Geometric Phase, Curvature, and Extrapotentials in Constrained Quantum Systems

We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian depends on quantities which are external to the constraint manifold, such as the external curvature of the constraint manifold, the (Riemannian) curvature of the ambient space, and the constraining potential. In particular, we find the remarkable fact that the twisting of the constraining potential appears as a gauge potential in the constrained Hamiltonian. This gauge potential is an example of geometric phase, closely related to that originally discussed by Berry. The constrained Hamiltonian also contains an effective potential depending on the external curvature of the constraint manifold, the curvature of the ambient space, and the twisting of the constraining potential. The general nature of our analysis allows applications to a wide variety of problems, such as rigid molecules, the evolution of molecular systems along reaction paths, and quantum strip waveguides.Comment: 27 pages with 1 figure, submitted to Phys. Rev.

Wetting problem for multi-component fluid mixtures

In this paper we propose an extension of the Cahn method to binary mixtures and study the problem of wetting near a two-phase critical point without any assumption on the form of intermolecular potentials. A comparison between Cahn's method and later works by Sullivan, Evans et al is made. By using an expression of the energy of interaction between solid surface and liquids proposed recently by Gouin, we obtain the equations of density profiles and the boundary conditions on a solid surface. In the case of a convex free energy, a one-dimensional solution of a linear problem is proposed for the density profiles between a bulk and on a solid wall. A non-linear model of binary mixtures extending Cahn's results for simple fluids is also studied. For the case of a purely attractive wall we have established a criterion of a first order transition in terms of the structure of the level set of the homogeneous part of the free energy. Additively, explicit expressions of density profiles near the wall are proposed. They allow one to consider the adsorption of mixture components by a solid wall.Comment: 20 pages and 4 figure

A new ultrafast and high-throughput mass spectrometric approach for the therapeutic drug monitoring of the multi-targeted anti-folate pemetrexed in plasma from lung cancer patients

An analytical assay has been developed and validated for ultrafast and high-throughput mass spectrometric determination of pemetrexed concentrations in plasma using matrix assisted laser desorption/ionization–triple quadrupole–tandem mass spectrometry. Patient plasma samples spiked with the internal standard methotrexate were measured by multiple reaction monitoring. The detection limit was 0.4 fmol/μL, lower limit of quantification was 0.9 fmol/μL, and upper limit of quantification was 60 fmol/μL, respectively. Overall observed pemetrexed concentrations in patient samples ranged between 8.7 (1.4) and 142.7 (20.3) pmol/μL (SD). The newly developed mass spectrometric assay is applicable for (routine) therapeutic drug monitoring of pemetrexed concentrations in plasma from non-small cell lung cancer patients

Stabilization of oscillations in a phase transition model

In this paper we analyze a model presenting formation of microstructure depending on the parameters and the initial data. In particular we investigate how the presence of stochastic perturbations affects this phenomenon in its asymptotic behavior. Two different sufficient conditions are provided in order to prevent the formation of microstructure: the first one for Stratonovich’s noise while the second for Itˆo’s noise. The main contribution of the paper is that these conditions are independent of the initial values unlike in the deterministic model. Thus, we can interpret our results as some kind of stabilization produced by both types of noise.Fondo Europeo de Desarrollo RegionalMinisterio de Economía y CompetitividadJunta de Andalucí

Analytical approximations for spatial stochastic gene expression in single cells and tissues

Gene expression occurs in an environment in which both stochastic and diffusive effects are significant. Spatial stochastic simulations are computationally expensive compared with their deterministic counterparts, and hence little is currently known of the significance of intrinsic noise in a spatial setting. Starting from the reaction–diffusion master equation (RDME) describing stochastic reaction–diffusion processes, we here derive expressions for the approximate steady-state mean concentrations which are explicit functions of the dimensionality of space, rate constants and diffusion coefficients. The expressions have a simple closed form when the system consists of one effective species. These formulae show that, even for spatially homogeneous systems, mean concentrations can depend on diffusion coefficients: this contradicts the predictions of deterministic reaction–diffusion processes, thus highlighting the importance of intrinsic noise. We confirm our theory by comparison with stochastic simulations, using the RDME and Brownian dynamics, of two models of stochastic and spatial gene expression in single cells and tissues

