Dynamic modelling and analysis of biochemical networks: mechanism-based models and model-based experiments

Systems biology applies quantitative, mechanistic modelling to study genetic networks, signal transduction pathways and metabolic networks. Mathematical models of biochemical networks can look very different. An important reason is that the purpose and application of a model are essential for the selection of the best mathematical framework. Fundamental aspects of selecting an appropriate modelling framework and a strategy for model building are discussed. Concepts and methods from system and control theory provide a sound basis for the further development of improved and dedicated computational tools for systems biology. Identification of the network components and rate constants that are most critical to the output behaviour of the system is one of the major problems raised in systems biology. Current approaches and methods of parameter sensitivity analysis and parameter estimation are reviewed. It is shown how these methods can be applied in the design of model-based experiments which iteratively yield models that are decreasingly wrong and increasingly gain predictive power.     

From molecular networks to qualitative cell behavior

Adaptation and behavior are characteristics of life which are fundamentally dynamic. If we want to model the living cell we have to describe it as a dynamic system. Typical dynamic models are based on quantitative differential equations requiring very detailed kinetic knowledge. Alternative modeling techniques for less fine-grained information are better suited to available functional genomics data. As such, constraint-based techniques and qualitative modeling have proven themselves to be valid approaches in cell biology. These approaches offer formal support to check the consistency of molecular networks against phenotypic observations in the light of dynamic systems.     

Quantitative modeling of biochemical networks

Today different database systems for molecular structures (genes and proteins) and metabolic pathways are available. All these systems are characterized by the static data representation. For progress in biotechnology the dynamic representation of this data is important. The metabolism can be characterized as a complex biochemical network. Different models for the quantitative simulation of biochemical networks are discussed, but no useful formalization is available. This paper shows that the theory of Petrinets is useful for the quantitative modeling of biochemical networks.     

From protein networks to biological systems

A system-level understanding of any biological process requires a map of the relationships among the various molecules involved. Technologies to detect and predict protein interactions have begun to produce very large maps of protein interactions, some including most of an organism's proteins. These maps can be used to study how proteins work together to form molecular machines and regulatory pathways. They also provide a framework for constructing predictive models of how information and energy flow through biological networks. In many respects, protein interaction maps are an entrée into systems biology.     

A Scalable Computational Framework for Establishing Long-Term Behavior of Stochastic Reaction Networks

Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology, epidemiology, immunology, systems biology and synthetic biology. It is now well-established that, for small population sizes, stochastic models for biochemical reaction networks are necessary to capture randomness in the interactions. The tools for analyzing such models, however, still lag far behind their deterministic counterparts. In this paper, we bridge this gap by developing a constructive framework for examining the long-term behavior and stability properties of the reaction dynamics in a stochastic setting. In particular, we address the problems of determining ergodicity of the reaction dynamics, which is analogous to having a globally attracting fixed point for deterministic dynamics. We also examine when the statistical moments of the underlying process remain bounded with time and when they converge to their steady state values. The framework we develop relies on a blend of ideas from probability theory, linear algebra and optimization theory. We demonstrate that the stability properties of a wide class of biological networks can be assessed from our sufficient theoretical conditions that can be recast as efficient and scalable linear programs, well-known for their tractability. It is notably shown that the computational complexity is often linear in the number of species. We illustrate the validity, the efficiency and the wide applicability of our results on several reaction networks arising in biochemistry, systems biology, epidemiology and ecology. The biological implications of the results as well as an example of a non-ergodic biological network are also discussed.     

