Limit cycles in the presence of convection, a travelling wave analysis

We consider a diffusion model with limit cycle reaction functions, in the presence of convection. We select a set of functions derived from a realistic reaction model: the Schnakenberg equations. This resultant form is unsymmetrical. We find a transformation which maps the irregular equations into model form. Next we transform the dependent variables into polar form. From here, a travelling wave analysis is performed on the radial variable. Results are complex, but we make some simple estimates. We carry out numerical experiments to test our analysis. An initial `knock' starts the propagation of pattern. The speed of the travelling wave is not quite as expected. We investigate further. The system demonstrates distinctly different behaviour to the left and the right. We explain how this phenomenon occurs by examining the underlying behaviour.Comment: 20 pages, 5 figure

The transition between stochastic and deterministic behavior in an excitable gene circuit

We explore the connection between a stochastic simulation model and an ordinary differential equations (ODEs) model of the dynamics of an excitable gene circuit that exhibits noise-induced oscillations. Near a bifurcation point in the ODE model, the stochastic simulation model yields behavior dramatically different from that predicted by the ODE model. We analyze how that behavior depends on the gene copy number and find very slow convergence to the large number limit near the bifurcation point. The implications for understanding the dynamics of gene circuits and other birth-death dynamical systems with small numbers of constituents are discussed.Comment: PLoS ONE: Research Article, published 11 Apr 201

Structural Analysis to Determine the Core of Hypoxia Response Network

The advent of sophisticated molecular biology techniques allows to deduce the structure of complex biological networks. However, networks tend to be huge and impose computational challenges on traditional mathematical analysis due to their high dimension and lack of reliable kinetic data. To overcome this problem, complex biological networks are decomposed into modules that are assumed to capture essential aspects of the full network's dynamics. The question that begs for an answer is how to identify the core that is representative of a network's dynamics, its function and robustness. One of the powerful methods to probe into the structure of a network is Petri net analysis. Petri nets support network visualization and execution. They are also equipped with sound mathematical and formal reasoning based on which a network can be decomposed into modules. The structural analysis provides insight into the robustness and facilitates the identification of fragile nodes. The application of these techniques to a previously proposed hypoxia control network reveals three functional modules responsible for degrading the hypoxia-inducible factor (HIF). Interestingly, the structural analysis identifies superfluous network parts and suggests that the reversibility of the reactions are not important for the essential functionality. The core network is determined to be the union of the three reduced individual modules. The structural analysis results are confirmed by numerical integration of the differential equations induced by the individual modules as well as their composition. The structural analysis leads also to a coarse network structure highlighting the structural principles inherent in the three functional modules. Importantly, our analysis identifies the fragile node in this robust network without which the switch-like behavior is shown to be completely absent

Equation-Free Analysis of Two-Component System Signalling Model Reveals the Emergence of Co-Existing Phenotypes in the Absence of Multistationarity

Phenotypic differences of genetically identical cells under the same environmental conditions have been attributed to the inherent stochasticity of biochemical processes. Various mechanisms have been suggested, including the existence of alternative steady states in regulatory networks that are reached by means of stochastic fluctuations, long transient excursions from a stable state to an unstable excited state, and the switching on and off of a reaction network according to the availability of a constituent chemical species. Here we analyse a detailed stochastic kinetic model of two-component system signalling in bacteria, and show that alternative phenotypes emerge in the absence of these features. We perform a bifurcation analysis of deterministic reaction rate equations derived from the model, and find that they cannot reproduce the whole range of qualitative responses to external signals demonstrated by direct stochastic simulations. In particular, the mixed mode, where stochastic switching and a graded response are seen simultaneously, is absent. However, probabilistic and equation-free analyses of the stochastic model that calculate stationary states for the mean of an ensemble of stochastic trajectories reveal that slow transcription of either response regulator or histidine kinase leads to the coexistence of an approximate basal solution and a graded response that combine to produce the mixed mode, thus establishing its essential stochastic nature. The same techniques also show that stochasticity results in the observation of an all-or-none bistable response over a much wider range of external signals than would be expected on deterministic grounds. Thus we demonstrate the application of numerical equation-free methods to a detailed biochemical reaction network model, and show that it can provide new insight into the role of stochasticity in the emergence of phenotypic diversity

Stochastic Delay Accelerates Signaling in Gene Networks

The creation of protein from DNA is a dynamic process consisting of numerous reactions, such as transcription, translation and protein folding. Each of these reactions is further comprised of hundreds or thousands of sub-steps that must be completed before a protein is fully mature. Consequently, the time it takes to create a single protein depends on the number of steps in the reaction chain and the nature of each step. One way to account for these reactions in models of gene regulatory networks is to incorporate dynamical delay. However, the stochastic nature of the reactions necessary to produce protein leads to a waiting time that is randomly distributed. Here, we use queueing theory to examine the effects of such distributed delay on the propagation of information through transcriptionally regulated genetic networks. In an analytically tractable model we find that increasing the randomness in protein production delay can increase signaling speed in transcriptional networks. The effect is confirmed in stochastic simulations, and we demonstrate its impact in several common transcriptional motifs. In particular, we show that in feedforward loops signaling time and magnitude are significantly affected by distributed delay. In addition, delay has previously been shown to cause stable oscillations in circuits with negative feedback. We show that the period and the amplitude of the oscillations monotonically decrease as the variability of the delay time increases