Exploring the Free Energy Landscape: From Dynamics to Networks and Back

The knowledge of the Free Energy Landscape topology is the essential key to understand many biochemical processes. The determination of the conformers of a protein and their basins of attraction takes a central role for studying molecular isomerization reactions. In this work, we present a novel framework to unveil the features of a Free Energy Landscape answering questions such as how many meta-stable conformers are, how the hierarchical relationship among them is, or what the structure and kinetics of the transition paths are. Exploring the landscape by molecular dynamics simulations, the microscopic data of the trajectory are encoded into a Conformational Markov Network. The structure of this graph reveals the regions of the conformational space corresponding to the basins of attraction. In addition, handling the Conformational Markov Network, relevant kinetic magnitudes as dwell times or rate constants, and the hierarchical relationship among basins, complete the global picture of the landscape. We show the power of the analysis studying a toy model of a funnel-like potential and computing efficiently the conformers of a short peptide, the dialanine, paving the way to a systematic study of the Free Energy Landscape in large peptides.Comment: PLoS Computational Biology (in press

Fixation, transient landscape and diffusion's dilemma in stochastic evolutionary game dynamics

Agent-based stochastic models for finite populations have recently received much attention in the game theory of evolutionary dynamics. Both the ultimate fixation and the pre-fixation transient behavior are important to a full understanding of the dynamics. In this paper, we study the transient dynamics of the well-mixed Moran process through constructing a landscape function. It is shown that the landscape playing a central theoretical "device" that integrates several lines of inquiries: the stable behavior of the replicator dynamics, the long-time fixation, and continuous diffusion approximation associated with asymptotically large population. Several issues relating to the transient dynamics are discussed: (i) multiple time scales phenomenon associated with intra- and inter-attractoral dynamics; (ii) discontinuous transition in stochastically stationary process akin to Maxwell construction in equilibrium statistical physics; and (iii) the dilemma diffusion approximation facing as a continuous approximation of the discrete evolutionary dynamics. It is found that rare events with exponentially small probabilities, corresponding to the uphill movements and barrier crossing in the landscape with multiple wells that are made possible by strong nonlinear dynamics, plays an important role in understanding the origin of the complexity in evolutionary, nonlinear biological systems.Comment: 34 pages, 4 figure

Quantizing Constrained Systems: New Perspectives

We consider quantum mechanics on constrained surfaces which have non-Euclidean metrics and variable Gaussian curvature. The old controversy about the ambiguities involving terms in the Hamiltonian of order hbar^2 multiplying the Gaussian curvature is addressed. We set out to clarify the matter by considering constraints to be the limits of large restoring forces as the constraint coordinates deviate from their constrained values. We find additional ambiguous terms of order hbar^2 involving freedom in the constraining potentials, demonstrating that the classical constrained Hamiltonian or Lagrangian cannot uniquely specify the quantization: the ambiguity of directly quantizing a constrained system is inherently unresolvable. However, there is never any problem with a physical quantum system, which cannot have infinite constraint forces and always fluctuates around the mean constraint values. The issue is addressed from the perspectives of adiabatic approximations in quantum mechanics, Feynman path integrals, and semiclassically in terms of adiabatic actions.Comment: 11 pages, 2 figure

An exact expression to calculate the derivatives of position-dependent observables in molecular simulations with flexible constraints

In this work, we introduce an algorithm to compute the derivatives of physical observables along the constrained subspace when flexible constraints are imposed on the system (i.e., constraints in which the hard coordinates are fixed to configuration-dependent values). The presented scheme is exact, it does not contain any tunable parameter, and it only requires the calculation and inversion of a sub-block of the Hessian matrix of second derivatives of the function through which the constraints are defined. We also present a practical application to the case in which the sought observables are the Euclidean coordinates of complex molecular systems, and the function whose minimization defines the constraints is the potential energy. Finally, and in order to validate the method, which, as far as we are aware, is the first of its kind in the literature, we compare it to the natural and straightforward finite-differences approach in three molecules of biological relevance: methanol, N-methyl-acetamide and a tri-glycine peptideComment: 13 pages, 8 figures, published versio