Methods for and results from the study of design principles in molecular systems

Quantitative Operating Principles of Yeast Metabolism during Adaptation to Heat Stress

Microorganisms evolved adaptive responses to survive stressful challenges in ever-changing environments. Understanding the relationships between the physiological/metabolic adjustments allowing cellular stress adaptation and gene expression changes being used by organisms to achieve such adjustments may significantly impact our ability to understand and/or guide evolution. Here, we studied those relationships during adaptation to various stress challenges in Saccharomyces cerevisiae, focusing on heat stress responses. We combined dozens of independent experiments measuring whole-genome gene expression changes during stress responses with a simplified kinetic model of central metabolism. We identified alternative quantitative ranges for a set of physiological variables in the model (production of ATP, trehalose, NADH, etc.) that are specific for adaptation to either heat stress or desiccation/rehydration. Our approach is scalable to other adaptive responses and could assist in developing biotechnological applications to manipulate cells for medical, biotechnological, or synthetic biology purposes.

Regulation of the Na+/K+-ATPase Ena1 Expression by Calcineurin/Crz1 under High pH Stress: A Quantitative Study

Regulated expression of the Ena1 Na+-ATPase is a crucial event for adaptation to high salt and/or alkaline pH stress in the budding yeast Saccharomyces cerevisiae. ENA1 expression is under the control of diverse signaling pathways, including that mediated by the calcium-regulatable protein phosphatase calcineurin and its downstream transcription factor Crz1. We present here a quantitative study of the expression of Ena1 in response to alkalinization of the environment and we analyze the contribution of Crz1 to this response. Experimental data and mathematical models substantiate the existence of two stress-responsive Crz1-binding sites in the ENA1 promoter and estimate that the contribution of Crz1 to the early response of the ENA1 promoter is about 60%. The models suggest the existence of a second input with similar kinetics, which would be likely mediated by high pH-induced activation of the Snf1 kinase.

The (Mathematical) Modeling Process in Biosciences

In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology.

A philosophical evaluation of adaptationism as a heuristic strategy

Adaptationism has prompted many a debate in philosophy of biology but the focus is usually on empirical and explanatory issues rather than methodological adaptationism (MA). Likewise, the context of evolutionary biology has provided the grounding for most discussions of the heuristic role of adaptationism. This paper extends the debate by drawing on case studies from physiology and systems biology to discuss the productive and problematic aspects of adaptationism in functional as well as evolutionary studies at different levels of biological organization. Gould and Lewontin's Spandrels-paper famously criticized adaptationist methodology for implying a risk of generating 'blind spots' with respect to non-selective effects on evolution. Some have claimed that this bias can be accommodated through the testing of evolutionary hypotheses. Although this is an important aspect of overcoming the pitfalls of adaptationism, I argue that the issue of methodological biases is broader than the question of testability. I demonstrate the productivity of adaptationist heuristics but also discuss the deeper problematic aspects associated with the imperialistic tendencies of the strong account of MA.

FOUNDATIONS FOR MODELING THE DYNAMICS OF GENE REGULATORY NETWORKS: A MULTILEVEL-PERSPECTIVE REVIEW

A promising alternative for unraveling the principles under which the dynamic interactions among genes lead to cellular phenotypes relies on mathematical and computational models at different levels of abstraction, from the molecular level of protein-DNA interactions to the system level of functional relationships among genes. This review article presents, under a bottom–up perspective, a hierarchy of approaches to modeling gene regulatory network dynamics, from microscopic descriptions at the single-molecule level in the spatial context of an individual cell to macroscopic models providing phenomenological descriptions at the population-average level. The reviewed modeling approaches include Molecular Dynamics, Particle-Based Brownian Dynamics, the Master Equation approach, Ordinary Differential Equations, and the Boolean logic abstraction. Each of these frameworks is motivated by a particular biological context and the nature of the insight being pursued. The setting of gene network dynamic models from such frameworks involves assumptions and mathematical artifacts often ignored by the non-specialist. This article aims at providing an entry point for biologists new to the field and computer scientists not acquainted with some recent biophysically-inspired models of gene regulation. The connections promoting intuition between different abstraction levels and the role that approximations play in the modeling process are highlighted throughout the paper.

Additive genetic architecture underlying a rapidly evolving sexual signaling phenotype in the Hawaiian cricket genus Laupala

Complex, quantitative traits are often the function of the coordinated action of many physically independent genetic factors. Interactive properties of multilocus genotypes, such as epistasis, are thought to be pervasive components of the genetic architecture of complex phenotypes. Here, we utilize a panel of interspecific backcross introgression lines to evaluate the genetic architecture of song variation, a quantitative sexual signaling phenotype, in the Hawaiian swordtail cricket genus Laupala. Allelic effects across five quantitative trait loci are consistent with a purely additive model of gene action, where alleles at multiple loci are found to have fully independent and discrete effects with respect to the sexual signaling phenotype. Whereas a more complex genetic architecture featuring non-additive dominance and epistasis components may constrain potential evolutionary trajectories and reduce the rate of evolutionary change, the polygenic, additive genetic architecture observed for sexual signaling in Laupala should respond rapidly to directional selection pressures and freely move throughout phenotypic space. This classic type I genetic architecture may facilitate the explosive radiation of song variation observed across the Laupala genus.

