Efficient parameter generation for constrained models using MCMC.

Mathematical models of complex systems rely on parameter values to produce a desired behavior. As mathematical and computational models increase in complexity, it becomes correspondingly difficult to find parameter values that satisfy system constraints. We propose a Markov Chain Monte Carlo (MCMC) approach for the problem of constrained model parameter generation by designing a Markov chain that efficiently explores a model's parameter space. We demonstrate the use of our proposed methodology to analyze responses of a newly constructed bistability-constrained model of protein phosphorylation to perturbations in the underlying protein network. Our results suggest that parameter generation for constrained models using MCMC provides powerful tools for modeling-aided analysis of complex natural processes.

Scalable Gromov-Wasserstein Based Comparison of Biological Time Series.

A time series is an extremely abundant data type arising in many areas of scientific research, including the biological sciences. Any method that compares time series data relies on a pairwise distance between trajectories, and the choice of distance measure determines the accuracy and speed of the time series comparison. This paper introduces an optimal transport type distance for comparing time series trajectories that are allowed to lie in spaces of different dimensions and/or with differing numbers of points possibly unequally spaced along each trajectory. The construction is based on a modified Gromov-Wasserstein distance optimization program, reducing the problem to a Wasserstein distance on the real line. The resulting program has a closed-form solution and can be computed quickly due to the scalability of the one-dimensional Wasserstein distance. We discuss theoretical properties of this distance measure, and empirically demonstrate the performance of the proposed distance on several datasets with a range of characteristics commonly found in biologically relevant data. We also use our proposed distance to demonstrate that averaging oscillatory time series trajectories using the recently proposed Fused Gromov-Wasserstein barycenter retains more characteristics in the averaged trajectory when compared to traditional averaging, which demonstrates the applicability of Fused Gromov-Wasserstein barycenters for biological time series. Fast and user friendly software for computing the proposed distance and related applications is provided. The proposed distance allows fast and meaningful comparison of biological time series and can be efficiently used in a wide range of applications.

Dynein localization and pronuclear movement in the C. elegans zygote.

Centrosomes serve as a site for microtubule nucleation and these microtubules will grow and interact with the motor protein dynein at the cortex. The position of the centrosomes determines where the mitotic spindle will develop across all cell types. Centrosome positioning is achieved through dynein and microtubule-mediated force generation. The mechanism and regulation of force generation during centrosome positioning are not fully understood. Centrosome and pronuclear movement in the first cell cycle of the Caenorhabditis elegans early embryo undergoes both centration and rotation prior to cell division. The proteins LET-99 and GPB-1 have been postulated to have a role in force generation associated with pronuclear centration and rotation dynamics. When the expression of these proteins is perturbed, pronuclear positioning exhibits a movement defect characterized by oscillatory ("wobble") behavior of the pronuclear complex (PNC). To determine if this movement defect is due to an effect on cortical dynein distribution, we utilize RNAi-mediated knockdown of LET-99 and GPB-1 to induce wobble and assay for any effects on GFP-tagged dynein localization in the early C. elegans embryo. To compare and quantify the movement defect produced by the knockdown of LET-99 and GPB-1, we devised a quantification method that measures the strength of wobble ("wobble metric") observed under these experimental conditions. Our quantification of pronuclear complex dynamics and dynein localization shows that loss of LET-99 and GPB-1 induces a similar movement defect which is independent of cortical dynein localization in the early C. elegans embryo.

Sustainability of agricultural and wild cereals to aerotechnogenic exposure.

