A minimal kinetic model for the interpretation of complex catalysis in single enzyme molecules.

Multi-exponential waiting-time distribution and randomness parameter greater than unity ascribe dynamic disorder in single-enzyme catalysis corroborated to the interplay of transforming conformers [English et al., Nat. Chem. Biol., 2006, 2, 87]. The associated multi-state model of enzymatic turnovers with statically heterogeneous catalytic rates misdescribes the non-linear uprising of the randomness parameter from unity in relation to the attributes of the fall-offs of the waiting-time distribution at different substrate concentrations. To resolve this crucial issue, we first employ a comprehensive stochastic reaction scenario and further rationalize and work out the minimal indispensable dynamic-disorder model that ensures the foregoing relationship upon comparison with the data. We elucidate that specific disregard for the transition rate coefficients in the multi-state model on account of the especially slow conformational transitions is the underlying reason for not achieving interrelation between the observables.

Nonequilibrium thermodynamic signatures of collective dynamical states around chimera in a chemical reaction network.

Different dynamical states ranging from coherent, incoherent to chimera, multichimera, and related transitions are addressed in a globally coupled nonlinear continuum chemical oscillator system by implementing a modified complex Ginzburg-Landau equation. Besides dynamical identifications of observed states using standard qualitative metrics, we systematically acquire nonequilibrium thermodynamic characterizations of these states obtained via coupling parameters. The nonconservative work profiles in collective dynamics qualitatively reflect the time-integrated concentration of the activator, and the majority of the nonconservative work contributes to the entropy production over the spatial dimension. It is illustrated that the evolution of spatial entropy production and semigrand Gibbs free-energy profiles associated with each state are connected yet completely out of phase, and these thermodynamic signatures are extensively elaborated to shed light on the exclusiveness and similarities of these states. Moreover, a relationship between the proper nonequilibrium thermodynamic potential and the variance of activator concentration is established by exhibiting both quantitative and qualitative similarities between a Fano factor like entity, derived from the activator concentration, and the Kullback-Leibler divergence associated with the transition from a nonequilibrium homogeneous state to an inhomogeneous state. Quantifying the thermodynamic costs for collective dynamical states would aid in efficiently controlling, manipulating, and sustaining such states to explore the real-world relevance and applications of these states.

Glycolytic Wave Patterns in a Simple Reaction-diffusion System with Inhomogeneous Influx: Dynamic Transitions.

An inhomogeneous profile of chemostatted species generates a rich variety of patterns in glycolytic waves depicted in a Selkov reaction-diffusion framework here. A key role played by diffusion amplitude and symmetry in the chemostatted species profile in dictating the fate of local spatial dynamics involving periodic, quasiperiodic, and chaotic patterns and transitions among them are investigated systematically. More importantly, various dynamic transitions, including wave propagation direction changes, are illustrated in interesting situations. Besides numerical results, our analytical formulation of the amplitude equation connecting complex Ginzburg-Landau and Lambda-omega representation shed light on the phase dynamics of the system. This systematic study of the glycolytic reaction-diffusion wave is in line with previous experimental results in open spatial reactor and will provide a knowledge about the dynamics that shape and control biological information processing and related phenomena.

Nonequilibrium thermodynamic characterization of chimeras in a continuum chemical oscillator system.

The emergence of the chimera state as the counterintuitive spatial coexistence of synchronous and asynchronous regimes is addressed here in a continuum chemical oscillator system by implementing a relevant complex Ginzburg-Landau equation with global coupling. This study systematically acquires and characterizes the evolution of nonequilibrium thermodynamic entities corresponding to the chimera state. The temporal evolution of the entropy production rate exhibits a beat pattern with a series of equidistant spectral lines in the frequency domain. Symmetric profiles associated with the incoherent regime appear in descriptions of the dynamics and thermodynamics of the chimera. It is shown that identifying the semigrand Gibbs free energy of the state as the Gabor elementary function can reveal the guiding role of the information uncertainty principle in shaping the chimera energetics.

Universality in bio-rhythms: A perspective from nonlinear dynamics.