Model building and model checking for biochemical processes

A central claim of computational systems biology is that, by drawing on mathematical approaches developed in the context of dynamic systems, kinetic analysis, computational theory and logic, it is possible to create powerful simulation, analysis, and reasoning tools for working biologists to decipher existing data, devise new experiments, and ultimately to understand functional properties of genomes, proteomes, cells, organs, and organisms. In this article, a novel computational tool is described that achieves many of the goals of this new discipline. The novelty of this system involves an automaton-based semantics of the temporal evolution of complex biochemical reactions starting from the representation given as a set of differential equations. The related tools also provide ability to qualitatively reason about the systems using a propositional temporal logic that can express an ordered sequence of events succinctly and unambiguously. The implementation of mathematical and computational models in the Simpathica and XSSYS systems is described briefly. Several example applications of these systems to cellular and biochemical processes are presented: the two most prominent are Leibler et al.'s repressilator (an artificial synthesized oscillatory network), and Curto-Voit-Sorribas-Cascante's purine metabolism reaction model.     

Methods of Model Reduction for Large-Scale Biological Systems: A Survey of Current Methods and Trends

Complex models of biochemical reaction systems have become increasingly common in the systems biology literature. The complexity of such models can present a number of obstacles for their practical use, often making problems difficult to intuit or computationally intractable. Methods of model reduction can be employed to alleviate the issue of complexity by seeking to eliminate those portions of a reaction network that have little or no effect upon the outcomes of interest, hence yielding simplified systems that retain an accurate predictive capacity. This review paper seeks to provide a brief overview of a range of such methods and their application in the context of biochemical reaction network models. To achieve this, we provide a brief mathematical account of the main methods including timescale exploitation approaches, reduction via sensitivity analysis, optimisation methods, lumping, and singular value decomposition-based approaches. Methods are reviewed in the context of large-scale systems biology type models, and future areas of research are briefly discussed.     

Training signaling pathway maps to biochemical data with constrained fuzzy logic: quantitative analysis of liver cell responses to inflammatory stimuli

Predictive understanding of cell signaling network operation based on general prior knowledge but consistent with empirical data in a specific environmental context is a current challenge in computational biology. Recent work has demonstrated that Boolean logic can be used to create context-specific network models by training proteomic pathway maps to dedicated biochemical data; however, the Boolean formalism is restricted to characterizing protein species as either fully active or inactive. To advance beyond this limitation, we propose a novel form of fuzzy logic sufficiently flexible to model quantitative data but also sufficiently simple to efficiently construct models by training pathway maps on dedicated experimental measurements. Our new approach, termed constrained fuzzy logic (cFL), converts a prior knowledge network (obtained from literature or interactome databases) into a computable model that describes graded values of protein activation across multiple pathways. We train a cFL-converted network to experimental data describing hepatocytic protein activation by inflammatory cytokines and demonstrate the application of the resultant trained models for three important purposes: (a) generating experimentally testable biological hypotheses concerning pathway crosstalk, (b) establishing capability for quantitative prediction of protein activity, and (c) prediction and understanding of the cytokine release phenotypic response. Our methodology systematically and quantitatively trains a protein pathway map summarizing curated literature to context-specific biochemical data. This process generates a computable model yielding successful prediction of new test data and offering biological insight into complex datasets that are difficult to fully analyze by intuition alone.     

Bistability and oscillations in chemical reaction networks

Bifurcation theory is one of the most widely used approaches for analysis of dynamical behaviour of chemical and biochemical reaction networks. Some of the interesting qualitative behaviour that are analyzed are oscillations and bistability (a situation where a system has at least two coexisting stable equilibria). Both phenomena have been identified as central features of many biological and biochemical systems. This paper, using the theory of stoichiometric network analysis (SNA) and notions from algebraic geometry, presents sufficient conditions for a reaction network to display bifurcations associated with these phenomena. The advantage of these conditions is that they impose fewer algebraic conditions on model parameters than conditions associated with standard bifurcation theorems. To derive the new conditions, a coordinate transformation will be made that will guarantee the existence of branches of positive equilibria in the system. This is particularly useful in mathematical biology, where only positive variable values are considered to be meaningful. The first part of the paper will be an extended introduction to SNA and algebraic geometry-related methods which are used in the coordinate transformation and set up of the theorems. In the second part of the paper we will focus on the derivation of bifurcation conditions using SNA and algebraic geometry. Conditions will be derived for three bifurcations: the saddle-node bifurcation, a simple branching point, both linked to bistability, and a simple Hopf bifurcation. The latter is linked to oscillatory behaviour. The conditions derived are sufficient and they extend earlier results from stoichiometric network analysis as can be found in (Aguda and Clarke in J Chem Phys 87:3461–3470, 1987; Clarke and Jiang in J Chem Phys 99:4464–4476, 1993; Gatermann et al. in J Symb Comput 40:1361–1382, 2005). In these papers some necessary conditions for two of these bifurcations were given. A set of examples will illustrate that algebraic conditions arising from given sufficient bifurcation conditions are not more difficult to interpret nor harder to calculate than those arising from necessary bifurcation conditions. Hence an increasing amount of information is gained at no extra computational cost. The theory can also be used in a second step for a systematic bifurcation analysis of larger reaction networks. We have added a dedication of the paper to K. Gatermann.     

