Extinction times in autocatalytic systems

Silk Cocoon-Derived Protein Bioinspired Gold Nanoparticles as a Formidable Anticancer Agent

We synthesized bioinspired sericin encapsulated gold nanoparticles (SGNPs) using HAuCl4 as the starting material in a bottom-up approach. Further, two-dimensional (2D) and three-dimensional (3D) conformational changes (folding and unfolding) in sericin were studied using circular dichroism (CD) and fluorescence spectroscopy, respectively, during and after the synthesis of particles. Finally, the synthesized SGNPs were characterized using several physical techniques to ensure their correct synthesis and study the size, stability, and charge over the surface of particles. At the beginning of the reaction, when gold was in the ionic form (Au+3), sericin exhibited maximum electrostatic interaction and underwent unfolding. Au+3 reduced to Au during the reaction, and sericin regained its 3D confirmation due to a decrease in its native electrostatic interactions. However, CD revealed the same patterns of unfolding and folding; a decrease in α helix and an increase inβ3 pleated sheets were noticed. Although the 3D structure of sericin was restored after the synthesis of SGNPs, it was substantially altered. In addition, certain changes in the 2D structure were observed; however, these did not alter the activity of sericin. Furthermore, Fourier-transform infrared spectroscopy (FTIR) confirmed these findings. The SGNPs were found to be effective against lung cancer (A549 cells), with an IC50 of 145.49 βM, without exerting any toxic effects on normal cells (NRK cells). The effectiveness of SGNPs was examined by MTT cytotoxicity and nuclear fragmentation assays. Furthermore, we assessed their ability to produce excessive ROS and release Cyt-c from the mitochondria for caspase-3-mediated apoptosis.

Master equations and the theory of stochastic path integrals

This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a 'generating functional', which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a 'forward' and a 'backward' path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.

Noise-induced multistability in the regulation of cancer by genes and pseudogenes

We extend a previously introduced model of stochastic gene regulation of cancer to a nonlinear case having both gene and pseudogene messenger RNAs (mRNAs) self-regulated. The model consists of stochastic Boolean genetic elements and possesses noise-induced multistability (multimodality). We obtain analytical expressions for probabilities for the case of constant but finite number of microRNA molecules which act as a noise source for the competing gene and pseudogene mRNAs. The probability distribution functions display both the global bistability regime as well as even-odd number oscillations for a certain range of model parameters. Statistical characteristics of the mRNA's level fluctuations are evaluated. The obtained results of the extended model advance our understanding of the process of stochastic gene and pseudogene expressions that is crucial in regulation of cancer.

The Life Story of Hydrogen Peroxide III: Chirality and Physical Effects at the Dawn of Life

It is a remarkable observed fact that all life on Earth is homochiral, its biology using exclusively the D-enantiomer of ribose, the sugar moiety of the ribonucleic acids, and the L-enantiomers of the chiral amino acids. Motivated by concurrent work that elaborates further the role of hydrogen peroxide in providing an oscillatory drive for the RNA world (Ball & Brindley 2015a, J. R. Soc. Interface 12, 20150366, and Ball & Brindley 2015b, this journal, in press), we reappraise the structure and physical properties of this small molecule within this context. Hydrogen peroxide is the smallest, simplest molecule to exist as a pair of non-superimposable mirror images, or enantiomers, a fact which leads us to develop the hypothesis that its enantiospecific interactions with ribonucleic acids led to enantioselective outcomes. We propose a mechanism by which these chiral interactions may have led to amplification of D-ribonucleic acids and extinction of L-ribonucleic acids.

Oscillations in probability distributions for stochastic gene expression

The phenomenon of oscillations in probability distribution functions of number of components is found for a model of stochastic gene expression. It takes place in cases of low levels of molecules or strong intracellular noise. The oscillations distinguish between more probable even and less probable odd number of particles. The even-odd symmetry restores as the number of molecules increases with the probability distribution function tending to Poisson distribution. We discuss the possibility of observation of the phenomenon in gene, protein, and mRNA expression experiments.

