Kinshuk Banerjee

Entropic estimate of cooperative binding of substrate on a single oligomeric enzyme: An index of cooperativity

Here we have systematically studied the cooperative binding of substrate molecules on the active sites of a single oligomeric enzyme in a chemiostatic condition. The average number of bound substrate and the net velocity of the enzyme catalyzed reaction are studied by the formulation of stochastic master equation for the cooperative binding classified here as spatial and temporal. We have estimated the entropy production for the cooperative binding schemes based on single trajectory analysis using a kinetic Monte Carlo technique. It is found that the total as well as the medium entropy production shows the same generic diagnostic signature for detecting the cooperativity, usually characterized in terms of the net velocity of the reaction. This feature is also found to be valid for the total entropy production rate at the non-equilibrium steady state. We have introduced an index of cooperativity, C, defined in terms of the ratio of the surprisals or equivalently, the stochastic system entropy associated with the fully bound state of the cooperative and non-cooperative cases. The criteria of cooperativity in terms of C is compared with that of the Hill coefficient of some relevant experimental result and gives a microscopic insight on the mechanism of cooperative binding of substrate on a single oligomeric enzyme which is usually estimated from the macroscopic reaction rate.

Spectra of conjugated polymer aggregates : Symmetry of the interchain dressed states

Here we consider an interchain interaction model to understand the spectral properties of aggregate of a class of conjugated polymers. The dressed eigenstates are calculated for the equivalent and inequivalent chain dimers and are symmetry classified. We have provided the Wigner function matrix to describe the quantum interference due to nonadiabaticity in the excitonic states, the energy distribution between the chains as well as the phase relation between the vibrational modes. The various disorder-induced effects on the spectra can be explained by the dimeric chains that are generally inequivalent.

Entropy production of a mechanically driven single oligomeric enzyme: a consequence of fluctuation theorem

In this work we have shown how an applied mechanical force affects an oligomeric enzyme kinetics in a chemiostatic condition where the statistical characteristics of random walk of the substrate molecules over a finite number of active sites of the enzyme plays important contributing factors in governing the overall rate and nonequilibrium thermodynamic properties. The analytical results are supported by the simulation of single trajectory based approach of entropy production using Gillespie’s stochastic algorithm. This microscopic numerical approach not only gives the macroscopic entropy production from the mean of the distribution of entropy production which depends on the force but also a broadening of the distribution by the applied mechanical force, a kind of power broadening. In the nonequilibrium steady state (NESS), both the mean and the variance of the distribution increases and then saturates with the rise in applied force corresponding to the situation when the net rate of product formation reaches a limiting value with an activationless transition. The effect of the system-size and force on the entropy production distribution is shown to be constrained by the detailed fluctuation theorem.

Electronic–nuclear entanglement in a conjugated polymer aggregate with a conical intersection: spectral signatures

We have studied the role of the electronic–nuclear entanglement in the emission properties of two interacting conjugated polymer chains forming an aggregate. The effect of disorder generally found in these systems is realized through a torsional degree of freedom which is responsible for a conical intersection of the adiabatic potential energy surfaces of the two excitonic states. The transition of the spectral nature of the aggregate from dimeric to monomeric form appears at the conical intersection point with vanishing entanglement of the emitting excitonic state. It is characterized by the nontrivial dependence of the emission rate for two perpendicular polarizations as a function of the torsion angle corresponding to different static disordered configurations. The exciton population dynamics shows direct connection to the entanglement evolution with the oscillations in population giving maximally entangled states as well as entanglement sudden death. A thorough analysis of the reduced densities of the nuclear degrees of freedom reveals that these extrema of entanglement can be connected to the passage of the system through the conical intersection for the range of interaction strength generally found in these systems.

Nonequilibrium thermodynamics and a fluctuation theorem for individual reaction steps in a chemical reaction network

We have introduced an approach to nonequilibrium thermodynamics of an open chemical reaction network in terms of the propensities of the individual elementary reactions and the corresponding reverse reactions. The method is a microscopic formulation of the dissipation function in terms of the relative entropy or Kullback-Leibler distance which is based on the analogy of phase space trajectory with the path of elementary reactions in a network of chemical process. We have introduced here a fluctuation theorem valid for each opposite pair of elementary reactions which is useful in determining the contribution of each sub-reaction on the nonequilibrium thermodynamics of overall reaction. The methodology is applied to an oligomeric enzyme kinetics at a chemiostatic condition that leads the reaction to a nonequilibrium steady state for which we have estimated how each step of the reaction is energy driven or entropy driven to contribute to the overall reaction.