Bio-rhythms are ubiquitous in all living organisms. A prototypical bio-rhythm originates from the chemical oscillation of intermediates or metabolites around the steady state of a thermodynamically open bio-chemical reaction network with autocatalysis and feedback and is often described by minimal kinetics with two state variables. It has been shown that notwithstanding the diverse nature of the underlying bio-chemical and biophysical processes, the associated kinetic equations can be mapped into the universal form of the Lie´nard equation which admits of mono-rhythmic and bi-rhythmic solutions. Several examples of bio-kinetic schemes are examined to illustrate this universality.

ApoE ε4 and IL-6-174G/C Polymorphism may Lead to Early Onset of Alzheimer's Disease with Atypical Presentation.

BACKGROUND: Alzheimer's disease (AD) is the most common cause of dementia. Although genetic mutations are known in rare familial form, exact cause of neurodegeneration in sporadic AD is still unknown. While ApoE ε4 and IL-6 C-174G/C patterns have been found to increase the risk of AD in Caucasians, the results are inconsistent in other ethnic groups. OBJECTIVE: The aim of this study was to evaluate the effect of ApoE and IL-6-174G/C polymorphisms among patients of AD in the Eastern part of India. MATERIALS AND METHODS: Consecutive patients of probable AD diagnosed as per National Institute on Aging-Alzheimer's Association (NIA-AA) criteria with age, gender, and education-matched healthy controls were recruited between December 2015 and September 2018. Patients were clinically evaluated and along with controls were genotyped for ApoE and IL-6-174G/C polymorphisms by the polymerase chain reaction method. RESULTS: A total 115 patients and 162 controls showed a similar pattern of ApoE and IL-6-174G/C polymorphism pattern. While ε3ε3 and GG patterns were the commonest, followed by ε3ε4 and GC pattern in ApoE and IL-6 respectively, the effect of ApoE ε4 and IL-6-174 C allele on AD symptoms could not be established. However, patients with onset before 50 years were found to have significantly higher proportion of ApoE ε4 and C allele of IL-6-174 in comparison to patients with onset above 50. These young patients were also having more atypical presentation than their older counterpart. CONCLUSION: Our study revealed a novel role of both ApoE ε4 and C allele of IL-6-174 together in developing early onset AD with more atypical clinical features.

Nonequilibrium thermodynamics of glycolytic traveling wave: Benjamin-Feir instability.

Evolution of the nonequilibrium thermodynamic entities corresponding to dynamics of the Hopf instabilities and traveling waves at a nonequilibrium steady state of a spatially extended glycolysis model is assessed here by implementing an analytically tractable scheme incorporating a complex Ginzburg-Landau equation (CGLE). In the presence of self and cross diffusion, a more general amplitude equation exploiting the multiscale Krylov-Bogoliubov averaging method serves as an essential tool to reveal the various dynamical instability criteria, especially Benjamin-Feir (BF) instability, to estimate the corresponding nonlinear dispersion relation of the traveling wave pattern. The critical control parameter, wave-number selection criteria, and magnitude of the complex amplitude for traveling waves are modified by self- and cross-diffusion coefficients within the oscillatory regime, and their variabilities are exhibited against the amplitude equation. Unlike the traveling waves, a low-amplitude broad region appears for the Hopf instability in the concentration dynamics as the system phase passes through minima during its variation with the control parameter. The total entropy production rate of the uniform Hopf oscillation and glycolysis wave not only qualitatively reflects the global dynamics of concentrations of intermediate species but almost quantitatively. Despite the crucial role of diffusion in generating and shaping the traveling waves, the diffusive part of the entropy production rate has a negligible contribution to the system's total entropy production rate. The Hopf instability shows a more complex and colossal change in the energy profile of the open nonlinear system than in the traveling waves. A detailed analysis of BF instability shows a contrary nature of the semigrand Gibbs free energy with discrete and continuous wave numbers for the traveling wave. We hope the Hopf and traveling wave pattern around the BF instability in terms of energetics and dissipation will open up new applications of such dynamical phenomena.

A Revisit to Turnover Kinetics of Individual Escherichia coli ß-Galactosidase Molecules.

