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Modeling biological systems with delays in Bio-PEPA
Giulio Caravagna,Jane Hillston
Electronic Proceedings in Theoretical Computer Science , 2010, DOI: 10.4204/eptcs.40.7
Abstract: Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed, or to provide abstraction of some behavior of the system resulting more compact models. In this paper we enrich the stochastic process algebra Bio-PEPA, with the possibility of assigning delays to actions, yielding a new non-Markovian process algebra: Bio-PEPAd. This is a conservative extension meaning that the original syntax of Bio-PEPA is retained and the delay specification which can now be associated with actions may be added to existing Bio-PEPA models. The semantics of the firing of the actions with delays is the delay-as-duration approach, earlier presented in papers on the stochastic simulation of biological systems with delays. These semantics of the algebra are given in the Starting-Terminating style, meaning that the state and the completion of an action are observed as two separate events, as required by delays. Furthermore we outline how to perform stochastic simulation of Bio-PEPAd systems and how to automatically translate a Bio-PEPAd system into a set of Delay Differential Equations, the deterministic framework for modeling of biological systems with delays. We end the paper with two example models of biological systems with delays to illustrate the approach.
The Interplay of Intrinsic and Extrinsic Bounded Noises in Biomolecular Networks
Giulio Caravagna, Giancarlo Mauri, Alberto d'Onofrio
PLOS ONE , 2013, DOI: 10.1371/journal.pone.0051174
Abstract: After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a biomolecular network. The influence of intrinsic and extrinsic noises on biomolecular networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks, i.e. the intrinsic noise, where the model jump rates are affected by colored bounded extrinsic noises synthesized by a suitable biochemical state-dependent Langevin system. These systems are described by a master equation, and a simulation algorithm to analyze them is derived. This new modeling paradigm should enlarge the class of systems amenable at modeling. We investigated the influence of both amplitude and autocorrelation time of a extrinsic Sine-Wiener noise on: the Michaelis-Menten approximation of noisy enzymatic reactions, which we show to be applicable also in co-presence of both intrinsic and extrinsic noise, a model of enzymatic futile cycle and a genetic toggle switch. In and we show that the presence of a bounded extrinsic noise induces qualitative modifications in the probability densities of the involved chemicals, where new modes emerge, thus suggesting the possible functional role of bounded noises.
Effects of delayed immune-response in tumor immune-system interplay
Giulio Caravagna,Alex Graudenzi,Marco Antoniotti,Giancarlo Mauri
Electronic Proceedings in Theoretical Computer Science , 2012, DOI: 10.4204/eptcs.92.8
Abstract: Tumors constitute a wide family of diseases kinetically characterized by the co-presence of multiple spatio-temporal scales. So, tumor cells ecologically interplay with other kind of cells, e.g. endothelial cells or immune system effectors, producing and exchanging various chemical signals. As such, tumor growth is an ideal object of hybrid modeling where discrete stochastic processes model agents at low concentrations, and mean-field equations model chemical signals. In previous works we proposed a hybrid version of the well-known Panetta-Kirschner mean-field model of tumor cells, effector cells and Interleukin-2. Our hybrid model suggested -at variance of the inferences from its original formulation- that immune surveillance, i.e. tumor elimination by the immune system, may occur through a sort of side-effect of large stochastic oscillations. However, that model did not account that, due to both chemical transportation and cellular differentiation/division, the tumor-induced recruitment of immune effectors is not instantaneous but, instead, it exhibits a lag period. To capture this, we here integrate a mean-field equation for Interleukins-2 with a bi-dimensional delayed stochastic process describing such delayed interplay. An algorithm to realize trajectories of the underlying stochastic process is obtained by coupling the Piecewise Deterministic Markov process (for the hybrid part) with a Generalized Semi-Markovian clock structure (to account for delays). We (i) relate tumor mass growth with delays via simulations and via parametric sensitivity analysis techniques, (ii) we quantitatively determine probabilistic eradication times, and (iii) we prove, in the oscillatory regime, the existence of a heuristic stochastic bifurcation resulting in delay-induced tumor eradication, which is neither predicted by the mean-field nor by the hybrid non-delayed models.
Aspects of multiscale modelling in a process algebra for biological systems
Roberto Barbuti,Giulio Caravagna,Paolo Milazzo,Andrea Maggiolo-Schettini
Electronic Proceedings in Theoretical Computer Science , 2010, DOI: 10.4204/eptcs.40.5
Abstract: We propose a variant of the CCS process algebra with new features aiming at allowing multiscale modelling of biological systems. In the usual semantics of process algebras for modelling biological systems actions are instantaneous. When different scale levels of biological systems are considered in a single model, one should take into account that actions at a level may take much more time than actions at a lower level. Moreover, it might happen that while a component is involved in one long lasting high level action, it is involved also in several faster lower level actions. Hence, we propose a process algebra with operations and with a semantics aimed at dealing with these aspects of multiscale modelling. We study behavioural equivalences for such an algebra and give some examples.
On the Interpretation of Delays in Delay Stochastic Simulation of Biological Systems
Roberto Barbuti,Giulio Caravagna,Paolo Milazzo,Andrea Maggiolo-Schettini
Electronic Proceedings in Theoretical Computer Science , 2009, DOI: 10.4204/eptcs.6.2
Abstract: Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed. Mathematical modeling of biological systems with delays is usually based on Delay Differential Equations (DDEs), a kind of differential equations in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. In the literature, delay stochastic simulation algorithms have been proposed. These algorithms follow a ``delay as duration'' approach, namely they are based on an interpretation of a delay as the elapsing time between the start and the termination of a chemical reaction. This interpretation is not suitable for some classes of biological systems in which species involved in a delayed interaction can be involved at the same time in other interactions. We show on a DDE model of tumor growth that the delay as duration approach for stochastic simulation is not precise, and we propose a simulation algorithm based on a ``purely delayed'' interpretation of delays which provides better results on the considered model.
