96 research outputs found
Population balances in case of crossing characteristic curves: Application to T-cells immune response
The progression of a cell population where each individual is characterized
by the value of an internal variable varying with time (e.g. size, weight, and
protein concentration) is typically modeled by a Population Balance Equation, a
first order linear hyperbolic partial differential equation. The
characteristics described by internal variables usually vary monotonically with
the passage of time. A particular difficulty appears when the characteristic
curves exhibit different slopes from each other and therefore cross each other
at certain times. In particular such crossing phenomenon occurs during T-cells
immune response when the concentrations of protein expressions depend upon each
other and also when some global protein (e.g. Interleukin signals) is also
involved which is shared by all T-cells. At these crossing points, the linear
advection equation is not possible by using the classical way of hyperbolic
conservation laws. Therefore, a new Transport Method is introduced in this
article which allowed us to find the population density function for such
processes. The newly developed Transport method (TM) is shown to work in the
case of crossing and to provide a smooth solution at the crossing points in
contrast to the classical PDF techniques.Comment: 18 pages, 10 figure
Numerical Integration of the Master Equation in Some Models of Stochastic Epidemiology
The processes by which disease spreads in a population of individuals are inherently stochastic. The master equation has proven to be a useful tool for modeling such processes. Unfortunately, solving the master equation analytically is possible only in limited cases (e.g., when the model is linear), and thus numerical procedures or approximation methods must be employed. Available approximation methods, such as the system size expansion method of van Kampen, may fail to provide reliable solutions, whereas current numerical approaches can induce appreciable computational cost. In this paper, we propose a new numerical technique for solving the master equation. Our method is based on a more informative stochastic process than the population process commonly used in the literature. By exploiting the structure of the master equation governing this process, we develop a novel technique for calculating the exact solution of the master equation – up to a desired precision – in certain models of stochastic epidemiology. We demonstrate the potential of our method by solving the master equation associated with the stochastic SIR epidemic model. MATLAB software that implements the methods discussed in this paper is freely available as Supporting Information S1
Simple, Fast and Accurate Implementation of the Diffusion Approximation Algorithm for Stochastic Ion Channels with Multiple States
The phenomena that emerge from the interaction of the stochastic opening and
closing of ion channels (channel noise) with the non-linear neural dynamics are
essential to our understanding of the operation of the nervous system. The
effects that channel noise can have on neural dynamics are generally studied
using numerical simulations of stochastic models. Algorithms based on discrete
Markov Chains (MC) seem to be the most reliable and trustworthy, but even
optimized algorithms come with a non-negligible computational cost. Diffusion
Approximation (DA) methods use Stochastic Differential Equations (SDE) to
approximate the behavior of a number of MCs, considerably speeding up
simulation times. However, model comparisons have suggested that DA methods did
not lead to the same results as in MC modeling in terms of channel noise
statistics and effects on excitability. Recently, it was shown that the
difference arose because MCs were modeled with coupled activation subunits,
while the DA was modeled using uncoupled activation subunits. Implementations
of DA with coupled subunits, in the context of a specific kinetic scheme,
yielded similar results to MC. However, it remained unclear how to generalize
these implementations to different kinetic schemes, or whether they were faster
than MC algorithms. Additionally, a steady state approximation was used for the
stochastic terms, which, as we show here, can introduce significant
inaccuracies. We derived the SDE explicitly for any given ion channel kinetic
scheme. The resulting generic equations were surprisingly simple and
interpretable - allowing an easy and efficient DA implementation. The algorithm
was tested in a voltage clamp simulation and in two different current clamp
simulations, yielding the same results as MC modeling. Also, the simulation
efficiency of this DA method demonstrated considerable superiority over MC
methods.Comment: 32 text pages, 10 figures, 1 supplementary text + figur
Models for synthetic biology
