Escape kinetics of self-propelled particles from a circular cavity.

We numerically investigate the mean exit time of an inertial active Brownian particle from a circular cavity with single or multiple exit windows. Our simulation results witness distinct escape mechanisms depending on the relative amplitudes of the thermal length and self-propulsion length compared to the cavity and pore sizes. For exceedingly large self-propulsion lengths, overdamped active particles diffuse on the cavity surface, and rotational dynamics solely governs the exit process. On the other hand, the escape kinetics of a very weakly damped active particle is largely dictated by bouncing effects on the cavity walls irrespective of the amplitude of self-propulsion persistence lengths. We show that the exit rate can be maximized for an optimal self-propulsion persistence length, which depends on the damping strength, self-propulsion velocity, and cavity size. However, the optimal persistence length is insensitive to the opening windows' size, number, and arrangement. Numerical results have been interpreted analytically based on qualitative arguments. The present analysis aims at understanding the transport controlling mechanism of active matter in confined structures.

Information transmission in a two-step cascade: interplay of activation and repression.

We present an information-theoretic formalism to study signal transduction in four architectural variants of a model two-step cascade with increasing input population. Our results categorize these four types into two classes depending upon the effect of activation and repression on mutual information, net synergy, and signal-to-noise ratio. Using the Gaussian framework and linear noise approximation, we derive the analytic expressions for these metrics to establish their underlying relationships in terms of the biochemical parameters. We also verify our approximations through stochastic simulations.

Structure elucidation and construction of isomerisation pathways in small to moderate-sized (6-27) MgO nanoclusters: an adaptive mutation simulated annealing based analysis with quantum chemical calculations.

Determination of global minimum structures and elucidation of reaction paths or minimum energy paths between low-lying minima are of great chemical importance. To that end, we have used our own Adaptive Mutation Simulated Annealing method to determine the global minimum and the minimum energy paths for various isomerisation reactions for small to moderate-sized (MgO)n (n = 6-27) clusters, using the Born-Mayer potential with suitable parameter values. The minimum energy structures obtained by us match well with previously reported data and are used as guess structures for further optimisation at the DFT level (using the B3LYP functional and DGDZVP basis set). Our optimised structures are found to match very well with the further DFT optimised structures, where the comparison is done by determining the root mean square deviation values as well as the radial distribution function profiles. A scheme is proposed to determine the minimum energy paths for isomerisation reactions for some cluster sizes where the transition state/s obtained by us, at very low computational cost, match well with those obtained from further optimisation using DFT calculations. We have shown the efficacy of our method in determining the reaction pathways, even for cases that involve multi-step reactions.

Restricted information in a two-step cascade.

A cell must sense extracellular and intracellular fluctuations and respond appropriately to survive for optimal cellular functioning. Accordingly, a cell builds up biochemical networks which can transduce information of extracellular and intracellular fluctuations accurately. We consider a generic two-step cascade as a model gene regulatory network containing three regulatory proteins S, X, and Y connected as S→X→Y. The intermediate node X is a stochastic variable, acts as an obstacle, and impedes the information flow from S to Y. We quantify the information that is restricted by X using the tools of information theory and term this as restricted information. In this context, we further propose two measurable quantities, restricted efficiency and information transfer efficiency. The former determines how efficiently X restricts the upstream information coming from S, while the latter computes the efficiency of X to pass the upstream information toward Y. We also quantify the information that is being uniquely transferred from X to Y, which determines the extent of the ability of X to act as a source of information. Our analysis shows that when the signal strength (or mean population of S, 〈s〉) is low, the intermediate X can carry forward the upstream information reliably as well, as it acts as a better source of information, thereby increasing the fidelity of the network. But at the high signal strength, X restricts most of the upstream information, and its ability to act as a source of information gets reduced. This leads to a loss of fidelity of the network.

Role of the vibrational contribution in Coulomb explosion of dicationic neon gas clusters: a parallel tempering based study.