Biochemical Systems Theory: A Review

Biochemical systems theory (BST) is the foundation for a set of analytical andmodeling tools that facilitate the analysis of dynamic biological systems. This paper depicts major developments in BST up to the current state of the art in 2012. It discusses its rationale, describes the typical strategies and methods of designing, diagnosing, analyzing, and utilizing BST models, and reviews areas of application. The paper is intended as a guide for investigators entering the fascinating field of biological systems analysis and as a resource for practitioners and experts.

Understanding regulation of metabolism through feasibility analysis

Understanding cellular regulation of metabolism is a major challenge in systems biology. Thus far, the main assumption was that enzyme levels are key regulators in metabolic networks. However, regulation analysis recently showed that metabolism is rarely controlled via enzyme levels only, but through non-obvious combinations of hierarchical (gene and enzyme levels) and metabolic regulation (mass action and allosteric interaction). Quantitative analyses relating changes in metabolic fluxes to changes in transcript or protein levels have revealed a remarkable lack of understanding of the regulation of these networks. We study metabolic regulation via feasibility analysis (FA). Inspired by the constraint-based approach of Flux Balance Analysis, FA incorporates a model describing kinetic interactions between molecules. We enlarge the portfolio of objectives for the cell by defining three main physiologically relevant objectives for the cell: function, robustness and temporal responsiveness. We postulate that the cell assumes one or a combination of these objectives and search for enzyme levels necessary to achieve this. We call the subspace of feasible enzyme levels the feasible enzyme space. Once this space is constructed, we can study how different objectives may (if possible) be combined, or evaluate the conditions at which the cells are faced with a trade-off among those. We apply FA to the experimental scenario of long-term carbon limited chemostat cultivation of yeast cells, studying how metabolism evolves optimally. Cells employ a mixed strategy composed of increasing enzyme levels for glucose uptake and hexokinase and decreasing levels of the remaining enzymes. This trade-off renders the cells specialized in this low-carbon flux state to compete for the available glucose and get rid of over-overcapacity. Overall, we show that FA is a powerful tool for systems biologists to study regulation of metabolism, interpret experimental data and evaluate hypotheses.

Two component systems: physiological effect of a third component

Signal transduction systems mediate the response and adaptation of organisms to environmental changes. In prokaryotes, this signal transduction is often done through Two Component Systems (TCS). These TCS are phosphotransfer protein cascades, and in their prototypical form they are composed by a kinase that senses the environmental signals (SK) and by a response regulator (RR) that regulates the cellular response. This basic motif can be modified by the addition of a third protein that interacts either with the SK or the RR in a way that could change the dynamic response of the TCS module. In this work we aim at understanding the effect of such an additional protein (which we call "third component") on the functional properties of a prototypical TCS. To do so we build mathematical models of TCS with alternative designs for their interaction with that third component. These mathematical models are analyzed in order to identify the differences in dynamic behavior inherent to each design, with respect to functionally relevant properties such as sensitivity to changes in either the parameter values or the molecular concentrations, temporal responsiveness, possibility of multiple steady states, or stochastic fluctuations in the system. The differences are then correlated to the physiological requirements that impinge on the functioning of the TCS. This analysis sheds light on both, the dynamic behavior of synthetically designed TCS, and the conditions under which natural selection might favor each of the designs. We find that a third component that modulates SK activity increases the parameter space where a bistable response of the TCS module to signals is possible, if SK is monofunctional, but decreases it when the SK is bifunctional. The presence of a third component that modulates RR activity decreases the parameter space where a bistable response of the TCS module to signals is possible.

The virtual liver: a multidisciplinary, multilevel challenge for systems biology

The liver is the central metabolic organ in human physiology, with functions that are fundamentally important to the detoxification of xenobiotics (drugs), the maintenance of homeostasis of numerous blood metabolites, and the production of mediators of the acute phase response. Liver toxicity, whether actual or implied is the reason for the failure of a significant proportion of many promising novel medicines that consequently never reach the market, and diseases such as atherosclerosis, diabetes, and fatty liver diseases, that are a major burden on current health resources, are directly linked to functional and structural disorders of the liver. This article presents the concepts and approaches underpinning one of the most exciting and ambitious modeling projects in the field of systems biology and systems medicine. This major multidisciplinary research program is aimed at developing a whole-organ model of the human liver, representing its central physiological functions under normal and pathological conditions The model will be composed of a larger battery of interconnected submodels representing liver anatomy and physiology, integrating processes across hierarchical levels in space, time, and structural organization. In this article, we outline the general architecture of the liver model and present first step taken to reach this ambitious goal.