Synthetic biological engineering is emerging from biology as a distinct discipline based on quantification. The technologies propelling synthetic biology are not new, nor is the concept of designing novel biological molecules. What is new is the emphasis on system behavior
Statistical abstraction for multi-scale spatio-temporal systems
Spatio-temporal systems exhibiting multi-scale behaviour are common in
applications ranging from cyber-physical systems to systems biology, yet they
present formidable challenges for computational modelling and analysis. Here we
consider a prototypic scenario where spatially distributed agents decide their
movement based on external inputs and a fast-equilibrating internal
computation. We propose a generally applicable strategy based on statistically
abstracting the internal system using Gaussian Processes, a powerful class of
non-parametric regression techniques from Bayesian Machine Learning. We show on
a running example of bacterial chemotaxis that this approach leads to accurate
and much faster simulations in a variety of scenarios.Comment: 14th International Conference on Quantitative Evaluation of SysTems
(QEST 2017
Stochastic analysis of the GAL genetic switch in Saccharomyces cerevisiae: Modeling and experiments reveal hierarchy in glucose repression
<p>Abstract</p> <p>Background</p> <p>Transcriptional regulation involves protein-DNA and protein-protein interactions. Protein-DNA interactions involve reactants that are present in low concentrations, leading to stochastic behavior. In addition, multiple regulatory mechanisms are typically involved in transcriptional regulation. In the <it>GAL </it>regulatory system of <it>Saccharomyces cerevisiae</it>, the inhibition of glucose is accomplished through two regulatory mechanisms: one through the transcriptional repressor Mig1p, and the other through regulating the amount of transcriptional activator Gal4p. However, the impact of stochasticity in gene expression and hierarchy in regulatory mechanisms on the phenotypic level is not clearly understood.</p> <p>Results</p> <p>We address the question of quantifying the effect of stochasticity inherent in these regulatory mechanisms on the performance of various genes under the regulation of Mig1p and Gal4p using a dynamic stochastic model. The stochastic analysis reveals the importance of both the mechanisms of regulation for tight expression of genes in the <it>GAL </it>network. The mechanism involving Gal4p is the dominant mechanism, yielding low variability in the expression of <it>GAL </it>genes. The mechanism involving Mig1p is necessary to maintain the switch-like response of certain <it>GAL </it>genes. The number of binding sites for Mig1p and Gal4p further influences the expression of the genes, with extra binding sites lowering the variability of expression. Our experiments involving growth on various substrates show that the trends predicted in mean expression and its variability are transmitted to the phenotypic level.</p> <p>Conclusion</p> <p>The mechanisms involved in the transcriptional regulation and their variability set up a hierarchy in the phenotypic response to growth on various substrates. Structural motifs, such as the number of binding sites and the mechanism of regulation, determine the level of stochasticity and eventually, the phenotypic response.</p
Engineering modular and orthogonal genetic logic gates for robust digital-like synthetic biology
Modular and orthogonal genetic logic gates are essential for building robust biologically based digital devices to customize cell signalling in synthetic biology. Here we constructed an orthogonal AND gate in Escherichia coli using a novel hetero-regulation module from Pseudomonas syringae. The device comprises two co-activating genes hrpR and hrpS controlled by separate promoter inputs, and a σ54-dependent hrpL promoter driving the output. The hrpL promoter is activated only when both genes are expressed, generating digital-like AND integration behaviour. The AND gate is demonstrated to be modular by applying new regulated promoters to the inputs, and connecting the output to a NOT gate module to produce a combinatorial NAND gate. The circuits were assembled using a parts-based engineering approach of quantitative characterization, modelling, followed by construction and testing. The results show that new genetic logic devices can be engineered predictably from novel native orthogonal biological control elements using quantitatively in-context characterized parts
Global parameter estimation methods for stochastic biochemical systems
