Allostery and conformational free energy changes in human tryptophanyl-tRNA synthetase from essential dynamics and structure networks

The interdependence of the concept of allostery and enzymatic catalysis, and they being guided by conformational mobility is gaining increased prominence. However, to gain a molecular level understanding of llostery and hence of enzymatic catalysis, it is of utter importance that the networks of amino acids participating in allostery be deciphered. Our lab has been exploring the methods of network analysis combined with molecular dynamics simulations to understand allostery at molecular level. Earlier we had outlined methods to obtain communication paths and then to map the rigid/flexible regions of proteins through network parameters like the shortest correlated paths, cliques, and communities. In this article, we advance the methodology to estimate the conformational populations in terms of cliques/communities formed by interactions including the side-chains and then to compute the ligand-induced population shift. Finally, we obtain the free-energy landscape of the protein in equilibrium, characterizing the free-energy minima accessed by the protein complexes. We have chosen human tryptophanyl-tRNA synthetase (hTrpRS), a protein esponsible for charging tryptophan to its cognate tRNA during protein biosynthesis for this investigation. This is a multidomain protein exhibiting excellent allosteric communication. Our approach has provided valuable structural as well as functional insights into the protein. The methodology adopted here is highly generalized to illuminate the linkage between protein structure networks and conformational mobility involved in the allosteric mechanism in any protein with known structure.

Beyond fractional derivatives: local approximation of other convolution integrals

Dynamic systems involving convolution integrals with decaying kernels, of which fractionally damped systems form a special case, are non-local in time and hence infinite dimensional. Straightforward numerical solution of such systems up to time t needs O(t(2)) computations owing to the repeated evaluation of integrals over intervals that grow like t. Finite-dimensional and local approximations are thus desirable. We present here an approximation method which first rewrites the evolution equation as a coupled in finite-dimensional system with no convolution, and then uses Galerkin approximation with finite elements to obtain linear, finite-dimensional, constant coefficient approximations for the convolution. This paper is a broad generalization, based on a new insight, of our prior work with fractional order derivatives (Singh & Chatterjee 2006 Nonlinear Dyn. 45, 183-206). In particular, the decaying kernels we can address are now generalized to the Laplace transforms of known functions; of these, the power law kernel of fractional order differentiation is a special case. The approximation can be refined easily. The local nature of the approximation allows numerical solution up to time t with O(t) computations. Examples with several different kernels show excellent performance. A key feature of our approach is that the dynamic system in which the convolution integral appears is itself approximated using another system, as distinct from numerically approximating just the solution for the given initial values; this allows non-standard uses of the approximation, e. g. in stability analyses.

The dynamics of magnetically trapped fluids. I - Implications for umbral dots and penumbral grains

A study of the magnetohydrodynamic system in which a nonmagnetized fluid in a gravitational field is surrounded by a fluid carrying a vertical magnetic field is presented. It is pointed out that this study can throw some light on the fine-structural features of a sunspot. The equilibrium configuration of the field-free fluid is a tapering column ending at an apex. The regions away form the apex can be studied by the slender flux tube approximation. A scheme developed to treat the apex indicates that, just below the apex, the radius of the tapering column opens up with a 3/2 power dependence on the depth below the apex. If the internal pressure of the field-free fluid is increased, the apex rises, and a static equilibrium may not be possible beyond a limit if the magnetic pressure drops quickly above a certain height. The nature of steady-flow solutions beyond this limit is investigated. Under conditions inside a sunspot, a column of field-free gas is found to rise with a velocity of about 100 km/hr. If umbral dots and penumbral grains are interpreted as regions where the field-free gas ultimately emerges, a very natural explanation of most of their observed properties is obtained.

A Model of Anomalous Chain Translocation Dynamics

A model of polymer translocation based on the stochastic dynamics of the number of monomers on one side of a pore-containing surface is formulated in terms of a one-dimensional generalized Langevin equation, in which the random force is assumed to be characterized by long-ranged temporal correlations. The model is introduced to rationalize anomalies in measured and simulated values of the average time of passage through the pore, which in general cannot be satisfactorily accounted for by simple Brownian diffusion mechanisms. Calculations are presented of the mean first passage time for barrier crossing and of the mean square displacement of a monomeric segment, in the limits of strong and weak diffusive bias. The calculations produce estimates of the exponents in various scaling relations that are in satisfactory agreement with available data.

