Heterogeneity of Stop Codon Readthrough in Single Bacterial Cells and Implications for Population Fitness.

Gene expression noise (heterogeneity) leads to phenotypic diversity among isogenic individual cells. Our current understanding of gene expression noise is mostly limited to transcription, as separating translational noise from transcriptional noise has been challenging. It also remains unclear how translational heterogeneity originates. Using a transcription-normalized reporter system, we discovered that stop codon readthrough is heterogeneous among single cells, and individual cells with higher UGA readthrough grow faster from stationary phase. Our work also revealed that individual cells with lower protein synthesis levels exhibited higher UGA readthrough, which was confirmed with ribosome-targeting antibiotics (e.g., chloramphenicol). Further experiments and mathematical modeling suggest that varied competition between ternary complexes and release factors perturbs the UGA readthrough level. Our results indicate that fluctuations in the concentrations of translational components lead to UGA readthrough heterogeneity among single cells, which enhances phenotypic diversity of the genetically identical population and facilitates its adaptation to changing environments.

Metabolic stress promotes stop-codon readthrough and phenotypic heterogeneity.

Accurate protein synthesis is a tightly controlled biological process with multiple quality control steps safeguarded by aminoacyl-transfer RNA (tRNA) synthetases and the ribosome. Reduced translational accuracy leads to various physiological changes in both prokaryotes and eukaryotes. Termination of translation is signaled by stop codons and catalyzed by release factors. Occasionally, stop codons can be suppressed by near-cognate aminoacyl-tRNAs, resulting in protein variants with extended C termini. We have recently shown that stop-codon readthrough is heterogeneous among single bacterial cells. However, little is known about how environmental factors affect the level and heterogeneity of stop-codon readthrough. In this study, we have combined dual-fluorescence reporters, mass spectrometry, mathematical modeling, and single-cell approaches to demonstrate that a metabolic stress caused by excess carbon substantially increases both the level and heterogeneity of stop-codon readthrough. Excess carbon leads to accumulation of acid metabolites, which lower the pH and the activity of release factors to promote readthrough. Furthermore, our time-lapse microscopy experiments show that single cells with high readthrough levels are more adapted to severe acid stress conditions and are more sensitive to an aminoglycoside antibiotic. Our work thus reveals a metabolic stress that promotes translational heterogeneity and phenotypic diversity.

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.

Elucidating interplay of speed and accuracy in biological error correction.

One of the most fascinating features of biological systems is the ability to sustain high accuracy of all major cellular processes despite the stochastic nature of underlying chemical processes. It is widely believed that such low error values are the result of the error-correcting mechanism known as kinetic proofreading. However, it is usually argued that enhancing the accuracy should result in slowing down the process, leading to the so-called speed-accuracy trade-off. We developed a discrete-state stochastic framework that allowed us to investigate the mechanisms of the proofreading using the method of first-passage processes. With this framework, we simultaneously analyzed the speed and accuracy of the two fundamental biological processes, DNA replication and tRNA selection during the translation. The results indicate that these systems tend to optimize speed rather than accuracy, as long as the error level is tolerable. Interestingly, for these processes, certain kinetic parameters lay in the suboptimal region where their perturbations can improve both speed and accuracy. Additional constraints due to the energetic cost of proofreading also play a role in the error correcting process. Our theoretical findings provide a microscopic picture of how complex biological processes are able to function so fast with high accuracy.

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.

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.

On the estimation of cooperativity in ion channel kinetics: activation free energy and kinetic mechanism of Shaker K+ channel.

