Stochastic Modeling of Complex Systems and Systems Biology: From Stochastic Transition Systems to Hybrid Systems

International audienceModeling complex dynamic systems requires to reuse and to combine models in a non-ambiguous way, integrating processes with different information levels and temporal dependences. System behaviors are consequence of interacting processes, which are affected by external factors often not controlled. In particular, biological functions are the result of processes that connect different hierarchy levels, associated by physical and chemical relations (H. Kitano (2002)). Each process works in different way and it is common to observe that changes in the conditions, such as quantity of nutrients or environment, modify the behavior of the systems. The firstt approach we discuss is the use of Stochastic Transition Systems (STSs, L.D. Alfaro (1998)). It considers the dynamics of system variables given by transitions, changing their values, described by Markov processes with continuous time. Transitions are provoked by specific conditions of system variables, which can be ambiguous and generate non-determinism. Although STSs allow us to incorporate randomness and non-determinism, we do not capture the complexity of behaviors nor the continuity of the variables. To describe the behavior of complex systems over time, it is convenient to combine different types of models: continuous models for gradual changes, discrete models for instantaneous changes, deterministic models for completely predictable behaviors, and stochastic or non-deterministic models to describe behaviors with imprecise or incomplete information. To do that, we use the Hybrid Systems theory and the composition of models. System variables evolve according to continuous models, but deterministic, stochastic and non-deterministic transitions can change the definition of these models. Composition is the action of combining different models into an integrated model. We connect them by using input-output relations, and by processes synchronization (e.g. activation or repression signals). A very intuitive example of hybrid system is the motion of an automobile with a manual gearbox. The dynamics of the velocity and position evolve in a continuous specific way depending of the engaged gear. With an automatic gearbox the gear changes are deterministic, but if it is manual many factors influence the decisions of the driver, and the transitions are stochastic or non-deterministic. According to the form of the model changes, we consider hybrid systems with coefficient switches, or with strong switches. For coefficient switches, the transitions provoke changes in specific coefficients of the continuous model. For strong switches, transitions control the activation of models allowing radical changes. First type favors the interpretation of the effect of transitions on the continuous model, while strong switches are useful for reconciling models with different nature (R. Assar (2011)). This approach allows us to build more complete descriptions of complex biological systems. As application, we built a hybrid model of the osteo-adipo differentiation process. It combines known validated models to predict the bone and fat formation in response to activation of pathways such as the Wnt pathway, stochastic factors, and changes of conditions affecting these functions (R. Assar et al. (2012)). This model is our first phase to simulate physiological responses to treatments of bone mass disorders in silico, and to explore the efficiency of new medical strategies before testing them in vitro or in vivo

Stochastic Modeling of Complex Systems and Systems Biology: From Stochastic Transition Systems to Hybrid Systems

International audienceModeling complex dynamic systems requires to reuse and to combine models in a non-ambiguous way, integrating processes with different information levels and temporal dependences. System behaviors are consequence of interacting processes, which are affected by external factors often not controlled. In particular, biological functions are the result of processes that connect different hierarchy levels, associated by physical and chemical relations (H. Kitano (2002)). Each process works in different way and it is common to observe that changes in the conditions, such as quantity of nutrients or environment, modify the behavior of the systems. The firstt approach we discuss is the use of Stochastic Transition Systems (STSs, L.D. Alfaro (1998)). It considers the dynamics of system variables given by transitions, changing their values, described by Markov processes with continuous time. Transitions are provoked by specific conditions of system variables, which can be ambiguous and generate non-determinism. Although STSs allow us to incorporate randomness and non-determinism, we do not capture the complexity of behaviors nor the continuity of the variables. To describe the behavior of complex systems over time, it is convenient to combine different types of models: continuous models for gradual changes, discrete models for instantaneous changes, deterministic models for completely predictable behaviors, and stochastic or non-deterministic models to describe behaviors with imprecise or incomplete information. To do that, we use the Hybrid Systems theory and the composition of models. System variables evolve according to continuous models, but deterministic, stochastic and non-deterministic transitions can change the definition of these models. Composition is the action of combining different models into an integrated model. We connect them by using input-output relations, and by processes synchronization (e.g. activation or repression signals). A very intuitive example of hybrid system is the motion of an automobile with a manual gearbox. The dynamics of the velocity and position evolve in a continuous specific way depending of the engaged gear. With an automatic gearbox the gear changes are deterministic, but if it is manual many factors influence the decisions of the driver, and the transitions are stochastic or non-deterministic. According to the form of the model changes, we consider hybrid systems with coefficient switches, or with strong switches. For coefficient switches, the transitions provoke changes in specific coefficients of the continuous model. For strong switches, transitions control the activation of models allowing radical changes. First type favors the interpretation of the effect of transitions on the continuous model, while strong switches are useful for reconciling models with different nature (R. Assar (2011)). This approach allows us to build more complete descriptions of complex biological systems. As application, we built a hybrid model of the osteo-adipo differentiation process. It combines known validated models to predict the bone and fat formation in response to activation of pathways such as the Wnt pathway, stochastic factors, and changes of conditions affecting these functions (R. Assar et al. (2012)). This model is our first phase to simulate physiological responses to treatments of bone mass disorders in silico, and to explore the efficiency of new medical strategies before testing them in vitro or in vivo

Modeling acclimatization by hybrid systems: Condition changes alter biological system behavior models.