An Insight to the Dynamics of Conserved Water Molecular Triad in IMPDH II (Human): Recognition of Cofactor and Substrate to Catalytic Arg 322

Inosine 5' monophosphate dehydrogenase (IMPDH II) is a key enzyme involved in the de novo biosynthesis pathway of purine nucleotides and is also considered to be an excellent target for cancer inhibitor design. The conserve R 322 residue (in human) is thought to play some role in the recognition of inhibitor and cofactor through the catalytic D 364 and N 303. The 15 ns simulation and the water dynamics of the three different PDB structures (1B3O, 1NF7, and 1NFB) of human IMPDH by CHARMM force field have clearly indicated the involvement of three conserved water molecules (W-L, W-M, and W-C) in the recognition of catalytic residues (R 322, D 364, and N 303) to inhibitor and cofactor. Both the guanidine nitrogen atoms (NH1 and NH 2) of the R 322 have anchored the di- and mono-nucleotide (cofactor and inhibitor) binding domains via the conserved W-C and W-L water molecules. Another conserved water molecule W-M seems to bridge the two domains including the R 322 and also the W-C and W-L through seven centers H-bonding coordination. The conserved water molecular triad (W-C - W-M - W-L) in the protein complex may thought to play some important role in the recognition of inhibitor and cofactor to the protein through R 322 residue.

A multistep transversal linearization (MTL) method in non-linear dynamics through a Magnus characterization

A new form of a multi-step transversal linearization (MTL) method is developed and numerically explored in this study for a numeric-analytical integration of non-linear dynamical systems under deterministic excitations. As with other transversal linearization methods, the present version also requires that the linearized solution manifold transversally intersects the non-linear solution manifold at a chosen set of points or cross-section in the state space. However, a major point of departure of the present method is that it has the flexibility of treating non-linear damping and stiffness terms of the original system as damping and stiffness terms in the transversally linearized system, even though these linearized terms become explicit functions of time. From this perspective, the present development is closely related to the popular practice of tangent-space linearization adopted in finite element (FE) based solutions of non-linear problems in structural dynamics. The only difference is that the MTL method would require construction of transversal system matrices in lieu of the tangent system matrices needed within an FE framework. The resulting time-varying linearized system matrix is then treated as a Lie element using Magnus’ characterization [W. Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math., VII (1954) 649–673] and the associated fundamental solution matrix (FSM) is obtained through repeated Lie-bracket operations (or nested commutators). An advantage of this approach is that the underlying exponential transformation could preserve certain intrinsic structural properties of the solution of the non-linear problem. Yet another advantage of the transversal linearization lies in the non-unique representation of the linearized vector field – an aspect that has been specifically exploited in this study to enhance the spectral stability of the proposed family of methods and thus contain the temporal propagation of local errors. A simple analysis of the formal orders of accuracy is provided within a finite dimensional framework. Only a limited numerical exploration of the method is presently provided for a couple of popularly known non-linear oscillators, viz. a hardening Duffing oscillator, which has a non-linear stiffness term, and the van der Pol oscillator, which is self-excited and has a non-linear damping term.

Buckled nano rod - a two state system: quantum effects on its dynamics

We consider a suspended elastic rod under longitudinal compression. The compression can be used to adjust potential energy for transverse displacements from the harmonic to the double well regime. The two minima in potential energy curve describe two possible buckled states. Using transition state theory (TST) we have calculated the rate of conversion from one state to other. If the strain epsilon = 4 epsilon c the simple TST rate diverges. We suggest a method to correct this divergence for quantum calculations. We also find that zero point energy contributions can be quite large so that single mode calculations can lead to large errors in the rate.

Dynamics and control of buckling type devices using SMA wire integrated beam

An analysis and design study using Shape Memory Alloy (SMA) wire integrated beam and its buckling shape control are reported. The dynamical system performance is analyzed with a mathematical set-up involving nonlocal and rate sensitive kinetics of phase transformation in the SMA wire. A standard phenomenological constitutive model reported by Brinson (1993) is modified by considering certain consistency conditions in the material property tensors and by eliminating spurious singularity. Considering the inhomogeneity effects, a finite element model of the SMA wire is developed. Simulations are carried out to study the buckling shape control of a beam integrated with SMA wire.

Fractional damping: Stochastic origin and finite approximations

Fractional-order derivatives appear in various engineering applications including models for viscoelastic damping. Damping behavior of materials, if modeled using linear, constant coefficient differential equations, cannot include the long memory that fractional-order derivatives require. However, sufficiently great rnicrostructural disorder can lead, statistically, to macroscopic behavior well approximated by fractional order derivatives. The idea has appeared in the physics literature, but may interest an engineering audience. This idea in turn leads to an infinite-dimensional system without memory; a routine Galerkin projection on that infinite-dimensional system leads to a finite dimensional system of ordinary differential equations (ODEs) (integer order) that matches the fractional-order behavior over user-specifiable, but finite, frequency ranges. For extreme frequencies (small or large), the approximation is poor. This is unavoidable, and users interested in such extremes or in the fundamental aspects of true fractional derivatives must take note of it. However, mismatch in extreme frequencies outside the range of interest for a particular model of a real material may have little engineering impact.

