This year we celebrate the 150th anniversary of the law of mass action. This law is often assumed to have been “there” forever, but it has its own history, background, and a definite starting point. The law has had an impact on chemistry, biochemistry, biomathematics, and systems biology that is difficult to overestimate. It is easily recognized that it is the direct basis for computational enzyme kinetics, ecological systems models, and models for the spread of diseases. The article reviews the explicit and implicit role of the law of mass action in systems biology and reveals how the original, more general formulation of the law emerged one hundred years later ab initio as a very general, canonical representation of biological processes.

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.

The complexity of morphogenesis poses a fundamental challenge to understanding the mechanisms governing the formation of biological patterns and structures. Over the past century, numerous processes have been identified as critically contributing to morphogenetic events, but the interplay between the various components and aspects of pattern formation have been much harder to grasp. The combination of traditional biology with mathematical and computational methods has had a profound effect on our current understanding of morphogenesis and led to significant insights and advancements in the field. In particular, the theoretical concepts of reaction–diffusion systems and positional information, proposed by Alan Turing and Lewis Wolpert, respectively, dramatically influenced our general view of morphogenesis, although typically in isolation from one another. In recent years, agent-based modeling has been emerging as a consolidation and implementation of the two theories within a single framework. Agent-based models (ABMs) are unique in their ability to integrate combinations of heterogeneous processes and investigate their respective dynamics, especially in the context of spatial phenomena. In this review, we highlight the benefits and technical challenges associated with ABMs as tools for examining morphogenetic events. These models display unparalleled flexibility for studying various morphogenetic phenomena at multiple levels and have the important advantage of informing future experimental work, including the targeted engineering of tissues and organs.

Background: The estimation of parameter values continues to be the bottleneck of the computational analysis of biological systems. It is therefore necessary to develop improved methods that are effective, fast, and scalable. Results: We show here that alternating regression (AR), applied to S-system models and combined with methods for decoupling systems of differential equations, provides a fast new tool for identifying parameter values from time series data. The key feature of AR is that it dissects the nonlinear inverse problem of estimating parameter values into iterative steps of linear regression. We show with several artificial examples that the method works well in many cases. In cases of no convergence, it is feasible to dedicate some computational effort to identifying suitable start values and search settings, because the method is fast in comparison to conventional methods that the search for suitable initial values is easily recouped. Because parameter estimation and the identification of system structure are closely related in S-system modeling, the AR method is beneficial for the latter as well. Specifically, we show with an example from the literature that AR is three to five orders of magnitudes faster than direct structure identifications in systems of nonlinear differential equations. Conclusion: Alternating regression provides a strategy for the estimation of parameter values and the identification of structure and regulation in S-systems that is genuinely different from all existing methods. Alternating regression is usually very fast, but its convergence patterns are complex and will require further investigation. In cases where convergence is an issue, the enormous speed of the method renders it feasible to select several initial guesses and search settings as an effective countermeasure.

The combination of high-throughput methods of molecular biology with advanced mathematical and computational techniques has propelled the emergent field of systems biology into a position of prominence. Unthinkable a decade ago, it has become possible to screen and analyze the expression of entire genomes, simultaneously assess large numbers of proteins and their prevalence, and characterize in detail the metabolic state of a cell population. Although very important, the focus on comprehensive networks of biological components is only one side of systems biology. Complementing large-scale assessments, and sometimes at the risk of being forgotten, are more subtle analyses that rationalize the design and functioning of biological modules in exquisite detail. This intricate side of systems biology aims at identifying the specific roles of processes and signals in smaller, fully regulated systems by computing what would happen if these signals were lacking or organized in a different fashion. We exemplify this type of approach with a detailed analysis of the regulation of glucose utilization in Lactococcus lactis . This organism is exposed to alternating periods of glucose availability and starvation. During starvation, it accumulates an intermediate of glycolysis, which allows it to take up glucose immediately upon availability. This notable accumulation poses a nontrivial control task that is solved with an unusual, yet ingeniously designed and timed feedforward activation system. The elucidation of this control system required high-precision, dynamic in vivo metabolite data, combined with methods of nonlinear systems analysis, and may serve as a paradigm for multidisciplinary approaches to fine-scaled systems biology.