Dynamic memory of a single voltage-gated potassium ion channel: A stochastic nonequilibrium thermodynamic analysis

In this work, we have studied the stochastic response of a single voltage-gated potassium ion channel to a periodic external voltage that keeps the system out-of-equilibrium. The system exhibits memory, resulting from time-dependent driving, that is reflected in terms of dynamic hysteresis in the current-voltage characteristics. The hysteresis loop area has a maximum at some intermediate voltage frequency and disappears in the limits of low and high frequencies. However, the (average) dissipation at long-time limit increases and finally goes to saturation with rising frequency. This raises the question: how diminishing hysteresis can be associated with growing dissipation? To answer this, we have studied the nonequilibrium thermodynamics of the system and analyzed different thermodynamic functions which also exhibit hysteresis. Interestingly, by applying a temporal symmetry analysis in the high-frequency limit, we have analytically shown that hysteresis in some of the periodic responses of the system does not vanish. On the contrary, the rates of free energy and internal energy change of the system as well as the rate of dissipative work done on the system show growing hysteresis with frequency. Hence, although the current-voltage hysteresis disappears in the high-frequency limit, the memory of the ion channel is manifested through its specific nonequilibrium thermodynamic responses.

Enzyme efficiency: An open reaction system perspective

A measure of enzyme efficiency is proposed for an open reaction network that, in suitable form, applies to closed systems as well. The idea originates from the description of classical enzyme kinetics in terms of cycles. We derive analytical expressions for the efficiency measure by treating the network not only deterministically but also stochastically. The latter accounts for any significant amount of noise that can be present in biological systems and hence reveals its impact on efficiency. Numerical verification of the results is also performed. It is found that the deterministic equation overestimates the efficiency, the more so for very small system sizes. Roles of various kinetics parameters and system sizes on the efficiency are thoroughly explored and compared with the standard definition k2/KM. Study of substrate fluctuation also indicates an interesting efficiency-accuracy balance.

On the flux-force partitioning and non-equilibrium thermodynamics near a steady state

The flux-force linear relationship is a basic building block in the development of irreversible thermodynamics near equilibrium. Here, we explore the fate of this relationship near a steady state in a finer detail by partitioning the fluxes and the forces into time-independent and time-dependent components. To this end, we use a master equation approach without assuming the condition of detailed balance. The connection of the flux-force components with various state functions and path functions provides a detailed picture of the variations of such quantities in terms of the deviation of probabilities from the steady state. Pilot calculations on an exactly-solvable case furnish insights into the energy-balance mechanism for non-equilibrium systems, revealing additionally how an out-of-equilibrium scenario can be favorable in realizing a minimized free energy state.

Emission rate, vibronic entanglement, and coherence in aggregates of conjugated polymers.

Here we have studied a dimer model of conjugated polymer aggregates based on the traditional J and H structures, with the extension in treating the electronic and vibrational degrees of freedom at par. We have considered various exchange symmetries corresponding to the parameters of the excited state Hamiltonian in assigning the symmetry of the vibronic states of the aggregate, going beyond the homodimer case. The emission rates are determined as a function of system parameters at low temperature for both types of aggregates. We have also determined the vibronic entanglement as a measure of the coupled electronic and vibrational motion as well as the exciton coherence number in the emitting state. As a function of interchain interaction strength, emission rate and entanglement grossly follow similar trends for the J-aggregate and opposite trends for the H-aggregate in totally symmetric as well as asymmetric cases. Variation of other system parameters, like electronic excitation energy and electron-vibration coupling parameter are also thoroughly investigated in governing these quantities. The role of symmetry of the wave function in governing the spectra and the exciton coherence are also analyzed thoroughly, which offers a way to realize the connection between such macroscopic and microscopic quantum features.

Realization of vibronic entanglement in terms of tunneling current in an artificial molecule

Based on the concept of molecular nonadiabatic processes, namely, curve crossing and electronic interstate coupling, here we have introduced a model of an artificial molecule composed of three coupled quantum dots in terms of displaced harmonic oscillators of the confinement potential. We have shown that the static and dynamic features of vibronic entanglement can be realized in terms of the tunneling current in our model. An entanglement sudden-death can be shown to be equivalent to the suppression of tunneling current at the appropriate parameters of the magnetic field. We have also provided the nonclassicality of the vibration of the dot confinement potential which maximizes at the anticrossing zone.