The problem of Coulomb explosion in dicationic neon gas clusters has been investigated with special emphasis on the role of the vibrational contribution. The problem has been handled by describing the dicationic neon gas system with an adequate potential energy surface comprising dispersive interaction, Coulombic and polarizability containing terms. This potential energy surface, if explored for various sizes of the clusters, shows Coulombic explosion features below a certain threshold size. However this classical treatment fails to account for the correct threshold predicted from other studies including experiments. This signifies that quantum effects play an important role. With the incorporation of the vibrational contribution as the quantum effect, it is seen that reduction in the threshold value indeed occurs and the amount of decrease significantly varies with temperature. The whole study has been done using the stochastic search strategy or parallel tempering to explore the potential energy surface of the system. The stochastic strategy guarantees the achievement of a low energy solution as it is not stuck in local energy basins.

Predicting stability limits for pure and doped dicationic noble gas clusters undergoing coulomb explosion: A parallel tempering based study.

We have used a replica exchange Monte-Carlo procedure, popularly known as Parallel Tempering, to study the problem of Coulomb explosion in homogeneous Ar and Xe dicationic clusters as well as mixed Ar-Xe dicationic clusters of varying sizes with different degrees of relative composition. All the clusters studied have two units of positive charges. The simulations reveal that in all the cases there is a cutoff size below which the clusters fragment. It is seen that for the case of pure Ar, the value is around 95 while that for Xe it is 55. For the mixed clusters with increasing Xe content, the cutoff limit for suppression of Coulomb explosion gradually decreases from 95 for a pure Ar to 55 for a pure Xe cluster. The hallmark of this study is this smooth progression. All the clusters are simulated using the reliable potential energy surface developed by Gay and Berne (Gay and Berne, Phys. Rev. Lett. 1982, 49, 194). For the hetero clusters, we have also discussed two different ways of charge distribution, that is one in which both positive charges are on two Xe atoms and the other where the two charges are at a Xe atom and at an Ar atom. The fragmentation patterns observed by us are such that single ionic ejections are the favored dissociating pattern. © 2017 Wiley Periodicals, Inc.

Beyond Born-Oppenheimer theory for ab initio constructed diabatic potential energy surfaces of singlet H3+ to study reaction dynamics using coupled 3D time-dependent wave-packet approach.

The workability of beyond Born-Oppenheimer theory to construct diabatic potential energy surfaces (PESs) of a charge transfer atom-diatom collision process has been explored by performing scattering calculations to extract accurate integral cross sections (ICSs) and rate constants for comparison with most recent experimental quantities. We calculate non-adiabatic coupling terms among the lowest three singlet states of H3+ system (11A', 21A', and 31A') using MRCI level of calculation and solve the adiabatic-diabatic transformation equation to formulate the diabatic Hamiltonian matrix of the same process [S. Mukherjee et al., J. Chem. Phys. 141, 204306 (2014)] for the entire region of nuclear configuration space. The nonadiabatic effects in the D+ + H2 reaction has been studied by implementing the coupled 3D time-dependent wave packet formalism in hyperspherical coordinates [S. Adhikari and A. J. C. Varandas, Comput. Phys. Commun. 184, 270 (2013)] with zero and non-zero total angular momentum (J) on such newly constructed accurate (ab initio) diabatic PESs of H3+. We have depicted the convergence profiles of reaction probabilities for the reactive non-charge transfer, non-reactive charge transfer, and reactive charge transfer processes for different collisional energies with respect to the helicity (K) and total angular momentum (J) quantum numbers. Finally, total and state-to-state ICSs are calculated as a function of collision energy for the initial rovibrational state (v = 0, j = 0) of the H2 molecule, and consequently, those quantities are compared with previous theoretical and experimental results.

An adaptive mutation simulated annealing based investigation of Coulombic explosion and identification of dissociation patterns in (CO2)n2+ clusters.

