[Show abstract][Hide abstract] ABSTRACT: For quantitative understanding of probabilistic behaviors of living cells, it is essential to construct a correct mathematical description of intracellular networks interacting with complex cell environments, which has been a formidable task. Here, we present a novel model and stochastic kinetics for an intracellular network interacting with hidden cell environments, employing a complete description of cell state dynamics and its coupling to the system network. Our analysis reveals that various environmental effects on the product number fluctuation of intracellular reaction networks can be collectively characterized by Laplace transform of the time-correlation function of the product creation rate fluctuation with the Laplace variable being the product decay rate. On the basis of the latter result, we propose an efficient method for quantitative analysis of the chemical fluctuation produced by intracellular networks coupled to hidden cell environments. By applying the present approach to the gene expression network, we obtain simple analytic results for the gene expression variability and the environment-induced correlations between the expression levels of mutually noninteracting genes. The theoretical results compose a unified framework for quantitative understanding of various gene expression statistics observed across a number of different systems with a small number of adjustable parameters with clear physical meanings.
[Show abstract][Hide abstract] ABSTRACT: Cell-to-cell variation in gene expression, or noise, is a general phenomenon observed within cell populations. Transcription is known to be the key stage of gene expression where noise is generated, however, how variation in RNA polymerase (RNAP) concentration contributes to gene expression noise is unclear. Here, we quantitatively investigate how variations in absolute amounts of RNAP molecules affect noise in the expression of two fluorescent protein reporters driven by identical promoters. We find that intrinsic noise is independent of variation in RNAP concentrations, whereas extrinsic noise, which is variation in gene expression due to varying cellular environments, scales linearly with variation in RNAP abundance. Specifically, the propagation of RNAP abundance variation to expressed protein noise is inversely proportional to the concentration of RNAP, which suggests that the change in noise that results from RNAP fluctuations is determined by the fraction of promoters that is not occupied by RNAP.
No preview · Article · Sep 2014 · Nature Communications
[Show abstract][Hide abstract] ABSTRACT: Liquid helium does not obey the Gibbs fluctuation-compressibility relation, which was noted more than six decades ago. However, still missing is a clear explanation of the reason for the deviation or the correct fluctuation-compressibility relation for the quantum liquid. Here we present the fluctuation-compressibility relation valid for any grand canonical system. Our result shows that the deviation from the Gibbs formula arises from a nonextensive part of thermodynamic potentials. The particle-exchange symmetry of many-body wave function of a strongly degenerate quantum gas is related to the thermodynamic extensivity of the system; a Bose gas does not always obey the Gibbs formula, while a Fermi gas does. Our fluctuation-compressibility relation works for classical systems as well as quantum systems. This work demonstrates that the application range of the Gibbs-Boltzmann statistical thermodynamics can be extended to encompass nonextensive open systems without introducing any postulate other than the principle of equal a priori probability.
No preview · Article · Jun 2014 · Physical Review E
[Show abstract][Hide abstract] ABSTRACT: We investigate the reaction event counting statistics (RECS) of an elementary biopolymer reaction in which the rate coefficient is dependent on states of the biopolymer and the surrounding environment and discover a universal kinetic phase transition in the RECS of the reaction system with dynamic heterogeneity. From an exact analysis for a general model of elementary biopolymer reactions, we find that the variance in the number of reaction events is dependent on the square of the mean number of the reaction events when the size of measurement time is small on the relaxation time scale of rate coefficient fluctuations, which does not conform to renewal statistics. On the other hand, when the size of the measurement time interval is much greater than the relaxation time of rate coefficient fluctuations, the variance becomes linearly proportional to the mean reaction number in accordance with renewal statistics. Gillespie’s stochastic simulation method is generalized for the reaction system with a rate coefficient fluctuation. The simulation results confirm the correctness of the analytic results for the time dependent mean and variance of the reaction event number distribution. On the basis of the obtained results, we propose a method of quantitative analysis for the reaction event counting statistics of reaction systems with rate coefficient fluctuations, which enables one to extract information about the magnitude and the relaxation times of the fluctuating reaction rate coefficient, without a bias that can be introduced by assuming a particular kinetic model of conformational dynamics and the conformation dependent reactivity. An exact relationship is established between a higher moment of the reaction event number distribution and the multitime correlation of the reaction rate for the reaction system with a nonequilibrium initial state distribution as well as for the system with the equilibrium initial state distribution.
No preview · Article · Mar 2012 · Journal of Chemical Theory and Computation
[Show abstract][Hide abstract] ABSTRACT: Chemosignaling of hydrazine by selective deprotection of levulinated coumarin was investigated. In the presence of hydrazine, levulinated coumarin was selectively deprotected, resulting in chromogenic and fluorescent turn-on type signaling. The selective naked-eye detectable signaling of hydrazine was possible in the presence of representative metal ions and common anions in an aqueous environment.
