A family tree of Markov models in systems biology

Motivated by applications in systems biology, we seek a probabilistic framework based on Markov processes to represent intracellular processes. We review the formal relationships between different stochastic models referred to in the systems biology literature. As part of this review, we present a novel derivation of the differential Chapman-Kolmogorov equation for a general multidimensional Markov process made up of both continuous and jump processes. We start with the definition of a time-derivative for a probability density but place no restrictions on the probability distribution, in particular, we do not assume it to be confined to a region that has a surface (on which the probability is zero). In our derivation, the master equation gives the jump part of the Markov process while the Fokker-Planck equation gives the continuous part. We thereby sketch a {}``family tree'' for stochastic models in systems biology, providing explicit derivations of their formal relationship and clarifying assumptions involved.Comment: 18 pages, 2 figure

A Plea for More Theory in Molecular Biology

The integrationist principles of systems theory have proven hugely successful in the physical sciences and engineering. It is an underlying assumption made in the systems approach to biology that they can also be used to understand biological phenomena at the level of an entire organism or organ. Within this holistic vision, the vastmajority of systems biology research projects investigate phenomena at the level of the cell, with the belief that unifying principles established at the most basic level can establish a framework within which we may understand phenomena at higher levels of organization. In this spirit, and to use a celestial analogy, if a disease effecting an organ or entire body is our universe of discourse, then the cell is the star we gaze at. In building an understanding of disease and the effect of drugs, systems biology makes an implicit assumption about direct causal entailment between cell function and physiology. A skeptic might argue that this is about the same as trying to predict the world economy from observations made at a local supermarket. However, assuming for the moment that the money and hope we are investing inmolecular biology, genomics, and systems biology is justified, how should this amazing 118 O. Wolkenhauer, M. Mesarovi´c, P. Wellstead intellectual achievement be possible? In this chapter we argue that an essential tool to progress is a systems theory that allows biological objects and their operational characteristics to be captured in a succinct yet general form. Armed with this conceptual framework, we construct mathematical representations of standard cellular and intercellular functions which can be integrated to describe more general processes of cell complexes, and potentially entire organ

A model checking approach to the parameter estimation of biochemical pathways

Model checking has historically been an important tool to verify models of a wide variety of systems. Typically a model has to exhibit certain properties to be classed ‘acceptable’. In this work we use model checking in a new setting; parameter estimation. We characterise the desired behaviour of a model in a temporal logic property and alter the model to make it conform to the property (determined through model checking). We have implemented a computational system called MC2(GA) which pairs a model checker with a genetic algorithm. To drive parameter estimation, the fitness of set of parameters in a model is the inverse of the distance between its actual behaviour and the desired behaviour. The model checker used is the simulation-based Monte Carlo Model Checker for Probabilistic Linear-time Temporal Logic with numerical constraints, MC2(PLTLc). Numerical constraints as well as the overall probability of the behaviour expressed in temporal logic are used to minimise the behavioural distance. We define the theory underlying our parameter estimation approach in both the stochastic and continuous worlds. We apply our approach to biochemical systems and present an illustrative example where we estimate the kinetic rate constants in a continuous model of a signalling pathway

Stronger computational modelling of signalling pathways using both continuous and discrete-state methods

Starting from a biochemical signalling pathway model expresses in a process algebra enriched with quantitative information, we automatically derive both continuous-space and discrete-space representations suitable for numerical evaluation. We compare results obtained using approximate stochastic simulation thereby exposing a flaw in the use of the differentiation procedure producing misleading results

Unraveling a tumor type-specific regulatory core underlying E2F1-mediated epithelial-mesenchymal transition to predict receptor protein signatures

Cancer is a disease of subverted regulatory pathways. In this paper, we reconstruct the regulatory network around E2F, a family of transcription factors whose deregulation has been associated to cancer progression, chemoresistance, invasiveness, and metastasis. We integrate gene expression profiles of cancer cell lines from two E2F1-driven highly aggressive bladder and breast tumors, and use network analysis methods to identify the tumor type-specific core of the network. By combining logic-based network modeling, in vitro experimentation, and gene expression profiles from patient cohorts displaying tumor aggressiveness, we identify and experimentally validate distinctive, tumor type-specific signatures of receptor proteins associated to epithelial-mesenchymal transition in bladder and breast cancer. Our integrative network-based methodology, exemplified in the case of E2F1-induced aggressive tumors, has the potential to support the design of cohort- as well as tumor type-specific treatments and ultimately, to fight metastasis and therapy resistance