In this communication, we would like to discuss the advantages of adaptive mutation simulated annealing (AMSA) over standard simulated annealing (SA) in studying the Coulombic explosion of (CO2)n2+ clusters for n = 20-68, where 'n' is the size of the cluster. We have demonstrated how AMSA itself can overcome the predicaments which can arise in conventional SA and carry out the search for better results by adapting the parameters (only when needed) dynamically during the simulations so that the search process can come out of high energy basins and not go astray for better exploration and convergence, respectively. This technique also has in-built properties for getting more than one minimum in a single run. For a (CO2)n2+ cluster system we have found the critical limit to be n = 43, above which the attractive forces between individual units become greater in value than that of the large repulsive forces and the clusters stay intact as the energetically favoured isomers. This result is in good concurrence with earlier studies. Moreover, we have studied the fragmentation patterns for the entire size range and we have found fission type fragmentation as the favoured mechanism nearly for all sizes.

An investigation on the structure, spectroscopy and thermodynamic aspects of Br2((-))(H2O)n clusters using a conjunction of stochastic and quantum chemical methods.

In this work we obtained global as well as local structures of Br2((-))(H2O)n clusters for n = 2 to 6 followed by the study of IR-spectral features and thermochemistry for the structures. The way adopted by us to obtain structures is not the conventional one used in most cases. Here we at first generated excellent quality pre-optimized structures by exploring the suitable empirical potential energy surface using stochastic optimizer simulated annealing. These structures are then further refined using quantum chemical calculations to obtain the final structures, and spectral and thermodynamic features. We clearly showed that our approach results in very quick and better convergence which reduces the computational cost and obviously using the strategy we are able to get one [i.e. global] or more than one [i.e. global and local(s)] energetically lower structures than those which are already reported for a given cluster size. Moreover, IR-spectral results and the evolutionary trends in interaction energy, solvation energy and vertical detachment energy for global structures of each size have also been presented to establish the utility of the procedure employed.

Enhancing the branching ratios in the dissociation channels for O(16)O(16)O(18) molecule by designing optimum laser pulses: A study using stochastic optimization.

We propose a strategy of using a stochastic optimization technique, namely, simulated annealing to design optimum laser pulses (both IR and UV) to achieve greater fluxes along the two dissociating channels (O(18) + O(16)O(16) and O(16) + O(16)O(18)) in O(16)O(16)O(18) molecule. We show that the integrated fluxes obtained along the targeted dissociating channel is larger with the optimized pulse than with the unoptimized one. The flux ratios are also more impressive with the optimized pulse than with the unoptimized one. We also look at the evolution contours of the wavefunctions along the two channels with time after the actions of both the IR and UV pulses and compare the profiles for unoptimized (initial) and optimized fields for better understanding the results that we achieve. We also report the pulse parameters obtained as well as the final shapes they take.

Role of relaxation time scale in noisy signal transduction.

Intra-cellular fluctuations, mainly triggered by gene expression, are an inevitable phenomenon observed in living cells. It influences generation of phenotypic diversity in genetically identical cells. Such variation of cellular components is beneficial in some contexts but detrimental in others. To quantify the fluctuations in a gene product, we undertake an analytical scheme for studying few naturally abundant linear as well as branched chain network motifs. We solve the Langevin equations associated with each motif under the purview of linear noise approximation and derive the expressions for Fano factor and mutual information in close analytical form. Both quantifiable expressions exclusively depend on the relaxation time (decay rate constant) and steady state population of the network components. We investigate the effect of relaxation time constraints on Fano factor and mutual information to indentify a time scale domain where a network can recognize the fluctuations associated with the input signal more reliably. We also show how input population affects both quantities. We extend our calculation to long chain linear motif and show that with increasing chain length, the Fano factor value increases but the mutual information processing capability decreases. In this type of motif, the intermediate components act as a noise filter that tune up input fluctuations and maintain optimum fluctuations in the output. For branched chain motifs, both quantities vary within a large scale due to their network architecture and facilitate survival of living system in diverse environmental conditions.

Role of functionality in two-component signal transduction: a stochastic study.