Insight into the early stages of thermal unfolding of peanut agglutinin by molecular dynamics simulations

Peanut agglutinin is a homotetrameric nonglycosylated protein. The protein has a unique open quaternary structure. Molecular dynamics simulations have been employed follow the atomistic details of its unfolding at different temperatures. The early events of the deoligomerization of the protein have been elucidated in the present study. Simulation trajectories of the monomer as well as those of the tetramer have been compared and the tetramer is found to be substantially more stable than its monomeric counterpart. The tetramer shows retention of most of its.. secondary structure but considerable loss of the tertiary structure at high temperature. e generation of a This observation impies the molten globule-like intermediate in the later stages of deoligomerization. The quaternary structure of the protein has weakened to a large extent, but none of the subunits are separated. In addition, the importance of the metal-binding to the stability of the protein structure has also been investigated. Binding of the metal ions not only enhances the local stability of the metal-ion binding loop, but also imparts a global stability to the overall structure. The dynamics of different interfaces vary significantly as probed through interface clusters. The differences are substantially enhanced at higher temperatures. The dynamics and the stability of the interfaces have been captured mainly by cluster analysis, which has provided detailed information on the thermal deoligomerization of the protein.

Dynamics after a sweep through a quantum critical point

The coherent quantum evolution of a one-dimensional many-particle system after slowly sweeping the Hamiltonian through a critical point is studied using a generalized quantum Ising model containing both integrable and nonintegrable regimes. It is known from previous work that universal power laws of the sweep rate appear in such quantities as the mean number of excitations created by the sweep. Several other phenomena are found that are not reflected by such averages: there are two different scaling behaviors of the entanglement entropy and a relaxation that is power law in time rather than exponential. The final state of evolution after the quench is not characterized by any effective temperature, and the Loschmidt echo converges algebraically for long times, with cusplike singularities in the integrable case that are dynamically broadened by nonintegrable perturbations.

Landau-Zener problem with waiting at the minimum gap and related quench dynamics of a many-body system

We discuss a technique for solving the Landau-Zener (LZ) problem of finding the probability of excitation in a two-level system. The idea of time reversal for the Schrodinger equation is employed to obtain the state reached at the final time and hence the excitation probability. Using this method, which can reproduce the well-known expression for the LZ transition probability, we solve a variant of the LZ problem, which involves waiting at the minimum gap for a time t(w); we find an exact expression for the excitation probability as a function of t(w). We provide numerical results to support our analytical expressions. We then discuss the problem of waiting at the quantum critical point of a many-body system and calculate the residual energy generated by the time-dependent Hamiltonian. Finally, we discuss possible experimental realizations of this work.

Melting of an Anchored Bilayer: Molecular Dynamics Simulations of the Structural Transition in (CnH2n+1NH3)(2)PbI4 (n=12, 14, 16, 18)

The thermally driven Structural phase transition in the organic-inorganic hybrid perovskite (CnH2n+1NH3)(2)PbI4 has been investigated using molecular dynamics (MD) simulations. This system consists of positively charged alkyl-amine chains anchored to a rigid negatively charged PbI4 sheet with the chains organized as bilayers with a herringbone arrangement. Atomistic simulations were performed using ail isothermal-isobaric ensemble over a wide temperature range from 65 to 665 K for different alkyl chain lengths, n = 12, 14, 16, and 18. The simulations are able to reproduce the essential Features of the experimental observations of this system, including the existence of a transition, the linear variation of the transition temperature with alkyl chain length, and the expansion of the bilayer thickness at the transition. By use of the distance fluctuation Criteria, it is Shown that the transition is associated With a Melting of the alkyl chains of the anchored bilayer. Ail analysis of the conformation of the alkyl chains shows increased disorder in the form of gauche defects above due melting transition. Simulations also show that the melting transition is characterized by the complete disappearance of all-trans alkyl chains in the anchored bilayer, in agreement with experimental observations. A conformationally disordered chain has a larger effective cross-sectional area, and above due transition a uniformly tilted arrangement of the anchored chains call no longer be Sustained. At the melt the angular distribution of the orientation of the chains are 110 longer uniform; the chains are splayed allowing for increased space for individual chains of the anchored bilayer. This is reflected in a sharp rise in the ratio of the mean head-to-head to tail-to-tail distance of the chains of the bilayer at the transition resulting in in expansion of the bilayer thickness. The present MD simulations provide a simple explanation as to how changes in conformation of individual alkyl-chains gives rise to the observed increase in the interlayer lattice spacing of (CnH2n+1NH3)(2)PbI4 at the melting transition.