Nonequilibrium Lyapunov function and a fluctuation relation for stochastic systems: Poisson-representation approach

We present a statistical physics framework for the description of nonlinear nonequilibrium stochastic processes, modeled via a chemical master equation, in the weak-noise limit. Using the Poisson-representation approach and applying the large-deviation principle, we first solve the master equation. Then we use the notion of the nonequilibrium free energy to derive an integral fluctuation relation for nonlinear nonequilibrium systems under feedback control. We point out that the free energy as well as some functionals can serve as a nonequilibrium Lyapunov function which has an important property to decay monotonously to its minimal value at all times. The Poisson-representation technique is illustrated via exact stochastic treatment of biophysical processes, such as bacterial chemosensing and molecular evolution.

The autocatalytic step is an integral part of the hydrogenase cycle

We earlier proved the involvement of an autocatalytic step in the oxidation of H(2) by HynSL hydrogenase from Thiocapsa roseopersicina, and demonstrated that two enzyme forms interact in this step. Using a modified thin-layer reaction chamber which permits quantitative analysis of the concentration of the reaction product (reduced benzyl viologen) in the reaction volume during the oxidation of H(2), we now show that the steady-state concentration of the product displays a strong enzyme concentration dependence. This experimental fact can be explained only if the previously detected autocatalytic step occurs inside the catalytic enzyme-cycle and not in the enzyme activation process. Consequently, both interacting enzyme forms should participate in the catalytic cycle of the enzyme. As far as we are aware, this is the first experimental observation of such a phenomenon resulting in an apparent inhibition of the enzyme. It is additionally concluded that the interaction of the two enzyme forms should result in a conformational change in the enzyme-substrate form. This scheme is very similar to that of prion reactions. Since merely a few molecules are involved at some point of the reaction, this process is entirely stochastic in nature. We have therefore developed a stochastic calculation method, calculations with which lent support to the conclusion drawn from the experiment.

Stochastic mapping of first order reaction networks: a systematic comparison of the stochastic and deterministic kinetic approaches

Stochastic maps are developed and used for first order reaction networks to decide whether the deterministic kinetic approach is appropriate for a certain evaluation problem or the use of the computationally more demanding stochastic approach is inevitable. On these maps, the decision between the two approaches is based on the standard deviation of the expectation of detected variables: when the relative standard deviation is larger than 1%, the use of the stochastic method is necessary. Four different systems are considered as examples: the irreversible first order reaction, the reversible first order reaction, two consecutive irreversible first order reactions, and the unidirectional triangle reaction. Experimental examples are used to illustrate the practical use of the theoretical results. It is shown that the maps do not only depend on particle numbers, but the influence of parameters such as time, rate constants, and the identity of the detected target variable is also an important factor.

Phylogenetic and epidemic modeling of rapidly evolving infectious diseases

Epidemic modeling of infectious diseases has a long history in both theoretical and empirical research. However the recent explosion of genetic data has revealed the rapid rate of evolution that many populations of infectious agents undergo and has underscored the need to consider both evolutionary and ecological processes on the same time scale. Mathematical epidemiology has applied dynamical models to study infectious epidemics, but these models have tended not to exploit--or take into account--evolutionary changes and their effect on the ecological processes and population dynamics of the infectious agent. On the other hand, statistical phylogenetics has increasingly been applied to the study of infectious agents. This approach is based on phylogenetics, molecular clocks, genealogy-based population genetics and phylogeography. Bayesian Markov chain Monte Carlo and related computational tools have been the primary source of advances in these statistical phylogenetic approaches. Recently the first tentative steps have been taken to reconcile these two theoretical approaches. We survey the Bayesian phylogenetic approach to epidemic modeling of infection diseases and describe the contrasts it provides to mathematical epidemiology as well as emphasize the significance of the future unification of these two fields.

Within-host demographic fluctuations and correlations in early retroviral infection

In this paper we analyze the demographic fluctuations and correlations present in within-host populations of viruses and their target cells during the early stages of infection. In particular, we present an exact treatment of a discrete-population, stochastic, continuous-time master equation description of HIV or similar retroviral infection dynamics, employing Monte Carlo simulations. The results of calculations employing Gillespie's direct method clearly demonstrate the importance of considering the microscopic details of the interactions which constitute the macroscopic dynamics. We then employ the τ-leaping approach to study the statistical characteristics of infections involving realistic absolute numbers of within-host viral and cellular populations, before going on to investigate the effect that initial viral population size plays on these characteristics. Our main conclusion is that cross-correlations between infected cell and virion populations alter dramatically over the course of the infection. We suggest that these statistical correlations offer a novel and robust signature for the acute phase of retroviral infection.