<p>Abstract</p> <p>Background</p> <p>The importance of stochasticity in cellular processes having low number of molecules has resulted in the development of stochastic models such as chemical master equation. As in other modelling frameworks, the accompanying rate constants are important for the end-applications like analyzing system properties (e.g. robustness) or predicting the effects of genetic perturbations. Prior knowledge of kinetic constants is usually limited and the model identification routine typically includes parameter estimation from experimental data. Although the subject of parameter estimation is well-established for deterministic models, it is not yet routine for the chemical master equation. In addition, recent advances in measurement technology have made the quantification of genetic substrates possible to single molecular levels. Thus, the purpose of this work is to develop practical and effective methods for estimating kinetic model parameters in the chemical master equation and other stochastic models from single cell and cell population experimental data.</p> <p>Results</p> <p>Three parameter estimation methods are proposed based on the maximum likelihood and density function distance, including probability and cumulative density functions. Since stochastic models such as chemical master equations are typically solved using a Monte Carlo approach in which only a finite number of Monte Carlo realizations are computationally practical, specific considerations are given to account for the effect of finite sampling in the histogram binning of the state density functions. Applications to three practical case studies showed that while maximum likelihood method can effectively handle low replicate measurements, the density function distance methods, particularly the cumulative density function distance estimation, are more robust in estimating the parameters with consistently higher accuracy, even for systems showing multimodality.</p> <p>Conclusions</p> <p>The parameter estimation methodologies described in this work have provided an effective and practical approach in the estimation of kinetic parameters of stochastic systems from either sparse or dense cell population data. Nevertheless, similar to kinetic parameter estimation in other modelling frameworks, not all parameters can be estimated accurately, which is a common problem arising from the lack of complete parameter identifiability from the available data.</p
An Environment-Sensitive Synthetic Microbial Ecosystem
Microbial ecosystems have been widely used in industrial production, but the inter-relationships of organisms within them haven't been completely clarified due to complex composition and structure of natural microbial ecosystems. So it is challenging for ecologists to get deep insights on how ecosystems function and interplay with surrounding environments. But the recent progresses in synthetic biology show that construction of artificial ecosystems where relationships of species are comparatively clear could help us further uncover the meadow of those tiny societies. By using two quorum-sensing signal transduction circuits, this research designed, simulated and constructed a synthetic ecosystem where various population dynamics formed by changing environmental factors. Coherent experimental data and mathematical simulation in our study show that different antibiotics levels and initial cell densities can result in correlated population dynamics such as extinction, obligatory mutualism, facultative mutualism and commensalism. This synthetic ecosystem provides valuable information for addressing questions in ecology and may act as a chassis for construction of more complex microbial ecosystems
Viral epidemics in a cell culture: novel high resolution data and their interpretation by a percolation theory based model
Because of its relevance to everyday life, the spreading of viral infections
has been of central interest in a variety of scientific communities involved in
fighting, preventing and theoretically interpreting epidemic processes. Recent
large scale observations have resulted in major discoveries concerning the
overall features of the spreading process in systems with highly mobile
susceptible units, but virtually no data are available about observations of
infection spreading for a very large number of immobile units. Here we present
the first detailed quantitative documentation of percolation-type viral
epidemics in a highly reproducible in vitro system consisting of tens of
thousands of virtually motionless cells. We use a confluent astroglial
monolayer in a Petri dish and induce productive infection in a limited number
of cells with a genetically modified herpesvirus strain. This approach allows
extreme high resolution tracking of the spatio-temporal development of the
epidemic. We show that a simple model is capable of reproducing the basic
features of our observations, i.e., the observed behaviour is likely to be
applicable to many different kinds of systems. Statistical physics inspired
approaches to our data, such as fractal dimension of the infected clusters as
well as their size distribution, seem to fit into a percolation theory based
interpretation. We suggest that our observations may be used to model epidemics
in more complex systems, which are difficult to study in isolation.Comment: To appear in PLoS ONE. Supporting material can be downloaded from
http://amur.elte.hu/BDGVirus
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