Financial asset bubbles in banking networks

We consider a banking network represented by a system of stochastic differential equations coupled by their drift. We assume a core-periphery structure, and that the banks in the core hold a bubbly asset. The banks in the periphery have not direct access to the bubble, but can take initially advantage from its increase by investing on the banks in the core. Investments are modeled by the weight of the links, which is a function of the robustness of the banks. In this way, a preferential attachment mechanism towards the core takes place during the growth of the bubble. We then investigate how the bubble distort the shape of the network, both for finite and infinitely large systems, assuming a non vanishing impact of the core on the periphery. Due to the influence of the bubble, the banks are no longer independent, and the law of large numbers cannot be directly applied at the limit. This results in a term in the drift of the diffusions which does not average out, and that increases systemic risk at the moment of the burst. We test this feature of the model by numerical simulations.Comment: 33 pages, 6 table

Stochastic Biological System-of-Systems Modelling for iPSC Culture

Large-scale manufacturing of induced pluripotent stem cells (iPSCs) is essential for cell therapies and regenerative medicines. Yet, iPSCs form large cell aggregates in suspension bioreactors, resulting in insufficient nutrient supply and extra metabolic waste build-up for the cells located at core. Since subtle changes in micro-environment can lead to cell stress and heterogeneous cell population, a novel Biological System-of-Systems (Bio-SoS) framework is proposed to characterize cell-to-cell interactions, spatial heterogeneity, and cell response to micro-environmental variation. Building on stochastic metabolic reaction network, aggregation kinetics, and reaction-diffusion mechanisms, the Bio-SoS model can quantify the impact of factors (i.e., aggregate size) on cell product health and quality heterogeneity, accounting for causal interdependencies at individual cell, aggregate, and cell population levels. This framework can accurately predict iPSC culture conditions for both monolayer and aggregate cultures, where these predictions can be leveraged to ensure the control of culture processes for successful cell growth and expansion.Comment: 36 pages, 10 figure

Programmable models of growth and mutation of cancer-cell populations

In this paper we propose a systematic approach to construct mathematical models describing populations of cancer-cells at different stages of disease development. The methodology we propose is based on stochastic Concurrent Constraint Programming, a flexible stochastic modelling language. The methodology is tested on (and partially motivated by) the study of prostate cancer. In particular, we prove how our method is suitable to systematically reconstruct different mathematical models of prostate cancer growth - together with interactions with different kinds of hormone therapy - at different levels of refinement.Comment: In Proceedings CompMod 2011, arXiv:1109.104

Bridging Time Scales in Cellular Decision Making with a Stochastic Bistable Switch

Cellular transformations which involve a significant phenotypical change of the cell's state use bistable biochemical switches as underlying decision systems. In this work, we aim at linking cellular decisions taking place on a time scale of years to decades with the biochemical dynamics in signal transduction and gene regulation, occuring on a time scale of minutes to hours. We show that a stochastic bistable switch forms a viable biochemical mechanism to implement decision processes on long time scales. As a case study, the mechanism is applied to model the initiation of follicle growth in mammalian ovaries, where the physiological time scale of follicle pool depletion is on the order of the organism's lifespan. We construct a simple mathematical model for this process based on experimental evidence for the involved genetic mechanisms. Despite the underlying stochasticity, the proposed mechanism turns out to yield reliable behavior in large populations of cells subject to the considered decision process. Our model explains how the physiological time constant may emerge from the intrinsic stochasticity of the underlying gene regulatory network. Apart from ovarian follicles, the proposed mechanism may also be of relevance for other physiological systems where cells take binary decisions over a long time scale.Comment: 14 pages, 4 figure

Fluctuation effects in metapopulation models: percolation and pandemic threshold

Metapopulation models provide the theoretical framework for describing disease spread between different populations connected by a network. In particular, these models are at the basis of most simulations of pandemic spread. They are usually studied at the mean-field level by neglecting fluctuations. Here we include fluctuations in the models by adopting fully stochastic descriptions of the corresponding processes. This level of description allows to address analytically, in the SIS and SIR cases, problems such as the existence and the calculation of an effective threshold for the spread of a disease at a global level. We show that the possibility of the spread at the global level is described in terms of (bond) percolation on the network. This mapping enables us to give an estimate (lower bound) for the pandemic threshold in the SIR case for all values of the model parameters and for all possible networks.Comment: 14 pages, 13 figures, final versio

Theory of Robustness of Irreversible Differentiation in a Stem Cell System: Chaos hypothesis

Based on extensive study of a dynamical systems model of the development of a cell society, a novel theory for stem cell differentiation and its regulation is proposed as the ``chaos hypothesis''. Two fundamental features of stem cell systems - stochastic differentiation of stem cells and the robustness of a system due to regulation of this differentiation - are found to be general properties of a system of interacting cells exhibiting chaotic intra-cellular reaction dynamics and cell division, whose presence does not depend on the detail of the model. It is found that stem cells differentiate into other cell types stochastically due to a dynamical instability caused by cell-cell interactions, in a manner described by the Isologous Diversification theory. This developmental process is shown to be stable not only with respect to molecular fluctuations but also with respect to removal of cells. With this developmental process, the irreversible loss of multipotency accompanying the change from a stem cell to a differentiated cell is shown to be characterized by a decrease in the chemical diversity in the cell and of the complexity of the cellular dynamics. The relationship between the division speed and this loss of multipotency is also discussed. Using our model, some predictions that can be tested experimentally are made for a stem cell system.Comment: 31 pages, 10 figures, submitted to Jour. Theor. Bio

Parallel implementation of stochastic simulation for large-scale cellular processes

Experimental and theoretical studies have shown the importance of stochastic processes in genetic regulatory networks and cellular processes. Cellular networks and genetic circuits often involve small numbers of key proteins such as transcriptional factors and signaling proteins. In recent years stochastic models have been used successfully for studying noise in biological pathways, and stochastic modelling of biological systems has become a very important research field in computational biology. One of the challenge problems in this field is the reduction of the huge computing time in stochastic simulations. Based on the system of the mitogen-activated protein kinase cascade that is activated by epidermal growth factor, this work give a parallel implementation by using OpenMP and parallelism across the simulation. Special attention is paid to the independence of the generated random numbers in parallel computing, that is a key criterion for the success of stochastic simulations. Numerical results indicate that parallel computers can be used as an efficient tool for simulating the dynamics of large-scale genetic regulatory networks and cellular processes