Reducing complexity in metabolic networks: making metabolic meshes manageable

The dynamics of complex systems can be effectively analyzed by judicious use of intrinsic time constants. Order of magnitude estimation based on time constants has been used successfully to examine the dynamic behavior of complicated processes. The main goal of this paper is to introduce this approach to the analysis of complex metabolic systems. Time constants and dynamic modes of motion are defined within the context of well-established linear algebra. The order of magnitude estimation is then introduced into the systemic framework. The main goals of the analysis are: to provide improved understanding of biochemical dynamics and their physiological significance, and to yield reduced dynamic models that are physiologically realistic but tractable for practical use.     

Synthetic biology of minimal systems

“Synthetic biology” is a concept that has developed together with, or slightly after, “systems biology”. But while systems biology aims at the full understanding of large systems by integrating more and more details into their models, synthetic biology phrases different questions, namely: what particular biological function could be obtained with a certain known subsystem of reduced complexity; can this function be manipulated or engineered in artificial environments or genetically modified organisms; and if so, how? The most prominent representation of synthetic biology has so far been microbial engineering by recombinant DNA technology, employing modular concepts known from information technology. However, there are an increasing number of biophysical groups who follow similar strategies of dissecting cellular processes and networks, trying to identify functional minimal modules that could then be combined in a bottom-up approach towards biology. These modules are so far not as particularly defined by their impact on DNA processing, but rather influenced by core fields of biophysics, such as cell mechanics and membrane dynamics. This review will give an overview of some classical and some quite new biophysical strategies for constructing minimal systems of certain cellular modules. We will show that with recent advances in understanding of cytoskeletal and membrane elements, the time might have come to experimentally challenge the concept of a minimal cell.     

E-photosynthesis: a comprehensive modeling approach to understand chlorophyll fluorescence transients and other complex dynamic features of photosynthesis in fluctuating light

Plants are exposed to a temporally and spatially heterogeneous environment, and photosynthesis is well adapted to these fluctuations. Understanding of the complex, non-linear dynamics of photosynthesis in fluctuating light requires novel-modeling approaches that involve not only the primary light and dark biochemical reactions, but also networks of regulatory interactions. This requirement exceeds the capacity of the existing molecular models that are typically reduced to describe a partial process, dynamics of a specific complex or its particular dynamic feature. We propose a concept of comprehensive model that would represent an internally consistent, integral framework combining information on the reduced models that led to its construction. This review explores approaches and tools that exist in engineering, mathematics, and in other domains of biology that can be used to develop a comprehensive model of photosynthesis. Equally important, we investigated techniques by which one can rigorously reduce such a comprehensive model to models of low dimensionality, which preserve dynamic features of interest and, thus, contribute to a better understanding of photosynthesis under natural and thus fluctuating conditions. The web-based platform www.e-photosynthesis.org is introduced as an arena where these concepts and tools are being introduced and tested.     