Single-molecule experiments on ß-galactosidase from Escherichia coli that catalyzes the hydrolysis of resorufin-ß-d-galactopyranoside revealed important observations like fluctuating catalytic rate, memory effects arising from temporal correlations between the enzymatic turnovers and nonexponential waiting time distributions. The root cause of the observed results is intrinsic fluctuations among the different conformers of the active species, during the course of the reaction, thereby imparting dynamic disorder in the system under investigation. Originally, a multistate stochastic kinetic theory was employed that, despite satisfying the measured waiting time distributions and the mean waiting times at different substrate concentrations, yields a constant estimate of the randomness parameter. Inevitably, this manifests a strong disagreement with the substrate-concentration-dependent time variations of the said distribution, which at the same time misinterprets the measured magnitudes of the randomness parameter at lower concentrations. Here, we suggest a dual approach to the single-enzyme reaction, independently, making important improvements over the parent study and the recently suggested two-state stochastic analyses followed by quantitative rationalization of the experimental data. In the first case, an off-pathway mechanism satisfied the Michaelis-Menten equation under the circumstance of prevailing disorder while tested against the single-molecule data. However, recovery of randomness data in the lower-concentration regime, albeit primarily marks a significant refinement, a qualitative agreement at the growing concentrations seems to be reasoned by an account of switching among the limited numbers of discrete conformers. Consequently, in the second case, we circumvented the conventional way of approaching the enzyme catalysis and mapped the dynamics of structural transitions of the biocatalyst with the temporal fluctuations of the spatial distance between the different locations along a coarse-grained polymer chain. Exploiting a general mechanism for dynamic disorder, a reaction-diffusion formalism yielded an analytical expression for the waiting time distribution of the enzymatic turnovers, from which the mean waiting time and the randomness parameter were readily determined. Application of our results to the findings of the experiment on single ß-galactosidase shows a quantitative agreement in each case. This soundly validates the usefulness of accounting for a more rigorous microscopic description pertinent to the conformational multiplicity in rationalizing the real-time data over the routine state-based sketch of the reaction system.

Electron-Vibration Entanglement of Resonating Dimers in Quantum Transport.

Electron transport in a single molecule resulting from the superposition of its vibronic states depends on the coupling strength with the metallic leads. However, dynamical coherence and Fermionic correlation in molecule-molecule and molecule-lead coupling necessitates a critical approach to treat the current and its noise level, especially in the presence of a variable external bias for temperature-dependent conduction. Primarily, this work is a generalization of the theoretical approach of the atomic dimers to incorporate the effect of vibrational modes in current and conductance characteristics. The variation of current and differential conductance due to the external bias reveals a vibrational Coulomb blockade structure corresponding to the functioning vibrational mode in the system. The numerical demonstration for a diverse class of molecules generically shows that electron-vibration interaction can quantitatively predict the nature of coherent electron transport and current noise. Secondly, an attempt has been made to illustrate the effect of magnitude of coherence-induced noise suppression of current as a signature of electron-vibration entanglement. Finally, temperature-dependent conductance of the molecular junction in dimer structure has been estimated along with the peak shifts due to the applied gate voltage.

On the Role of Magnesium Ions in the DNA-Scissoring Activity of the Restriction Endonuclease ApaI: Stochastic Kinetics from a Single Molecule to Mesoscopic Paradigm.

Biochemical reactions occurring inside cells have significant stochastic signatures due to the low copy number of reacting species. Kinetics of DNA cleavage by restriction endonucleases are no exception as established by single-molecule experiments. Here, we propose a simple reaction scheme to understand the role of the cofactor magnesium ion in the action of the endonuclease ApaI. The methodology is based on the waiting time distribution of cleavage product formation that enables us to determine the corresponding rate both analytically and numerically. The theory is developed at the single-molecule level and then generalized to the biologically relevant case of a population of DNA-endonuclease complexes present inside a cell. The theoretical rate versus cofactor concentration curve is matched with relevant single-molecule experimental data that reveals positive cooperativity of cofactor binding and provides a reliable estimate of model parameters. Furthermore, a parameter range is identified where the dispersion of the waiting time, measured using the coefficient of variation, is significantly lower than the Poisson limit and becomes minimum at the in vivo magnesium ion concentration level. Such low dispersion can play a role in the robust DNA-scissoring activity of ApaI under in vivo conditions.

Kinetics of Allosteric Inhibition of Single Enzyme by Product Molecules.

