Derivation of unstirred-layer transport number equations from the Nernst-Planck flux equations.

Since the late 1960s it has been known that the passage of current across a membrane can give rise to local changes in salt concentration in unstirred layers or regions adjacent to that membrane, which in turn give rise to the development of slow transient diffusion potentials and osmotic flows across those membranes. These effects have been successfully explained in terms of transport number discontinuities at the membrane-solution interface, the transport number of an ion reflecting the proportion of current carried by that ion. Using the standard definitions for transport numbers and the regular diffusion equations, these polarization or transport number effects have been analyzed and modeled in a number of papers. Recently, the validity of these equations has been questioned. This paper has demonstrated that, by going back to the Nernst-Planck flux equations, exactly the same resultant equations can be derived and therefore that the equations derived directly from the transport number definitions and standard diffusion equations are indeed valid.     

Cell number estimation via fluorescence measurement

Summary Spectrofluorometry was applied to estimate cell number in anchorage dependent cell culture. Ethidium bromide was employed to stain the DNA molecule. Good agreement of cell count was obtained between a Coulter counter and the peak fluorescent intensity of ethidium bromide intercalated within the DNA of lysed cells. This procedure can be utilized to estimate the number of cells growing on surfaces from which trypsinization is ineffective.     

Measurement of monomer-oligomer distributions via fluorescence moment image analysis

We present higher-order moment analysis of fluorescence intensity fluctuations from individual laser scanning microscopy images applied to study monomer-oligomer distributions. We demonstrate that the number densities and brightness ratios of a mixed population of monomers and oligomers can be determined by analyzing higher-order moments of the fluorescence intensity fluctuations from individual images for specific ranges of densities and particle brightness ratios. Computer simulations and experiments with fluorescent microspheres and cells were performed to illustrate the detection limits and accuracy of this statistical approach. The simulation results show that the concentration of the dimer or oligomer population should be less than or equal to the monomeric concentration for the method to provide accurate results, and that the upper density detection limit of the population of monomers is one order-of-magnitude higher than the concentration of the oligomers. We implemented this technique to resolve two populations of fluorescent microspheres with different brightness ratios and we also applied the moment-analysis method to examine the distribution of aggregation states of PDGF-beta receptors in human fibroblast cells. The method was able to resolve a tetrameric population of the PDGF-beta receptors relative to the background distribution of nonspecifically bound fluorophore.     

General solution of the chemical master equation and modality of marginal distributions for hierarchic first-order reaction networks

Journal of Mathematical Biology - Multimodality is a phenomenon which complicates the analysis of statistical data based exclusively on mean and variance. Here, we present criteria for...     

Characterizing rare-event property distributions via replicate molecular dynamics simulations of proteins

As computational resources increase, molecular dynamics simulations of biomolecules are becoming an increasingly informative complement to experimental studies. In particular, it has now become feasible to use multiple initial molecular configurations to generate an ensemble of replicate production-run simulations that allows for more complete characterization of rare events such as ligand-receptor unbinding. However, there are currently no explicit guidelines for selecting an ensemble of initial configurations for replicate simulations. Here, we use clustering analysis and steered molecular dynamics simulations to demonstrate that the configurational changes accessible in molecular dynamics simulations of biomolecules do not necessarily correlate with observed rare-event properties. This informs selection of a representative set of initial configurations. We also employ statistical analysis to identify the minimum number of replicate simulations required to sufficiently sample a given biomolecular property distribution. Together, these results suggest a general procedure for generating an ensemble of replicate simulations that will maximize accurate characterization of rare-event property distributions in biomolecules.     

The twist, writhe, and linking number distributions in closed circular DNA

We discuss the predictions which follow from the assumption of statistically independent twist and writhe distributions of given variances in circular DNA with single-strand nicks. The nature of the topoisomer distribution produced upon covalent closure of the nicks is described, as well as the nature of the twist and writhe distributions in the fully-closed molecules. In particular, we show how the distributions depend on the magnitudes of the given variances, and how the relative magnitudes of the variances can be deduced from experiment. One additional consequence of the theory is the prediction of a necessary difference between the temperature coefficient of the twist in nicked versus fully-closed circular DNA. The ratio of the two twist coefficients turns out to depend only on the ratio of the twist and writhe variances in nicked DNA.     