On-the-fly Uniformization of Time-Inhomogeneous Infinite Markov Population Models

This paper presents an on-the-fly uniformization technique for the analysis of time-inhomogeneous Markov population models. This technique is applicable to models with infinite state spaces and unbounded rates, which are, for instance, encountered in the realm of biochemical reaction networks. To deal with the infinite state space, we dynamically maintain a finite subset of the states where most of the probability mass is located. This approach yields an underapproximation of the original, infinite system. We present experimental results to show the applicability of our technique

Dynamics of learning motives and barriers in the context of changing human life roles

This paper promotes a theoretical discussion that focuses on the motives and barriers that make impact on adults learning as well as on their dynamics related to the change of social roles. The adult learning motives and barriers change and vary according to the prevailing social roles at different periods of one’s life. This dynamics of adult learning motives and barriers is mostly influenced by the importance and compatibility of acquired social roles, responsibility areas and spaces of a person and other factors. The qualitative data was gathered in March – April 2016 in Kaunas, Lithuania. The sample consisted of 30 narratives, written by informants, aged 35 to 65 years that were participating in professional training courses. There has been prepared 30 self-reflections that were analysed using content analysis. The analysis of empirical data shows that external learning motives and barriers prevail in the period when an individual is active in the labour market while the personal motives remain overshadowed. However, personal barriers prevail in the expression of learning barriers. This is influenced by the society’s attitude towards the performance of pupil and student roles and the value attitudes of surrounding people that partially control it

Systems biologists seek fuller integration of systems biology approaches in new cancer research programs

Systems biology takes an interdisciplinary approach to the systematic study of complex interactions in biological systems. This approach seeks to decipher the emergent behaviors of complex systems rather than focusing only on their constituent properties. As an increasing number of examples illustrate the value of systems biology approaches to understand the initiation, progression, and treatment of cancer, systems biologists from across Europe and the United States hope for changes in the way their field is currently perceived among cancer researchers. In a recent EU-US workshop, supported by the European Commission, the German Federal Ministry for Education and Research, and the National Cancer Institute of the NIH, the participants discussed the strengths, weaknesses, hurdles, and opportunities in cancer systems biology

Global parameter identification of stochastic reaction networks from single trajectories

We consider the problem of inferring the unknown parameters of a stochastic biochemical network model from a single measured time-course of the concentration of some of the involved species. Such measurements are available, e.g., from live-cell fluorescence microscopy in image-based systems biology. In addition, fluctuation time-courses from, e.g., fluorescence correlation spectroscopy provide additional information about the system dynamics that can be used to more robustly infer parameters than when considering only mean concentrations. Estimating model parameters from a single experimental trajectory enables single-cell measurements and quantification of cell--cell variability. We propose a novel combination of an adaptive Monte Carlo sampler, called Gaussian Adaptation, and efficient exact stochastic simulation algorithms that allows parameter identification from single stochastic trajectories. We benchmark the proposed method on a linear and a non-linear reaction network at steady state and during transient phases. In addition, we demonstrate that the present method also provides an ellipsoidal volume estimate of the viable part of parameter space and is able to estimate the physical volume of the compartment in which the observed reactions take place.Comment: Article in print as a book chapter in Springer's "Advances in Systems Biology

Harmonizing semantic annotations for computational models in biology

Life science researchers use computational models to articulate and test hypotheses about the behavior of biological systems. Semantic annotation is a critical component for enhancing the interoperability and reusability of such models as well as for the integration of the data needed for model parameterization and validation. Encoded as machine-readable links to knowledge resource terms, semantic annotations describe the computational or biological meaning of what models and data represent. These annotations help researchers find and repurpose models, accelerate model composition and enable knowledge integration across model repositories and experimental data stores. However, realizing the potential benefits of semantic annotation requires the development of model annotation standards that adhere to a community-based annotation protocol.Without such standards, tool developers must account for a variety of annotation formats and approaches, a situation that can become prohibitively cumbersome and which can defeat the purpose of linking model elements to controlled knowledge resource terms. Currently, no consensus protocol for semantic annotation exists among the larger biological modeling community. Here, we report on the landscape of current annotation practices among the Computational Modeling in BIology NEtwork community and provide a set of recommendations for building a consensus approach to semantic annotation