We present a stochastic formalism for signal transduction processes in a bacterial two-component system. Using elementary mass action kinetics, the proposed model takes care of signal transduction in terms of a phosphotransfer mechanism between the cognate partners of a two-component system, viz., the sensor kinase and the response regulator. Based on the difference in functionality of the sensor kinase, the noisy phosphotransfer mechanism has been studied for monofunctional and bifunctional two-component systems using the formalism of the linear noise approximation. Steady-state analysis of both models quantifies different physically realizable quantities, e.g., the variance, the Fano factor (variance/mean), and mutual information. The resultant data reveal that both systems reliably transfer information of extracellular environment under low external stimulus and in a high-kinase-and-phosphatase regime. We extend our analysis further by studying the role of the two-component system in downstream gene regulation.

Breathing dynamics based parameter sensitivity analysis of hetero-polymeric DNA.

We study the parameter sensitivity of hetero-polymeric DNA within the purview of DNA breathing dynamics. The degree of correlation between the mean bubble size and the model parameters is estimated for this purpose for three different DNA sequences. The analysis leads us to a better understanding of the sequence dependent nature of the breathing dynamics of hetero-polymeric DNA. Out of the 14 model parameters for DNA stability in the statistical Poland-Scheraga approach, the hydrogen bond interaction ε(hb)(AT) for an AT base pair and the ring factor ξ turn out to be the most sensitive parameters. In addition, the stacking interaction ε(st)(TA-TA) for an TA-TA nearest neighbor pair of base-pairs is found to be the most sensitive one among all stacking interactions. Moreover, we also establish that the nature of stacking interaction has a deciding effect on the DNA breathing dynamics, not the number of times a particular stacking interaction appears in a sequence. We show that the sensitivity analysis can be used as an effective measure to guide a stochastic optimization technique to find the kinetic rate constants related to the dynamics as opposed to the case where the rate constants are measured using the conventional unbiased way of optimization.

Investigation of plausible mechanistic pathways in hydrogenation of η5-(C5H5)2Ta(H)=CH2: an analysis using DFT and AIM techniques.

In this manuscript, we investigate two plausible pathways for addition of H2 across the bond Ta=C in η5-(C5H5)2Ta(H)=CH2. One of the investigated reaction pathways involves a single concerted step with a four-membered transition state keeping the oxidation state of tantalum unaltered, where as the other pathway deals with a two step reaction with α-insertion of H2 to produce a 16e⁻ Ta(III)-methyl species and a subsequent oxidative addition. We must emphasize that an experimental study by Bregel et al. [J Am Chem Soc 2002, 124:13827-13832] on a derivative of the investigated chemical system in the present study showed that the two step strategy of α-insertion followed by subsequent oxidative addition is the preferred one. Our numerical investigations using DFT and AIM calculations lead to a similar conclusion. To establish our conclusion, we employ various basis sets to obtain the free energy of activation of the reaction. The AIM technique especially helps us to characterize the bond critical points at the optimized geometries of the reactants, products, transition states, and intermediates for the two step mechanism.

Structural, spectroscopic aspects, and electronic properties of (TiO2)n clusters: a study based on the use of natural algorithms in association with quantum chemical methods.

In this article, we propose a stochastic search-based method, namely genetic algorithm (GA) and simulated annealing (SA) in conjunction with density functional theory (DFT) to evaluate global and local minimum structures of (TiO2)n clusters with n = 1-12. Once the structures are established, we evaluate the infrared spectroscopic modes, cluster formation energy, vertical excitation energy, vertical ionization potential, vertical electron affinity, highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gaps, and so forth. We show that an initial determination of structure using stochastic techniques (GA/SA), also popularly known as natural algorithms as their working principle mimics certain natural processes, and following it up with density functional calculations lead to high-quality structures for these systems. We have shown that the clusters tend to form three-dimensional networks. We compare our results with the available experimental and theoretical results. The results obtained from SA/GA-DFT technique agree well with available theoretical and experimental data of literature.

A parallel tempering based study of Coulombic explosion and identification of dissociating fragments in charged noble gas clusters.