Reduction of calcium release site models via moment fitting of phase-type distributions

Models of calcium (Ca(2 +)) release sites derived from continuous-time Markov chain (CTMC) models of intracellular Ca(2 +) channels exhibit collective gating reminiscent of the experimentally observed phenomenon of Ca(2 +) puffs and sparks. In order to overcome the state-space explosion that occurs in compositionally defined Ca(2 +) release site models, we have implemented an automated procedure for model reduction that replaces aggregated states of the full release site model with much simpler CTMCs that have similar within-group phase-type sojourn times and inter-group transitions. Error analysis based on comparison of full and reduced models validates the method when applied to release site models composed of 20 three-state channels that are both activated and inactivated by Ca(2 +). Although inspired by existing techniques for fitting moments of phase-type distributions, the automated reduction method for compositional Ca(2 +) release site models is unique in several respects and novel in this biophysical context.     

Emergence of visual saliency from natural scenes via context-mediated probability distributions coding

Visual saliency is the perceptual quality that makes some items in visual scenes stand out from their immediate contexts. Visual saliency plays important roles in natural vision in that saliency can direct eye movements, deploy attention, and facilitate tasks like object detection and scene understanding. A central unsolved issue is: What features should be encoded in the early visual cortex for detecting salient features in natural scenes? To explore this important issue, we propose a hypothesis that visual saliency is based on efficient encoding of the probability distributions (PDs) of visual variables in specific contexts in natural scenes, referred to as context-mediated PDs in natural scenes. In this concept, computational units in the model of the early visual system do not act as feature detectors but rather as estimators of the context-mediated PDs of a full range of visual variables in natural scenes, which directly give rise to a measure of visual saliency of any input stimulus. To test this hypothesis, we developed a model of the context-mediated PDs in natural scenes using a modified algorithm for independent component analysis (ICA) and derived a measure of visual saliency based on these PDs estimated from a set of natural scenes. We demonstrated that visual saliency based on the context-mediated PDs in natural scenes effectively predicts human gaze in free-viewing of both static and dynamic natural scenes. This study suggests that the computation based on the context-mediated PDs of visual variables in natural scenes may underlie the neural mechanism in the early visual cortex for detecting salient features in natural scenes.     

Control of secondary metabolite congener distributions via modulation of the dissolved oxygen tension

Many secondary metabolites, including various polyketides, require complex enzymatic pathways for modification into their final biologically active forms. Limitation of the dissolved oxygen supplied during cultivation of various microbial strains can decrease the activity of cytochrome P-450 monooxygenases required for the processing of pathway intermediates into their final forms, resulting in the accumulation of these intermediates as the primary products. Here, a generalized oxygen-limited cultivation strategy is specifically demonstrated with a myxobacterial strain engineered to heterologously express the epothilone polyketide synthase (PKS) gene cluster under either an excess (the dissolved oxygen tension is maintained at 50% of saturation) or a depleted (no residual dissolved oxygen detected) level of oxygenation during cultivation. Cultivation of this myxobacterial strain with excess oxygenation resulted in the production of epothilones A and B as the primary products, while cultivation of this same strain under depleted oxygenation resulted in the production of epothilones C and D as the primary products. Additionally, the peak cell density in the oxygen-depleted cultivations was 60% higher than that observed in oxygen-excess cultivations. Finally, an active EpoK epoxidase was found to catalyze the production of a novel epothilone (Epo506) with an unexpected structure during the cultivation of another myxobacterial strain expressing a genetically modified epothilone PKS under excess oxygenation. The structure of Epo506 was determined by high-resolution mass spectrometry and one- and two-dimensional NMR.     

An SIQ delay differential equations model for disease control via isolation

Journal of Mathematical Biology - Infectious diseases are among the most prominent threats to mankind. When preventive health care cannot be provided, a viable means of disease control is the...     

