Udayan Mohanty

Probing the α‐Helical Structural Stability of Stapled p53 Peptides: Molecular Dynamics Simulations and Analysis

Reactivation of the p53 cell apoptosis pathway through inhibition of the p53‐hDM2 interaction is a viable approach to suppress tumor growth in many human cancers and stabilization of the helical structure of synthetic p53 analogs via a hydrocarbon cross‐link (staple) has been found to lead to increased potency and inhibition of protein–protein binding (J. Am. Chem. Soc. 129: 5298). However, details of the structure and dynamic stability of the stapled peptides are not well understood. Here, we use extensive all‐atom molecular dynamics simulations to study a series of stapled α‐helical peptides over a range of temperatures in solution. The peptides are found to exhibit substantial variations in predicted α‐helical propensities that are in good agreement with the experimental observations. In addition, we find significant variation in local structural flexibility of the peptides with the position of the linker, which appears to be more closely related to the observed differences in activity than the absolute α‐helical stability. These simulations provide new insights into the design of α‐helical stapled peptides and the development of potent inhibitors of α‐helical protein–protein interfaces.

Thermodynamic interpretation of the scaling of the dynamics of supercooled liquids.

The recently discovered scaling law for the relaxation times, tau(T,upsilon) = I(Tupsilon(gamma)), where T is temperature and upsilon the specific volume, is derived by a revision of the entropy model of the glass transition dynamics originally proposed by Avramov [J. Non-Cryst. Solids 262, 258 (2000)]. In this modification the entropy is calculated by an alternative route. The resulting expression for the variation of the relaxation time with T and upsilon is shown to accurately fit experimental data for several glass-forming liquids and polymers over an extended range encompassing the dynamic crossover. From this analysis, which is valid for any model in which the relaxation time is a function of the entropy, we find that the scaling exponent gamma can be identified with the Gruneisen constant.The recently discovered scaling law for the relaxation times, tau=f(T,V^g), where T is temperature and V the specific volume, is derived by a revision of the entropy model of the glass transition dynamics originally proposed by Avramov [I. Avramov, J. Non-Cryst. Solids 262, 258 (2000).]. In this modification the entropy is calculated by an alternative route, while retaining the approximation that the heat capacity is constant with T and P. The resulting expression for the variation of the relaxation time with T and V is shown to accurately fit experimental data for several glass-forming liquids and polymers over an extended range encompassing the dynamic crossover. From this analysis, which is valid for any model in which the relaxation time is a function of the entropy. we find that the scaling exponent g can be identified with the Gruneisen constant.

Exponential intermolecular dynamics in optical Kerr effect spectroscopy of small-molecule liquids

Optical Kerr effect spectroscopy has been employed to study the behavior of six symmetric-top liquids (acetonitrile, acetonitrile-d3, benzene, carbon disulfide, chloroform, and methyl iodide) over a broad range of temperatures. In all of the liquids, an exponential intermolecular response is observed on a time scale of a few hundreds of femtoseconds. Comparison of the temperature dependence of the time scale of this relaxation with the viscosity and single-molecule and collective orientational times in the liquids suggests that the exponential relaxation arises from motional narrowing.

A lattice field theory for polymer systems with nearest‐neighbor interaction energies

We generalize a lattice field theory that formally provides an exact description of the statistical mechanical entropy of nonoverlapping flexible polymers to enable treatment of nearest‐neighbor interaction energies. The theory is explicitly solved within an extended mean field approximation for a system of polymer chains and voids, and we also provide mean field results for polymer–solvent–void and binary blend–void mixtures. In addition to recovering the Flory–Huggins mean field approximation for these systems, our extended definition of the mean field approximation contains a set of corrections to Flory–Huggins theory in the form of an expansion in powers of the nearest‐neighbor interaction energies.

A lattice model for self‐avoiding polymers with controlled length distributions. II. Corrections to Flory–Huggins mean field

We continue the analysis of the lattice spin‐field theory which is introduced in paper I and which formally gives the exact entropy for a set of completely flexible self‐avoiding polymers on a lattice. The model allows for arbitrary chain length distributions and arbitrary polymer volume fractions. Use of random fields produces a field theory from which Flory–Huggins results are recovered in the mean field limit. Here we recast the mean field formulation to allow for the rigorous and systematic evaluation of corrections by means of a cluster expansion. We then calculate corrections to the mean field directly up to fourth order and provide a systematic diagrammatic method for evaluating general order corrections. Our results illustrate the polymer concentration dependence of the corrections to the Flory–Huggins mean field results as well as provide the origins for the entropic contribution to the Flory χ parameter and its concentration dependence. Generalizations to treat rods and semiflexible polymers wil...