[Show abstract][Hide abstract] ABSTRACT: Fluctuating turnover times of a single enzyme become observable with the advent of modern cutting-edge, single enzyme experimental techniques. Although the conventional chemical kinetics and its modern generalizations could provide a good quantitative description for the mean of the enzymatic turnover times, to our knowledge there has not yet been a successful quantitative interpretation for the variance or the randomness of the enzymatic turnover times. In this review, we briefly review several theories in this field, and compare predictions of these theories to the randomness parameter data reported for β-galactosidase enzyme. We find the recently proposed kinetics for renewal reaction processes could provide an excellent quantitative interpretation of the randomness parameter data. From the analysis of the randomness parameter data of the single enzyme reaction, one can extract quantitative information about the mean lifetime of enzyme-substrate complex; the success or the failure probability of the catalytic reaction per each formation of ES complex; and the non-Poisson character of the reaction dynamics of the ES complex (which is beyond reach of the long-standing paradigm of the conventional chemical kinetics).
Preview · Article · Aug 2011 · Biophysical Journal
[Show abstract][Hide abstract] ABSTRACT: We present a theory for a unified characterization of a substrate–receptor system with an arbitrary binding affinity distribution. On the basis of a universal expression obtained for the bound fraction isotherm of a monovalent receptor system, we propose a novel experimental analysis method for characterization of the receptor system, introducing a new type of experimental plot. From our analysis method, one can extract key physical parameters that mostly determine the shape of bound fraction isotherm, which include the mean binding affinity, the mean binding free energy, and the parameters that measure the magnitude of fluctuation and the asymmetry of the binding free energy distribution for receptor–substrate system, without any bias that can be introduced by presuming a particular functional form for the binding free energy distribution or for the bound fraction isotherm.Graphical abstractHighlights► We report a theory for an objective characterization of a substrate-receptor system with an arbitrary binding affinity distribution. ►We propose a quantitative analysis method applicable to a heterogeneous receptor system with use of a novel experimental plot, named Θ0 plot. ►Our analysis method enables one toestimatekey physical parameters that mostly determine the shape of the bound fraction isotherm.
No preview · Article · Jun 2011 · Chemical Physics
[Show abstract][Hide abstract] ABSTRACT: We introduce a new method of solution for the Fredholm integral equations of the second kind. The method would be useful when the direct iterative approach leads to a divergent perturbation series solution. By using the method, we obtain an accurate expression of the propagator for diffusive dynamics of a pair of particles interacting via an arbitrary central potential and hydrodynamic interaction. We test the accuracy of the propagator expression by calculating the diffusion-controlled geminate and bimolecular reaction rates. It is shown that our propagator expression provides very accurate results for the whole time region.
Full-text · Article · Mar 2011 · The Journal of Chemical Physics
[Show abstract][Hide abstract] ABSTRACT: We report a robust quadratic relation between the inverse substrate concentration and the second moment, <t(2)>, of the catalytic turnover time distribution for enzyme reactions. The results hold irrespective of the mechanism and dynamics of the enzyme reaction and suggest a novel single molecule experimental analysis that provides information about reaction processes of the enzyme-substrate complex and ergodicity of the enzyme reaction system, which is beyond the reach of the conventional analysis for the mean reaction time, . It turns out that <t(2)> - 2 (2) is linear in inverse substrate concentration for an ergodic homogeneous enzyme system given that the enzyme substrate encounter is a simple rate process, and its value at the high substrate concentration limit provides direct information about if any non-Poisson reaction process of the enzyme-substrate complex. For a nonergodic heterogeneous reaction system, the corresponding quantity becomes a quadratic function of the inverse substrate concentration. This leads us to suggest an ergodicity measure for single enzyme reaction systems. We obtain a simple analytic expression of the randomness parameter for the single catalytic turnover time, which could provide a quantitative explanation about the previously reported randomness data of the beta-galactosidase enzyme. In obtaining the results, we introduce novel chemical kinetics applicable to a non-Poisson reaction network with arbitrary connectivity, as a generalization of the conventional chemical kinetics.
No preview · Article · Aug 2010 · The Journal of Physical Chemistry B
[Show abstract][Hide abstract] ABSTRACT: New type-II structures of CdSe/InP and InP/CdSe core-shell nanocrystals which have staggered bandgap alignment were fabricated. Using a simple model for the wave function for electrons and holes in InP/CdSe and CdSe/InP core/shell nanocrystals showed the wave function of the electron and hole spread into the shell, respectively. The probability density of the InP/CdSe and CdSe/InP core/shell QDs also showed a similar tendency. As a result, the structure exhibits increased delocalization of electrons and holes, leading to a red-shift in absorption and emission. Quantum yield increased in the InP/CdSe, however decreased in the CdSe/InP. The reason may be due to the surface trap and high activation barrier for de-trapping in the InP shell.
No preview · Article · Mar 2010 · Journal of Colloid and Interface Science
[Show abstract][Hide abstract] ABSTRACT: We investigate the effects of surface heterogeneity on molecular adsorption. From an exact model study, we find that (1-θ)-1 with θ being the surface coverage as a function of density of ligand molecules has a negative curvature of which magnitude increases with the surface heterogeneity. We also propose a novel experimental observable, χ, which can be used to quantify the surface heterogeneity.