Single-molecule experiment probed the catalytic conversions of Amplex Red to resorufin by horseradish peroxidase in which the product molecules were found to act as the allosteric inhibitor for the individual enzyme. While broad distributions of the initial reaction velocities and the number of product molecules required to cease the reaction unraveled the underlying dynamic disorder in the reaction pathway, bulk experimental measurements established the particularity of noncompetitive inhibition of the enzyme species. In this work, to rationalize the observed phenomena, we present a stochastic kinetic model of the enzymatic reaction taking into account the inhibitions of the enzyme and enzyme-substrate complex in the circumstance of their structural fluctuations. Starting from a chemical master equation that can further be reduced into a set of ordinary differential equations for the case of single-enzyme kinetics, we derived an analytical expression for the turnover time distribution, the first moment of which yielded the mean turnover time. The inverse of the latter showed excellent agreement with the bulk data of the initial enzymatic velocities measured in the presence of varying inhibitor concentrations. This supports the observed nature of inhibition which we further confirmed by constructing double-reciprocal plots for the inhibited kinetics. In addition, we successfully recovered ensemble data from another experiment that redesigned the aforesaid single-molecule catalysis to investigate the effects of molecular crowders on reaction velocity; the latter was greatly alleviated with increasing the molecular weight of the crowders. On the other hand, the calculated randomness parameter, determined from the higher moment of the turnover time distribution, clearly inferred dynamic disorder in the catalytic turnovers. Our work under a unified framework provides a robust theoretical description for the experimental kinetic study and eradicates the necessity of assuming an alternative mode of inhibition in analyzing the data, not consistent with the experiments, considered earlier.

An Exactly Solvable Stochastic Kinetic Theory of Single-Molecule Force Experiments.

The unfolding of a protein in single-molecule pulling experiments subjected to a constant force (force-clamp) and constant velocity (force-ramp) is analyzed by introducing an exactly solvable two-state kinetic model framed based on the general stochastic approach of discrete state and continuous time formulation. The effect of perturbation is interpreted in the presence of dynamic disorder, resulting from intrinsic conformational fluctuations, by deriving an exact analytical expression for the unfolding time distribution, which in turn allowed us to calculate the expressions for the quantities of experimental interest explicitly. In particular, the novelty of our method lies in the fact that it reduced the need for a lengthy calculation, contrary to the previous dynamic disorder studies, and provides a fairly concise but sufficient mathematical analysis, which becomes much easier to implement quantitatively. We tested our results against the measured data from a number of force unfolding experiments on various proteins, ubiquitin, titin, and filamin, and the force unzipping of DNA and observed excellent agreement in each case. This asserts the reliability of the present technique, which suggests a plausible extension of the stochastic kinetic theory in single-molecule force experiments beyond its present-day widespread implications.

Stochastic Kinetic Approach to the Escape of DNA Hairpins from an α-Hemolysin Channel.

Escape experiments probed the dynamics of DNA hairpins inside a membrane-embedded α-hemolysin channel, which revealed the orientation and voltage-dependent nature of the DNA-pore interactions. The mean escape times measured at different assisting voltages were strongly influenced by these interactions. Clearly, an escape process from the nanopore was stochastic in nature that occurred in milliseconds. In this paper, we present a new methodology for describing the experimental observations based on the stochastic kinetic approach of discrete-state and continuous-time formulations. Our model considers that a hairpin attains different states inside and out of the pore, and we derived the expression for the escape time distribution from which survival probability of the hairpin that still exists inside the nanopore is determined. On the other hand, the first moment of the above distribution readily yields the mean escape time. Importantly, we show that the recovery of the experimental results was possible taking into account the slow structural fluctuations of the combined DNA-pore system. Additional investigation tested the profound influence of conformational dynamics by considering a pure kinetic scheme, which satisfied the measured data only partially. Therefore, the single stochastic framework suggested here provides a powerful tool that leads to a significant improvement in the theoretical analysis of the experimental results over a range of applied voltages by removing the inadequacy of the original attempt constructed following a number of formulations in the absence of intrinsic fluctuations.

Mechanical Unfolding of Single Polyubiquitin Molecules Reveals Evidence of Dynamic Disorder.