A density functional-variational treatment of the hard sphere transition

A density functional-variational version of the Ramakrishnan-Yussouff theory of freezing is used to reconsider the problem of the hard sphere transition. This calculation differs from previous ones in that the solid density and the lattice constant are included as independent variational parameters. Besides giving an unambiguous method for determining the lattice constant of the solid this method allows the computation of the average density of defects in the solid. In addition, we use real, rather than Fourier, space techniques in solving the resulting equations. We argue that real space techniques are numerically more accurate for the narrow distributions found by these methods. Our results for the densities of the coexisting solid and liquid phases are very close to those given by molecular dynamics studies. The width of the solid density peaks is too small as is the case with previous calculations. The average density of defects has the correct sign but is much too large (ρD ⋍ -0·1) for a realistic solid.

Compact and ordered collapse of randomly generated RNA sequences

As the raw material for evolution, arbitrary RNA sequences represent the baseline for RNA structure formation and a standard to which evolved structures can be compared. Here, we set out to probe, using physical and chemical methods, the structural properties of RNAs having randomly generated oligonucleotide sequences that were of sufficient length and information content to encode complex, functional folds, yet were unbiased by either genealogical or functional constraints. Typically, these unevolved, nonfunctional RNAs had sequence-specific secondary structure configurations and compact magnesium-dependent conformational states comparable to those of evolved RNA isolates. But unlike evolved sequences, arbitrary sequences were prone to having multiple competing conformations. Thus, for RNAs the size of small ribozymes, natural selection seems necessary to achieve uniquely folding sequences, but not to account for the well-ordered secondary structures and overall compactness observed in nature.

Magnesium fluctuations modulate RNA dynamics in the SAM-I riboswitch.

Experiments demonstrate that Mg(2+) is crucial for structure and function of RNA systems, yet the detailed molecular mechanism of Mg(2+) action on RNA is not well understood. We investigate the interplay between RNA and Mg(2+) at atomic resolution through ten 2-μs explicit solvent molecular dynamics simulations of the SAM-I riboswitch with varying ion concentrations. The structure, including three stemloops, is very stable on this time scale. Simulations reveal that outer-sphere coordinated Mg(2+) ions fluctuate on the same time scale as the RNA, and that their dynamics couple. Locally, Mg(2+) association affects RNA conformation through tertiary bridging interactions; globally, increasing Mg(2+) concentration slows RNA fluctuations. Outer-sphere Mg(2+) ions responsible for these effects account for 80% of Mg(2+) in our simulations. These ions are transiently bound to the RNA, maintaining interactions, but shuttled from site to site. Outer-sphere Mg(2+) are separated from the RNA by a single hydration shell, occupying a thin layer 3-5 Å from the RNA. Distribution functions reveal that outer-sphere Mg(2+) are positioned by electronegative atoms, hydration layers, and a preference for the major groove. Diffusion analysis suggests transient outer-sphere Mg(2+) dynamics are glassy. Since outer-sphere Mg(2+) ions account for most of the Mg(2+) in our simulations, these ions may change the paradigm of Mg(2+)-RNA interactions. Rather than a few inner-sphere ions anchoring the RNA structure surrounded by a continuum of diffuse ions, we observe a layer of outer-sphere coordinated Mg(2+) that is transiently bound but strongly coupled to the RNA.

The elastic constants of condensed matter: A direct‐correlation function approach

We describe a simple, systematic and physically transparent method for calculating the elastic constants of condensed matter. This approach is equally useful when applied to such diverse materials as alkali halides and nematic and smectic A liquid crystals, as we report in this paper. Our analysis involves regarding the periodic density of the ordered phase to be representable as a small perturbation to the uniform density distribution of the corresponding fluid phase. We implement this idea by making use of recent work on the density wave theory of freezing and the statistical mechanics of nonuniform systems. The theory makes the role of the structure of the medium explicit while leaving the role of the intermolecular potential implicit. We find, for example, that the elastic constants of an alkali halide crystal can be expressed in terms of the curvatures of the Fourier transforms of the charge–charge and number–number direct correlation functions of the corresponding fluid evaluated at the reciprocal l...

Counterion condensation on ionic oligomers

The Ramanathan-Woodbury formulas representing the charge density critical for the onset of counterion condensation on finite-length polymers are derived by three alternate methods, an extension of Debye-Huckel theory, a theory of end effects, and by density functional theory. For charged oligomers with length of the same order as the Debye length, the threshold for condensation is the same as for polymers of length much greater than the Debye lenght. However, the threshold depends both on length and salt concentration if the oligomer is shorter than the Debye length, in such a way as to recede to infinity as the ratio of oligomer length to Debye length tends to zero (i.e., condensation vanishes in this limit). The extended Debye-Huckel theory additionally provides a new result for the partition function of the condensed layer, showing that the free energy of the condensed counterions is different on an oligomer and a polymer, even when the fractional extent of condensation is the same. The end effect theory discloses a hitherto unnoticed connection between the number of counterions condensed at the ends of a long polymer and the number condensed on a short oligomer.