In this communication, we would like to test the feasibility of a parallel tempering based study of dissociation in dicationic noble gas clusters, namely, Ar(n)(2+), Kr(n)(2+), and Xe(n)(2+), where "n" is the size of the cluster units. We would like to find out the correct limit for sizes of each of these systems, above which the clusters stay intact as a single unit and does not dissociate into fragments by the process of Coulomb explosion. Moreover, we would also like to, for a specific case, i.e., Ar(n)(2+), study in detail the fragmentation patterns and point out the switchover from the non-fission way to the fission mechanism of dissociation. In all these calculations, we would like to analyse, how close we are in our predictions with that of experimental results. As a further check on the dissociating patterns found out by parallel tempering, we also conduct basin hopping based study on representative sizes of the clusters and find that parallel tempering, as used for this present work as an optimizer, is able to predict correct features when compared with other celebrated methods like the basin hopping algorithm.

Quantification of noise in bifunctionality-induced post-translational modification.

We present a generic analytical scheme for the quantification of fluctuations due to bifunctionality-induced signal transduction within the members of a bacterial two-component system. The proposed model takes into account post-translational modifications in terms of elementary phosphotransfer kinetics. Sources of fluctuations due to autophosphorylation, kinase, and phosphatase activity of the sensor kinase have been considered in the model via Langevin equations, which are then solved within the framework of linear noise approximation. The resultant analytical expression of phosphorylated response regulators are then used to quantify the noise profile of biologically motivated single and branched pathways. Enhancement and reduction of noise in terms of extra phosphate outflux and influx, respectively, have been analyzed for the branched system. Furthermore, the role of fluctuations of the network output in the regulation of a promoter with random activation-deactivation dynamics has been analyzed.

Selective bond breaking mediated by state specific vibrational excitation in model HOD molecule through optimized femtosecond IR pulse: a simulated annealing based approach.

The selective control of O-H/O-D bond dissociation in reduced dimensionality model of HOD molecule has been explored through IR+UV femtosecond pulses. The IR pulse has been optimized using simulated annealing stochastic approach to maximize population of a desired low quanta vibrational state. Since those vibrational wavefunctions of the ground electronic states are preferentially localized either along the O-H or O-D mode, the femtosecond UV pulse is used only to transfer vibrationally excited molecule to the repulsive upper surface to cleave specific bond, O-H or O-D. While transferring from the ground electronic state to the repulsive one, the optimization of the UV pulse is not necessarily required except specific case. The results so obtained are analyzed with respect to time integrated flux along with contours of time evolution of probability density on excited potential energy surface. After preferential excitation from [line]0, 0> ([line]m, n> stands for the state having m and n quanta of excitations in O-H and O-D mode, respectively) vibrational level of the ground electronic state to its specific low quanta vibrational state ([line]1, 0> or [line]0, 1> or [line]2, 0> or [line]0, 2>) by using optimized IR pulse, the dissociation of O-D or O-H bond through the excited potential energy surface by UV laser pulse appears quite high namely, 88% (O-H ; [line]1, 0>) or 58% (O-D ; [line]0, 1>) or 85% (O-H ; [line]2, 0>) or 59% (O-D ; [line]0, 2>). Such selectivity of the bond breaking by UV pulse (if required, optimized) together with optimized IR one is encouraging compared to the normal pulses.

Structure and spectroscopic aspects of water-halide ion clusters: a study based on a conjunction of stochastic and quantum chemical methods.

In this article, we propose a stochastic search based method, namely genetic algorithm in conjunction with density functional theory to evaluate structures of water-halide microclusters, with the halide ion being Cl(-), Br(-), and I(-). Once the structures are established, we evaluate the infrared spectroscopic modes, vertical detachment energies and natural population analysis based charges. We compare our results with available experimental and theoretical results.

Structure and spectroscopy of water-fluoride microclusters: a combined genetic algorithm and DFT-based study.

In this article, we explore the efficiency of using a coupled genetic algorithm (GA) and density functional theory (DFT) based strategy to evaluate probable structures of (H(2) O)(n) F(-) micro-clusters, with n = 1 - 6. We use the stochastic optimization technique of GA to arrive at structures of the cluster systems and once the structures are obtained, do a DFT calculation with the optimized coordinates from the GA calculation as input to get the infra-red spectrum of all the systems. The results of our work closely resembles the pure quantum chemical results obtained by Baik et al. (J Chem Phys 1999, 110, 9116-9127).