEC) of poly(dT) is entropic in origin and could be described by a standard polymer model. We also show that the persistence length of double-stranded DNA, formed from two complementary ssDNAs, is consistent with the prediction based on the worm-like chain. The persistence length, which decreases with increasing salt concentration, is in accord with the Odijk-Skolnick-Fixman theory intended for stiff polyelectrolyte chains near the rod limit. Our model predicts the melting temperatures of DNA hairpins with excellent accuracy, and we are able to recover the experimentally known sequence-specific trends. The range of applications, which did not require adjusting any parameter after the initial construction based solely on PDB structures and melting profiles of dimers, attests to the transferability and robustness of the TIS model for ssDNA and dsDNA.

RNA molecules cannot fold in the absence of counterions. Experiments are typically performed in the presence of monovalent and divalent cations. How to treat the impact of a solution containing a mixture of both ion types on RNA folding has remained a challenging problem for decades. By exploiting the large concentration difference between divalent and monovalent ions used in experiments, we develop a theory based on the reference interaction site model (RISM), which allows us to treat divalent cations explicitly while keeping the implicit screening effect due to monovalent ions. Our theory captures both the inner shell and outer shell coordination of divalent cations to phosphate groups, which we demonstrate is crucial for an accurate calculation of RNA folding thermodynamics. The RISM theory for ion–phosphate interactions when combined with simulations based on a transferable coarse-grained model allows us to predict accurately the folding of several RNA molecules in a mixture containing monovalent and divalent ions. The calculated folding free energies and ion-preferential coefficients for RNA molecules (pseudoknots, a fragment of the rRNA, and the aptamer domain of the adenine riboswitch) are in excellent agreement with experiments over a wide range of monovalent and divalent ion concentrations. Because the theory is general, it can be readily used to investigate ion and sequence effects on DNA properties.

Although it is known that RNA undergoes liquid-liquid phase separation (LLPS), the interplay between the molecular driving forces and the emergent features of the condensates, such as their morphologies and dynamical properties, is not well understood. We introduce a coarse-grained model to simulate phase separation of trinucleotide repeat RNAs, which are implicated in neurological disorders such as Huntington disease and amyotrophic lateral sclerosis. After establishing that the simulations reproduce key experimental findings (length and concentration dependence of the phase transition in (CAG) n repeats), we show that once recruited inside the liquid droplets, the monomers transition from hairpin-like structures to extended states. Interactions between the monomers in the condensates result in the formation of an intricate and dense intermolecular network, which severely restrains the fluctuations and mobilities of the RNAs inside large droplets. In the largest densely packed high viscosity droplets, the mobility of RNA chains is best characterized by reptation, reminiscent of the dynamics in polymer melts.

The highly charged RNA molecules, with each phosphate carrying a single negative charge, cannot fold into well-defined architectures with tertiary interactions, in the absence of ions. For ribozymes, divalent cations are known to be more efficient than monovalent ions in driving them to a compact state although Mg 2+ ions are needed for catalytic activities. Therefore, how ions interact with RNA is relevant in understanding RNA folding. It is often thought that most of the ions are territorially and non-specifically bound to the RNA, as predicted by the counterion condensation (CIC) theory. Here, we show using simulations of Azoarcus ribozyme, based on an accurate coarse-grained Three Site Interaction (TIS) model, with explicit divalent and monovalent cations, that ion condensation is highly specific and depends on the nucleotide position. The regions with high coordination between the phosphate groups and the divalent cations are discernible even at very low Mg 2+ concentrations when the ribozyme does not form tertiary interactions. Surprisingly, these regions also contain the secondary structural elements that nucleate subsequently in the self-assembly of RNA, implying that ion condensation is determined by the architecture of the folded state. These results are in sharp contrast to interactions of ions (monovalent and divalent) with rigid charged rods in which ion condensation is uniform and position independent. The differences are explained in terms of the dramatic non-monotonic shape fluctuations in the ribozyme as it folds with increasing Mg 2+ or Ca 2+ concentration.