A Non-Death Role of the Yeast Metacaspase: Yca1p Alters Cell Cycle Dynamics

Caspase proteases are a conserved protein family predominantly known for engaging and executing apoptotic cell death. Nevertheless, in higher eukaryotes, caspases also influence a variety of cell behaviors including differentiation, proliferation and growth control. S. cerevisiae expresses a primordial caspase, yca1, and exhibits apoptosis-like death under certain stresses; however, the benefit of a dedicated death program to single cell organisms is controversial. In the absence of a clear rationale to justify the evolutionary retention of a death only pathway, we hypothesize that yca1 also influences non-apoptotic events. We report that genetic ablation and/or catalytic inactivation of Yca1p leads to a longer G1/S transition accompanied by slower growth in fermentation conditions. Downregulation of Yca1p proteolytic activity also results in failure to arrest during nocodazole treatment, indicating that Yca1p participates in the G2/M mitotic checkpoint. 20s proteasome activity and ROS staining of the Δyca1 strain is indistinguishable from its isogenic control suggesting that putative regulation of the oxidative stress response by Yca1p does not instigate the cell cycle phenotype. Our results demonstrate multiple non-death roles for yca1 in the cell cycle

Modeling Stem Cell Induction Processes

Technology for converting human cells to pluripotent stem cell using induction processes has the potential to revolutionize regenerative medicine. However, the production of these so called iPS cells is still quite inefficient and may be dominated by stochastic effects. In this work we build mass-action models of the core regulatory elements controlling stem cell induction and maintenance. The models include not only the network of transcription factors NANOG, OCT4, SOX2, but also important epigenetic regulatory features of DNA methylation and histone modification. We show that the network topology reported in the literature is consistent with the observed experimental behavior of bistability and inducibility. Based on simulations of stem cell generation protocols, and in particular focusing on changes in epigenetic cellular states, we show that cooperative and independent reaction mechanisms have experimentally identifiable differences in the dynamics of reprogramming, and we analyze such differences and their biological basis. It had been argued that stochastic and elite models of stem cell generation represent distinct fundamental mechanisms. Work presented here suggests an alternative possibility that they represent differences in the amount of information we have about the distribution of cellular states before and during reprogramming protocols. We show further that unpredictability and variation in reprogramming decreases as the cell progresses along the induction process, and that identifiable groups of cells with elite-seeming behavior can come about by a stochastic process. Finally we show how different mechanisms and kinetic properties impact the prospects of improving the efficiency of iPS cell generation protocols.Fundação para a Ciência e a Tecnologia (BD 42942)MIT-Portugal ProgramNational Institutes of Health (U.S.) (CA112967)Singapore–MIT Alliance for Research and TechnologyIntel Corporatio

Endoglin (CD105) expression in ovarian serous carcinoma effusions is related to chemotherapy status

Endoglin (CD105), a cell surface co-receptor for transforming growth factor-β, is expressed in proliferating endothelial cells, as well as in cancer cells. We studied endoglin expression and its clinical relevance in effusions, primary tumors, and solid metastatic lesions from women with advanced-stage ovarian serous carcinoma. Endoglin expression was analyzed by immunohistochemistry in effusions (n = 211; 174 peritoneal, 37 pleural). Cellular endoglin staining was analyzed for association with the concentration of soluble endoglin (previously determined by ELISA) in 95 corresponding effusions and analyzed for correlation with clinicopathologic parameters, including survival. Endoglin expression was additionally studied in 34 patient-matched primary tumors and solid metastases. Carcinoma and mesothelial cells expressed endoglin in 95/211 (45%) and 133/211 (63%) effusions, respectively. Carcinoma cell endoglin expression was more frequent in effusions from patients aged ≤60 years (p = 0.048) and in post- compared to prechemotherapy effusions (p = 0.014), whereas mesothelial cell endoglin expression was higher in prechemotherapy effusions (p = 0.021). No association was found between cellular endoglin expression and its soluble effusion concentration. Endoglin was expressed in 17/34 (50%) primary tumors and 19/34 (56%) metastases, with significantly higher percentage of immunostained cells in solid metastases compared to effusions (p = 0.036). Endoglin expression did not correlate with survival. Tumor cell endoglin expression is higher in post- vs. prechemotherapy effusions, whereas the opposite is seen in mesothelial cells. Together with its upregulation in solid metastases, this suggests that the expression and biological role of endoglin may differ between cell populations and change along tumor progression in ovarian carcinoma

Programmable disorder in random DNA tilings

Scaling up the complexity and diversity of synthetic molecular structures will require strategies that exploit the inherent stochasticity of molecular systems in a controlled fashion. Here we demonstrate a framework for programming random DNA tilings and show how to control the properties of global patterns through simple, local rules. We constructed three general forms of planar network—random loops, mazes and trees—on the surface of self-assembled DNA origami arrays on the micrometre scale with nanometre resolution. Using simple molecular building blocks and robust experimental conditions, we demonstrate control of a wide range of properties of the random networks, including the branching rules, the growth directions, the proximity between adjacent networks and the size distribution. Much as combinatorial approaches for generating random one-dimensional chains of polymers have been used to revolutionize chemical synthesis and the selection of functional nucleic acids, our strategy extends these principles to random two-dimensional networks of molecules and creates new opportunities for fabricating more complex molecular devices that are organized by DNA nanostructures