All-atom structure-based model of RNA. Our description of RNA is based on all-atom structure-based model (SBM), which incorporates all heavy atoms. The potential is designed so that native contacts are energetically stabilized and would lead to energy landscapes, which are smoother. The minimum of energy in the SBM is computed to be that given by the crystal structure. Geometric parameters in the structure-based potential that describe harmonic motions of bonds and bond angles, including planar or improper terms, are defined by the values they acquire in the crystal structure. Native local contacts are described by attractive 6-12 potential. Excluded volume interactions between Mg2+- Mg2+ and Mg2+-RNA ions are of the form Γ -12. Energetic parameters in SBM are also calibrated.
We are carrying out all-atom structure-based model MD simulations to investigate properties such as excess ion atmosphere around an RNA in aqueous solution containing Group-II (Mg2+) and Group-I (X+) cations from added salts. Other experimentally relevant quantities of interest to us are the difference in the free energies of Mg2+-RNA interactions between extended and compact states ensembles; the characteristics of the dense outer-sphere population of ions that govern the competitive displacement of monovalent counterions (X+) by divalent counterions (Mg2+), polyelectrolyte effects beyond the native basin. The RNAs that are being investigated are pseudoknot RNA, Tar- Tar* RNA kissing loops, and group IIB introns.
Figure.The excess Mg2+ ion atmosphere around SAM-I riboswitch as predicted by structure-based model simulation is compared with explicit solvent simulations and non-linear Poisson-Boltzmann analysis. Uncertainty in analysis is plotted as error bars. There are no experimental data on Γ 2+ at 100 mM KCl. Compared with explicitly solvent simulations, Γ 2+ predicted by SBM is higher. K+ dehydrates in explicit solvent simulations This pushes Mg2+ away and K+ associates with RNA more effectively. NMR experiments indicate that K+ remains hydrated in presence of RNA.
Generalization of Manning counterion condensation model for RNA. We have developed an electrostatic model for any RNA in aqueous solution by statistical mechanical generalization of Manning theory. In this approach, monovalent ions are treated implicitly, full atomic structure of the RNA is included, and we have only placed charges on the phosphates. The charges interact by Debye-Hückel electrostatics. We have synthesized the electrostatics with the all-atom structure-based MD simulations of RNA in which divalent ions described explicitly. The overall potential is expressed in terms of Manning condensation variables for counterions and coions, particle coordinates, and atomic coordinates of RNA. This characteristic allows calculation of forces. It is this feature of the generalized counterion condensation model that permits quantitative interpretation of the number of excess Mg2+ associated with the RNA, Mg2+-RNA interaction free energies, as well as assessment of the two metrics with experimental data.
Rare fluctuations. Chemical reactions generally involve a wide range of time scales from femtosecond to seconds. Chemical reactions and conformation changes in macromolecules could involve large thermal fluctuations. Such activated processes lead to wide separation of time scales. A fundamental problem is the development of theoretical tools to describe rare fluctuations in systems for which reaction pathways are not known. To address this problem, we are developing and making use of a variety of techniques from stochastic process to supersymmetry, Morse theory, stochastic partial differential equation, and min-max principle methodology for solving Hamilton-Jacobi equations. We have recently shown that the probability of such a rare process is localized around the most likely configuration. This configuration is obtained by minimizing an action functional with an appropriate constraint.
Figure. Rare event: ternary complex in the ribosome undergoes large thermal fluctuation (denoted by xc ). These fluctuations involve configurational searches that are in the tail end of the probability distribution.