In this paper, we have explored generic criteria of cooperative behavior in ion channel kinetics treating it on the same footing with multistate receptor-ligand binding in a compact theoretical framework. We have shown that the characterization of cooperativity of ion channels in terms of the Hill coefficient violates the standard Hill criteria defined for allosteric cooperativity of ligand binding. To resolve the issue, an alternative measure of cooperativity is proposed here in terms of the cooperativity index that sets a unified criteria for both the systems. More importantly, for ion channel this index can be very useful to describe the cooperative kinetics as it can be readily determined from the experimentally measured ionic current combined with theoretical modelling. We have analyzed the correlation between the voltage value and slope of the voltage-activation curve at the half-activation point and consequently determined the standard free energy of activation of the ion channel using two well-established mechanisms of cooperativity, namely, Koshland-Nemethy-Filmer (KNF) and Monod-Wyman-Changeux (MWC) models. Comparison of the theoretical results for both the models with appropriate experimental data of mutational perturbation of Shaker K(+) channel supports the experimental fact that the KNF model is more suitable to describe the cooperative behavior of this class of ion channels, whereas the performance of the MWC model is unsatisfactory. We have also estimated the mechanistic performance through standard free energy of channel activation for both the models and proposed a possible functional disadvantage in the MWC scheme.

Propensity approach to nonequilibrium thermodynamics of a chemical reaction network: controlling single E-coli ß-galactosidase enzyme catalysis through the elementary reaction steps.

In this work, we develop an approach to nonequilibrium thermodynamics of an open chemical reaction network in terms of the elementary reaction propensities. The method is akin to the microscopic formulation of the dissipation function in terms of the Kullback-Leibler distance of phase space trajectories in Hamiltonian system. The formalism is applied to a single oligomeric enzyme kinetics at chemiostatic condition that leads the reaction system to a nonequilibrium steady state, characterized by a positive total entropy production rate. Analytical expressions are derived, relating the individual reaction contributions towards the total entropy production rate with experimentally measurable reaction velocity. Taking a real case of Escherichia coli ß-galactosidase enzyme obeying Michaelis-Menten kinetics, we thoroughly analyze the temporal as well as the steady state behavior of various thermodynamic quantities for each elementary reaction. This gives a useful insight in the relative magnitudes of various energy terms and the dissipated heat to sustain a steady state of the reaction system operating far-from-equilibrium. It is also observed that, the reaction is entropy-driven at low substrate concentration and becomes energy-driven as the substrate concentration rises.

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.

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.

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.

Accuracy of Substrate Selection by Enzymes Is Controlled by Kinetic Discrimination.

Enzymes have the remarkable ability to select the correct substrate from the pool of chemically similar molecules. The accuracy of such a selection is determined by differences in the free-energy profiles for the right and wrong reaction pathways. Here, we investigate which features of the free-energy landscape govern the variation and minimization of selectivity error. It is generally believed that minimal error is affected by both kinetic (activation barrier heights) and thermodynamic (binding stability) factors. In contrast, using first-passage theoretical analysis, we show that the steady-state selectivity error is determined only by the differences in transition-state energies between the pathways and is independent of the energies of the stable complexes. The results are illustrated for two common catalytic mechanisms: (i) the Michaelis-Menten scheme and (ii) an error-correcting kinetic proofreading scheme with tRNA selection and DNA replication as guiding biological examples. Our theoretical analysis therefore suggests that the selectivity mechanisms are always kinetically controlled.

Entropy hysteresis and nonequilibrium thermodynamic efficiency of ion conduction in a voltage-gated potassium ion channel.

Here we have studied the nonequilibrium thermodynamic response of a voltage-gated Shaker potassium ion channel using a stochastic master equation. For a constant external voltage, the system reaches equilibrium indicated by the vanishing total entropy production rate, whereas for oscillating voltage the current and entropy production rates show dynamic hysteretic behavior. Here we have shown quantitatively that although the hysteresis loop area vanishes in low and high frequency domains of the external voltage, they are thermodynamically distinguishable. In the very low frequency domain, the system remains close to equilibrium, whereas at high frequencies it goes to a nonequilibrium steady state (NESS) associated with a finite value of dissipation function. At NESS, the efficiency of the ion conduction can also be related with the nonlinear dependence of the dissipation function on the power of the external field. Another intriguing aspect is that, at the high frequency limit, the total entropy production rate oscillates at NESS with half of the time period of the external voltage.