Investigating the Relation between Stochastic Differentiation, Homeostasis and Clonal Expansion in Intestinal Crypts via Multiscale Modeling
Alex Graudenzi, Giulio Caravagna, Giovanni De Matteis, Marco Antoniotti
PLOS ONE , 2014, DOI: 10.1371/journal.pone.0097272
Abstract: Colorectal tumors originate and develop within intestinal crypts. Even though some of the essential phenomena that characterize crypt structure and dynamics have been effectively described in the past, the relation between the differentiation process and the overall crypt homeostasis is still only partially understood. We here investigate this relation and other important biological phenomena by introducing a novel multiscale model that combines a morphological description of the crypt with a gene regulation model: the emergent dynamical behavior of the underlying gene regulatory network drives cell growth and differentiation processes, linking the two distinct spatio-temporal levels. The model relies on a few a priori assumptions, yet accounting for several key processes related to crypt functioning, such as: dynamic gene activation patterns, stochastic differentiation, signaling pathways ruling cell adhesion properties, cell displacement, cell growth, mitosis, apoptosis and the presence of biological noise. We show that this modeling approach captures the major dynamical phenomena that characterize the regular physiology of crypts, such as cell sorting, coordinate migration, dynamic turnover, stem cell niche correct positioning and clonal expansion. All in all, the model suggests that the process of stochastic differentiation might be sufficient to drive the crypt to homeostasis, under certain crypt configurations. Besides, our approach allows to make precise quantitative inferences that, when possible, were matched to the current biological knowledge and it permits to investigate the role of gene-level perturbations, with reference to cancer development. We also remark the theoretical framework is general and may be applied to different tissues, organs or organisms.
Inference of Cancer Progression Models with Biological Noise
Ilya Korsunsky,Daniele Ramazzotti,Giulio Caravagna,Bud Mishra
Computer Science , 2014,
Abstract: Many applications in translational medicine require the understanding of how diseases progress through the accumulation of persistent events. Specialized Bayesian networks called monotonic progression networks offer a statistical framework for modeling this sort of phenomenon. Current machine learning tools to reconstruct Bayesian networks from data are powerful but not suited to progression models. We combine the technological advances in machine learning with a rigorous philosophical theory of causation to produce Polaris, a scalable algorithm for learning progression networks that accounts for causal or biological noise as well as logical relations among genetic events, making the resulting models easy to interpret qualitatively. We tested Polaris on synthetically generated data and showed that it outperforms a widely used machine learning algorithm and approaches the performance of the competing special-purpose, albeit clairvoyant algorithm that is given a priori information about the model parameters. We also prove that under certain rather mild conditions, Polaris is guaranteed to converge for sufficiently large sample sizes. Finally, we applied Polaris to point mutation and copy number variation data in Prostate cancer from The Cancer Genome Atlas (TCGA) and found that there are likely three distinct progressions, one major androgen driven progression, one major non-androgen driven progression, and one novel minor androgen driven progression.
Proceedings Wivace 2013 - Italian Workshop on Artificial Life and Evolutionary Computation
Alex Graudenzi,Giulio Caravagna,Giancarlo Mauri,Marco Antoniotti
Computer Science , 2013, DOI: 10.4204/EPTCS.130
Abstract: The Wivace 2013 Electronic Proceedings in Theoretical Computer Science (EPTCS) contain some selected long and short articles accepted for the presentation at Wivace 2013 - Italian Workshop on Artificial Life and Evolutionary Computation, which was held at the University of Milan-Bicocca, Milan, on the 1st and 2nd of July, 2013.
Analysis of the spatial and dynamical properties of a multiscale model of intestinal crypts
Giulio Caravagna,Alex Graudenzi,Marco Antoniotti,Giovanni de Matteis
Computer Science , 2013, DOI: 10.4204/EPTCS.130.12
Abstract: The preliminary analyses on a multiscale model of intestinal crypt dynamics are here presented. The model combines a morphological model, based on the Cellular Potts Model (CPM), and a gene regulatory network model, based on Noisy Random Boolean Networks (NRBNs). Simulations suggest that the stochastic differentiation process is itself sufficient to ensure the general homeostasis in the asymptotic states, as proven by several measures.
Gene switching rate determines response to extrinsic perturbations in a transcriptional network motif
Sebastiano de Franciscis,Giulio Caravagna,Alberto d'Onofrio
Quantitative Biology , 2014,
Abstract: It is well-known that gene activation/deactivation dynamics may be a major source of randomness in genetic networks, also in the case of large concentrations of the transcription factors. In this work, we investigate the effect of realistic extrinsic noises acting on gene deactivation in a common network motif - the positive feedback of a transcription factor on its own synthesis - under a variety of settings, i.e., distinct cellular types, distribution of proteins and properties of the external perturbations. At variance with standard models where the perturbations are Gaussian unbounded, we focus here on bounded extrinsic noises to better mimic biological reality. Our results suggest that the gene switching velocity is a key parameter to modulate the response of the network. Simulations suggest that, if the gene switching is fast and many proteins are present, an irreversible noise-induced first order transition is observed as a function of the noise intensity. If noise intensity is further increased a second order transition is also observed. When gene switching is fast, a similar scenario is observed even when few proteins are present, provided that larger cells are considered, which is mainly influenced by noise autocorrelation. On the contrary, if the gene switching is slow, no fist order transitions are observed. In the concluding remarks possible implications of the irreversible transitions for cellular differentiation are briefly discussed.
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