Mechanical unfolding of single polyubiquitin molecules subjected to a constant stretching force showed nonexponentiality in the measured probability density of unfolding (waiting time distribution) and the survival probability of the folded state during the course of the measurements. These observations explored the relevance of disorder present in the system under study with implications for a static disorder approach to rationalize the experimental results. Here, an approach for dynamic disorder is presented based on Zwanzig's fluctuating bottleneck (FB) model, in which the rate of the reaction is controlled by the passage through the cross-sectional area of the bottleneck. The radius of the latter undergoes stochastic fluctuations that in turn is described in terms of the end-to-end distance fluctuations of the Rouse-like dynamics using a non-Markovian generalized Langevin equation with a memory kernel and Gaussian colored noise. Our results are comprised of analytical expressions for the survival probability and waiting time distribution, which show excellent agreement with the experimental data throughout the range of the applied forces. In addition, by fitting the survival probabilities at different stretching forces, we quantify two system parameters, namely, the average free energy ΔG av and the average distance to the transition state Δx av, both perfectly recovered the experimental estimates. These agreements validate the present model of polymer dynamics, which captures the very essence of dynamic disorder in single-molecule pulling experiments.

Energetic and entropic cost due to overlapping of Turing-Hopf instabilities in the presence of cross diffusion.

A systematic introduction to nonequilibrium thermodynamics of dynamical instabilities are considered for an open nonlinear system beyond conventional Turing pattern in presence of cross diffusion. An altered condition of Turing instability in presence of cross diffusion is best reflected through a critical control parameter and wave number containing both the self- and cross-diffusion coefficients. Our main focus is on entropic and energetic cost of Turing-Hopf interplay in stationary pattern formation. Depending on the relative dispositions of Turing-Hopf codimensional instabilities from the reaction-diffusion equation it clarifies two aspects: energy cost of pattern formation, especially how Hopf instability can be utilized to dictate a stationary concentration profile, and the possibility of revealing nonequilibrium phase transition. In the Brusselator model, to understand these phenomena, we have analyzed through the relevant complex Ginzberg-Landau equation using multiscale Krylov-Bogolyubov averaging method. Due to Hopf instability it is observed that the cross-diffusion parameters can be a source of huge change in free-energy and concentration profiles.

MnO2 flowery nanocomposites for efficient and fast removal of mercury(ii) from aqueous solution: a facile strategy and mechanistic interpretation.

We report the synthesis of MnO2 flowery nanocomposites consisting of MnO2 nanoflowers grown over the surface of clay nanomaterials using an easy and green approach. The MnO2 nanocomposites were explored as a cost-effective nanoadsorbent for mercury removal from aqueous solution and they demonstrated excellent efficiency towards mercury uptake. Monolayer molecular adsorption of Hg(ii) was attained over the surface of the MnO2 nanocomposites and the experimental data acquired in the kinetic study demonstrated that the Hg(ii) adsorption kinetics proceeded via a pseudo-second-order kinetic model. pH dependent adsorption study revealed that their sorption capacity increases until pH 7.0 and then gradually decreases with increasing pH. Apart from the experimental study, we have provided a mechanistic interpretation to illustrate the mechanism of kinetics and thermodynamics during Hg(ii) adsorption. Theoretical understanding along with experimental results indicates a spontaneous and highly favorable Hg(ii) uptake up to 50 °C, representing endothermicity of the adsorption process and then exothermicity above 50 °C, resulting in reduced sorption capacity. The exceptional adsorption performance of the MnO2 nanocomposites may be attributed to their negative surfaces, which facilitated the binding of positively charged Hg(ii) ions through electrostatic interaction. Hence, MnO2 nanocomposites proved to be an effective and inexpensive nanoadsorbent for the removal of Hg(ii) from aqueous solution and may hold a promise for wastewater treatment.

The guiding role of dissipation in kinetic proofreading networks: Implications for protein synthesis.