International audience: In order to describe the dynamic behavior of a complex biological system, it is useful to combine models integrating processes at different levels and with temporal dependencies. Such combinations are necessary for modeling acclimatization, a phenomenon where changes in environmental conditions can induce drastic changes in the behavior of a biological system. In this article we formalize the use of hybrid systems as a tool to model this kind of biological behavior. A modeling scheme called strong switches is proposed. It allows one to take into account both minor adjustments to the coefficients of a continuous model, and, more interestingly, large-scale changes to the structure of the model. We illustrate the proposed methodology with two applications: acclimatization in wine fermentation kinetics, and acclimatization of osteo-adipo differentiation system linking stimulus signals to bone mass

Reusing and composing models of cell fate regulation of human bone precursor cells.

International audienceIn order to treat osteoporosis and other bone mass disorders it is necessary to understand the regulatory processes that control the cell fate decisions responsible for going from bone precursor cells to bone tissue. Many processes interact to regulate cell division, differentiation and apoptosis. There are models for these basic processes, but not for their interactions. In this work we use the theory of switched systems, reuse and composition of validated models to describe the cell fate decisions leading to bone and fat formation. We describe the differentiation of osteo-adipo progenitor cells by composing its model with differentiation stimuli. We use the activation of the Wnt pathway as stimulus to osteoblast lineage, including regulation of cell division and apoptosis. This model is our first step to simulate physiological responses in silico to treatments for bone mass disorders

Primary lung cancer cell culture from transthoracic needle biopsy samples

Lung cancer is the leading cause of cancer death in the world. The high mortality rate of this pathology is directly related to its late detection, since its symptoms can be masked by other diseases of lower risk. Although in recent years the number of research related to this subject has increased, molecular mechanisms that trigger this disease remains poorly understood. Experimental models are therefore vital for use in research. Immortalized cell lines have inherent limitations. Explanted tumoral cells obtained by transthoracic needle biopsy can be a potential source of primary culture of human lung tumor cells. Tumor specimens from 14 patients suspected of primary or metastatic lung cancer were obtained by CT-guided transthoracic lung biopsy. Solid tumors were mechanically disaggregated under a stereoscope. Cells were cultured in Base C growth media supplemented with 5% fetal bovine serum in 24-well cell culture plates. Primary lung cancer cell culture was successfully cultured from 12 out of 14 patients. Once a confluent monolayer was obtained, cells were enzymatically harvested and passaged to Petri culture dishes. These primary cell cultures were characterized by cytogenetic tests and gene expression analysis of diagnostic markers. These primary cell cultures revealed chromosome rearrangements and changes in their chromosome complement typical of tumoral cells. Additionally, Fluorescence in situ hybridization analysis demonstrated that three cultures exhibited EGFR amplification. Finally, expression profiles of CK7, NAPSIN A, TTF1, and P63 genes allowed in some cases to confirm sample tumor phenotype. These results demonstrate that primary lung cancer cell culture is possible from percutaneous puncture and provides an important biological source to asses and investigate the molecular mechanisms of lung cancer

Whole Genome Sequence, Variant Discovery and Annotation in Mapuche-Huilliche Native South Americans

Abstract Whole human genome sequencing initiatives help us understand population history and the basis of genetic diseases. Current data mostly focuses on Old World populations, and the information of the genomic structure of Native Americans, especially those from the Southern Cone is scant. Here we present annotation and variant discovery from high-quality complete genome sequences of a cohort of 11 Mapuche-Huilliche individuals (HUI) from Southern Chile. We found approximately 3.1 × 106 single nucleotide variants (SNVs) per individual and identified 403,383 (6.9%) of novel SNVs events. Analyses of large-scale genomic events detected 680 copy number variants (CNVs) and 4,514 structural variants (SVs), including 398 and 1,910 novel events, respectively. Global ancestry composition of HUI genomes revealed that the cohort represents a sample from a marginally admixed population from the Southern Cone, whose main genetic component derives from Native American ancestors. Additionally, we found that HUI genomes contain variants in genes associated with 5 of the 6 leading causes of noncommunicable diseases in Chile, which may have an impact on the risk of prevalent diseases in Chilean and Amerindian populations. Our data represents a useful resource that can contribute to population-based studies and for the design of early diagnostics or prevention tools for Native and admixed Latin American populations