In recent decades, the problem of the constantly increasin level of anthropogenic load on the environment is becoming more and more acute. Some of the most dangerous pollutants entering the environment from industrial emissions are heavy metals. These pollutants are not susceptible to biodegradation over time, which leads to their accumulation in the environment in dangerous concentrations. The purpose of this work is to study the sustainability of cultivated and wild plants of the Poaceae family to aerotechnogenic pollution in the soil. The content of heavy metals in couch grass (Elytrigia repens (L.) Nevski), meadow bluegrass (Poa pratensis L.) and soft wheat (Triticum aestivum) plants grown in the impact zone of Novocherkassk Power Station has been analyzed. Contamination of cultivated and wild cereals with Pb, Zn, Ni and Cd has been established. It has been shown that the accumulation of heavy metals is individual for each plant species. An average and close correlation have been established between the total HM content and the content of their mobile forms in the soil and their content in plants. For the plants studied, the translocation factor (TF) and the distribution coefficient (DC) of HM have been calculated. The TF is formed by the ratio of the concentration of an element in the root plant dry weight to the content of its mobile compounds in the soil. The DC value makes it possible to estimate the capacity of the aboveground parts of plants to absorb and accumulate elements under soil pollution conditions and is determined as the ratio of the metal content in the aboveground biomass to its concentration in the roots. TF and DC values have shown a significant accumulation of elements by plants from the soil, as well as their translocation from the root system to the aboveground part. It has been revealed that even within the same Poaceae family, cultural species are more sensitive to man-made pollution than wild-growing ones.

A computational model predicts genetic nodes that allow switching between species-specific responses in a conserved signaling network.

Cell signaling networks regulate a variety of developmental and physiological processes, and changes in their response to external stimuli are often implicated in disease initiation and progression. To elucidate how different responses can arise from conserved signaling networks, we have developed a mathematical model of the well-characterized Caenorhabditis vulval development network involving EGF, Wnt and Notch signaling that recapitulates biologically observed behaviors. We experimentally block a specific element of the EGF pathway (MEK), and find different behaviors in vulval development in two Caenorhabditis species, C. elegans and C. briggsae. When we separate our parameters into subsets that correspond to these two responses, they yield model behaviors that are consistent with observed experimental results, despite the initial parameter grouping based on perturbation in a single node of the EGF pathway. Finally, our analysis predicts specific parameters that may be critical for the theoretically and experimentally observed differences, suggesting modifications that might allow intentional switching between the two species' responses. Our results indicate that all manipulations within a signal transduction pathway do not yield the same outcome, and provide a framework to identify the specific genetic perturbations within a conserved network that will confer unique behaviors on the network.

Metabolic and immunologic aspects of fetoplacental insufficiency.

PROBLEM: The chronic placental insufficiency is the most common cause of intrauterine hypoxia, retardation of fetal growth, and other threatening conditions. Immune disturbances may occur in the system "mother-placenta-fetus." METHOD OF STUDY: Biochemical blood indicators were studied on an automated biochemical analyzer. Pattern of lymphocyte subpopulations was detected by direct membrane immunofluorescence. RESULTS: Study revealed imbalance of immune parameters, caused by placental insufficiency (increase natural killers (CD16(+) , CD56(+) ), B lymphocytes (CD19(+) CD3(-) ), T and B lymphocytes with HLA-DR(+) antigen, and early activation of immune cells (by CD25(+) ), as well as disorders in apoptotic mechanisms (by CD95(+) )). CONCLUSION: Placental insufficiency leads to abnormalities of the immune system in pregnant, parturient women and maternity patients which were evaluated by localization of activation markers CD25(+) CD95(+) on the CD3(+) , CD4(+) , CD8(+) , CD16(+) , CD56(+) lymphocytes. This is reflected in the change of lymphocyte functions in newborns.

Actomyosin regulation and symmetry breaking in a model of polarization in the early Caenorhabditis elegans embryo : symmetry breaking in cell polarization.

Polarization, whereby a cell defines a spatial axis by segregating specific determinants to distinct regions, is an essential and highly conserved biological process. The process of polarization is initiated by a cue that breaks an initially symmetric distribution of determinants, allowing for a spatially asymmetric redistribution. The nature of this cue is currently not well understood. Utilizing the conservation of polarization process and its determinants, we theoretically investigate the nature of the cue and the regulation of contractility that enables the establishment of polarity in early embryos of the nematode worm Caenorhabditis elegans (C. elegans). Our biologically based model, which consists of coupled partial differential equations, suggests that a biochemical but not mechanical cue is sufficient for symmetry breaking, and inhibition of contractile elements by specific determinants is needed for sustained spatial redistribution.