Nutritional strategies to modulate inflammation and oxidative stress pathways via activation of the master antioxidant switch Nrf2

The nuclear factor E2-related factor 2 (Nrf2) plays an important role in cellular protection against cancer, renal, pulmonary, cardiovascular and neurodegenerative diseases where oxidative stress and inflammation are common conditions. The Nrf2 regulates the expression of detoxifying enzymes by recognizing the human Antioxidant Response Element (ARE) binding site and it can regulate antioxidant and anti-inflammatory cellular responses, playing an important protective role on the development of the diseases. Studies designed to investigate how effective Nrf2 activators or modulators are need to be initiated. Several recent studies have shown that nutritional compounds can modulate the activation of Nrf2–Keap1 system. This review aims to discuss some of the key nutritional compounds that promote the activation of Nrf2, which may have impact on the human health.     

Calculation of the number of samples needed to estimate the species richness of a taxocene

A formula to calculate the area of samples that would provide the necessary level of completeness for a species richness survey of a cenosis has been deduced. The model is based on a stochastic differential equation that describes random fluctuations in species abundance and on the assumption that a Poisson distribution of individuals in space occurs. The calculations are illustrated based on the example of the littoral polychaete taxocene in Vityaz Bay of Possiet Bay of the Sea of Japan.     

On identifying the optimal number of population clusters via the deviance information criterion

Inferring population structure using bayesian clustering programs often requires a priori specification of the number of subpopulations, K, from which the sample has been drawn. Here, we explore the utility of a common bayesian model selection criterion, the Deviance Information Criterion (DIC), for estimating K. We evaluate the accuracy of DIC, as well as other popular approaches, on datasets generated by coalescent simulations under various demographic scenarios. We find that DIC outperforms competing methods in many genetic contexts, validating its application in assessing population structure.     

Poisson-Nernst-Planck equations for simulating biomolecular diffusion-reaction processes II: size effects on ionic distributions and diffusion-reaction rates

The effects of finite particle size on electrostatics, density profiles, and diffusion have been a long existing topic in the study of ionic solution. The previous size-modified Poisson-Boltzmann and Poisson-Nernst-Planck models are revisited in this article. In contrast to many previous works that can only treat particle species with a single uniform size or two sizes, we generalize the Borukhov model to obtain a size-modified Poisson-Nernst-Planck (SMPNP) model that is able to treat nonuniform particle sizes. The numerical tractability of the model is demonstrated as well. The main contributions of this study are as follows. 1), We show that an (arbitrarily) size-modified PB model is indeed implied by the SMPNP equations under certain boundary/interface conditions, and can be reproduced through numerical solutions of the SMPNP. 2), The size effects in the SMPNP effectively reduce the densities of highly concentrated counterions around the biomolecule. 3), The SMPNP is applied to the diffusion-reaction process for the first time, to our knowledge. In the case of low substrate density near the enzyme reactive site, it is observed that the rate coefficients predicted by SMPNP model are considerably larger than those by the PNP model, suggesting both ions and substrates are subject to finite size effects. 4), An accurate finite element method and a convergent Gummel iteration are developed for the numerical solution of the completely coupled nonlinear system of SMPNP equations.     

Calculation of the duration of mitosis for a population with an exponential growth of the cell number

A formula was received for the mean mitotic duration of a cell population being at the phase of exponential growth of the cell number with the cell loss: tM = nM.tD.(1-phi)/ln 2, where nM is the mitotic index, tD is the doubling time of the cell number, and phi is the Steel cell loss factor. In the case when after irradiation of such a population a 100% radiation G2-block arises, the method of calculation of the tM according to the curve of the relative mitotic index decrease was shown to be independent on the value of parameter phi and to coincide with the same method to be used in the case when the cell population is at the steady state before irradiation. As the result of analysis of literary experimental data the following values were received: tM = 20 min and tM = 37-42 min for two cell subpopulations of the Ehrlich ascite tumour, resp., tM = 39 min for epithelial cells of the mouse cornea, and tM = 29 min for enterocytes of the mouse jejunum. It has been also shown that the values of the dose of cell irradiation and of the mean duration tG2" of the subphase G2" localized at the end of phase G2 and preceded by the G2-block satisfy the next formula: Ig D = -a . Ig tG2" + b.