[Show abstract][Hide abstract] ABSTRACT: We report that an external field can drive inherently extensive systems into nonextensive ones. For the correct grand canonical description of nonextensive systems, it is necessary to take into account the excess grand potential, X, in addition to the conventional grand potential proportional to the thermodynamic pressure, which has long been overlooked in the literature in this field. We present the statistical mechanical expression for X of a system as a functional of the external field imposed on the system, from which we establish the criterion for the external field that drives an inherently extensive macroscopic system into a nonextensive one.
No preview · Article · Jun 2009 · The Journal of Physical Chemistry B
[Show abstract][Hide abstract] ABSTRACT: New quantum dots were fabricated with a core/shell/shell structure consisting of CdTe core/InP shell/ZnS shell of which the InP shell causes a red-shift to the NIR region and the ZnS shell imparts photo-stability; toxicity tests on mammalian cells and NIR imaging of a mouse highlight their potential applications in biomedical imaging.
No preview · Article · Apr 2009 · Chemical Communications
[Show abstract][Hide abstract] ABSTRACT: We present a theoretical model for description of real polyreceptor molecular wire sensors (MWS), whose conductance signal may dramatically reduce upon analyte binding to one of the receptors coupled to the molecular wire but may not vanish as completely as assumed in the ideal MWS model. For the present nonideal MWS model, we establish the exact relationship between analyte concentration and the sensory signal intensity. It turns out that, whereas the Stern-Volmer curve of the ideal MWS always has a positive curvature, the Stern-Volmer curve of the imperfect MWS can have a negative curvature, consistent with experimental data. We find that the MWS still performs better than the corresponding ideal monoreceptor sensor, unless the nonideality of the imperfect MWS is egregiously large. We establish the conditions for the imperfect polyreceptor MWS to have a sensitivity and detection limit superior to the traditional monoreceptor sensor.
No preview · Article · Jan 2009 · Analytical Chemistry
[Show abstract][Hide abstract] ABSTRACT: On the basis of the recently developed optimized Rouse-Zimm theory of chain polymers with excluded volume interactions, we calculate the long-time first-order rate constant k(1) for end-to-end cyclization of linear chain polymers. We first find that the optimized Rouse-Zimm theory provides the longest chain relaxation times tau(1) of excluded volume chains that are in excellent agreement with the available Brownian dynamics simulation results. In the free-draining limit, the cyclization rate is diffusion-controlled and k(1) is inversely proportional to tau(1), and the k(1) values calculated using the Wilemski-Fixman rate theory are in good agreement with Brownian dynamics simulation results. However, when hydrodynamic interactions are included, noticeable deviations are found. The main sources of errors are fluctuating hydrodynamic interaction and correlation hole effects as well as the non-Markovian reaction dynamic effect. The physical natures of these factors are discussed, and estimates for the magnitudes of required corrections are given. When the corrections are included, the present theory allows the prediction of accurate k(1) values for the cyclization of finite-length chains in good solvents as well as the correct scaling exponent in the long-chain limit.
Full-text · Article · Jun 2008 · The Journal of Physical Chemistry B
[Show abstract][Hide abstract] ABSTRACT: We investigate a simple, exactly solvable model for interacting adsorbates. From the model study, we find that (1-theta)(-1) as a function of density of molecules in bulk media can have a positive curvature only in the presence of attractive interaction between adsorbed molecules. We propose a novel experimental observable, chi. Positive chi is the sufficient condition for the presence of attractive interactions between adsorbate molecules.
[Show abstract][Hide abstract] ABSTRACT: Jarzynski's equation (JE) has been known to relate free energy change of a system to statistical distribution of work done on the system for an arbitrary process. In the present work, we first establish the validity condition of JE for boundary switching processes. The validity condition of JE is examined for an example of spontaneous irreversible processes, for which, obviously, JE does not hold. We find that the free energy difference between two configurational states with different phase-space volume cannot be correctly estimated by JE for any adiabatic boundary switching process.
No preview · Article · Apr 2008 · Physical Review E
[Show abstract][Hide abstract] ABSTRACT: We investigate the first passage times for the contact between the ends of a Rouse chain, whose initial separation is greater than a predefined contact distance, sigma, and equilibrium-distributed. An approximate analytic expression for the mean first passage time is obtained and compared with the results of previous theories and Brownian dynamics simulations. We find that the results of the present theory are in better agreement with Brownian dynamics simulation results than those of previously reported theories.
No preview · Article · Oct 2007 · The Journal of Physical Chemistry B
[Show abstract][Hide abstract] ABSTRACT: We present an exact theoretical test of Jarzynski's equality (JE) for reversible volume-switching processes of an ideal gas system. The exact analysis shows that the prediction of JE for the free energy difference is the same as the work done on the gas system during the reversible process that is dependent on the shape of path of the reversible volume-switching process.
No preview · Article · Aug 2007 · Physical Review E