Major biological polymerization processes achieve remarkable accuracy while operating out of thermodynamic equilibrium by utilizing the mechanism known as kinetic proofreading. Here, we study the interplay of the thermodynamic and kinetic aspects of proofreading by exploring the dissipation and catalytic rate, respectively, under the realistic constraint of fixed chemical potential difference. Theoretical analyses reveal no-monotonic variations of the catalytic rate and total entropy production rate (EPR), the latter quantifying the dissipation, at steady state. Applying this finding to a tRNA selection network in protein synthesis, we observe that the network tends to maximize both the EPR and catalytic rate, but not the accuracy. Simultaneously, the system tries to minimize the ratio of the EPRs due to the proofreading steps and the catalytic steps. Therefore, dissipation plays a guiding role in the optimization of the catalytic rate in the tRNA selection network of protein synthesis.

Large deviation theory for the kinetics and energetics of turnover of enzyme catalysis in a chemiostatic flow.

In the framework of large deviation theory, we have characterized nonequilibrium turnover statistics of enzyme catalysis in a chemiostatic flow with externally controllable parameters, like substrate injection rate and mechanical force. In the kinetics of the process, we have shown the fluctuation theorems in terms of the symmetry of the scaled cumulant generating function (SCGF) in the transient and steady state regime and a similar symmetry rule is reflected in a large deviation rate function (LDRF) as a property of the dissipation rate through boundaries. Large deviation theory also gives the thermodynamic force of a nonequilibrium steady state, as is usually recorded experimentally by a single molecule technique, which plays a key role responsible for the dynamical symmetry of the SCGF and LDRF. Using some special properties of the Legendre transformation, here, we have provided a relation between the fluctuations of fluxes and dissipation rates, and among them, the fluctuation of the turnover rate is routinely estimated but the fluctuation in the dissipation rate is yet to be characterized for small systems. Such an enzymatic reaction flow system can be a very good testing ground to systematically understand the rare events from the large deviation theory which is beyond fluctuation theorem and central limit theorem.

Clay-Based Nanocomposites as Recyclable Adsorbent toward Hg(II) Capture: Experimental and Theoretical Understanding.

Here, we report the development of inorganic-organic hybrid nanocomposites through selective modification of the negative outer surfaces of halloysite nanoclays with two different organosilanes having primary or secondary amine sites to be explored them as novel and cost-effective adsorbents for the extraction of toxic inorganic contaminants from aqueous solution. They possess excellent selectivity for the adsorption of mercury, which shows monolayer molecular adsorption over the nanocomposites. The adsorption kinetics of Hg(II) is very fast and follows pseudo-second-order model compared to pseudo-first-order model. A combined experimental and theoretical study demonstrated that Hg(II) uptake by these nanocomposites is highly favorable and spontaneous up to 40 °C, and beyond this temperature, the uptake capacity gradually reduced. Temperature-dependent adsorption study exhibits endothermicity at low temperature (≤40 °C) and exothermicity beyond 40 °C. pH-dependent adsorption study showed their high uptake capacity until pH 7, which reduced at alkaline pH. All of the nanocomposites hold excellent adsorption capacity even at low concentration of adsorbate, along with multicycle sorption capability. The outstanding adsorption capacity as well as the easy synthetic route to achieve these nanocomposites may attract researchers to develop low-cost adsorbents to capture toxic metals, which in turn regulate the permissible limit of these toxic metals in drinking water.

Nonequilibrium response of a voltage gated sodium ion channel and biophysical characterization of dynamic hysteresis.

Here we have studied the dynamic as well as the non-equilibrium thermodynamic response properties of voltage-gated Na-ion channel. Using sinusoidally oscillating external voltage protocol we have both kinetically and energetically studied the non-equilibrium steady state properties of dynamic hysteresis in details. We have introduced a method of estimating the work done associated with the dynamic memory due to a cycle of oscillating voltage. We have quantitatively characterised the loop area of ionic current which gives information about the work done to sustain the dynamic memory only for ion conduction, while the loop area of total entropy production rate gives the estimate of work done for overall gating dynamics. The maximum dynamic memory of Na-channel not only depends on the frequency and amplitude but it also depends sensitively on the mean of the oscillating voltage and here we have shown how the system optimize the dynamic memory itself in the biophysical range of field parameters. The relation between the average ionic current with increasing frequency corresponds to the nature of the average dissipative work done at steady state. It is also important to understand that the utilization of the energy from the external field can not be directly obtained only from the measurement of ionic current but also requires nonequilibrium thermodynamic study.