Mathematical description of gene regulatory units

Revealing the control mechanisms responsible for the cell's surprisingly well-organized functions should lead directly to a better understanding of how the cell adapts to extraordinarily changing environments. A general framework for describing models that can represent diverse biochemical regulatory functions systematically would help not only systematic interpretation of the various models proposed for certain systems but also further understanding of the general control mechanism and design principles underlying different biological systems. This article presents a unified mathematical framework for describing gene regulatory units. The proposed framework is fairly compatible with the classical control theoretical framework, so it should serve as a connecting bridge between engineering control theory and biological control mechanisms. It should also provide a unified view of different regulatory units and facilitate systematic comparison of different mathematical models proposed in a variety of literature.     

Biomimetic modelling

Biomimetics is seen as a path from biology to engineering. The only path from engineering to biology in current use is the application of engineering concepts and models to biological systems. However, there is another pathway: the verification of biological mechanisms by manufacture, leading to an iterative process between biology and engineering in which the new understanding that the engineering implementation of a biological system can bring is fed back into biology, allowing a more complete and certain understanding and the possibility of further revelations for application in engineering. This is a pathway as yet unformalized, and one that offers the possibility that engineers can also be scientists.     

A high-quality catalog of the Drosophila melanogaster proteome

Understanding how proteins and their complex interaction networks convert the genomic information into a dynamic living organism is a fundamental challenge in biological sciences. As an important step towards understanding the systems biology of a complex eukaryote, we cataloged 63% of the predicted Drosophila melanogaster proteome by detecting 9,124 proteins from 498,000 redundant and 72,281 distinct peptide identifications. This unprecedented high proteome coverage for a complex eukaryote was achieved by combining sample diversity, multidimensional biochemical fractionation and analysis-driven experimentation feedback loops, whereby data collection is guided by statistical analysis of prior data. We show that high-quality proteomics data provide crucial information to amend genome annotation and to confirm many predicted gene models. We also present experimentally identified proteotypic peptides matching approximately 50% of D. melanogaster gene models. This library of proteotypic peptides should enable fast, targeted and quantitative proteomic studies to elucidate the systems biology of this model organism.     

Combinatorial metabolic pathway assembly approaches and toolkits for modular assembly

Synthetic Biology is a rapidly growing interdisciplinary field that is primarily built upon foundational advances in molecular biology combined with engineering design principles such as modularity and interoperability. The field considers living systems as programmable at the genetic level and has been defined by the development of new platform technologies and methodological advances. A key concept driving the field is the Design-Build-Test-Learn cycle which provides a systematic framework for building new biological systems. One major application area for synthetic biology is biosynthetic pathway engineering that requires the modular assembly of different genetic regulatory elements and biosynthetic enzymes. In this review we provide an overview of modular DNA assembly and describe and compare the plethora of in vitro and in vivo assembly methods for combinatorial pathway engineering. Considerations for part design and methods for enzyme balancing are also presented, and we briefly discuss alternatives to intracellular pathway assembly including microbial consortia and cell-free systems for biosynthesis. Finally, we describe computational tools and automation for pathway design and assembly and argue that a deeper understanding of the many different variables of genetic design, pathway regulation and cellular metabolism will allow more predictive pathway design and engineering.     

Brain evolution by brain pathway duplication

Understanding the mechanisms of evolution of brain pathways for complex behaviours is still in its infancy. Making further advances requires a deeper understanding of brain homologies, novelties and analogies. It also requires an understanding of how adaptive genetic modifications lead to restructuring of the brain. Recent advances in genomic and molecular biology techniques applied to brain research have provided exciting insights into how complex behaviours are shaped by selection of novel brain pathways and functions of the nervous system. Here, we review and further develop some insights to a new hypothesis on one mechanism that may contribute to nervous system evolution, in particular by brain pathway duplication. Like gene duplication, we propose that whole brain pathways can duplicate and the duplicated pathway diverge to take on new functions. We suggest that one mechanism of brain pathway duplication could be through gene duplication, although other mechanisms are possible. We focus on brain pathways for vocal learning and spoken language in song-learning birds and humans as example systems. This view presents a new framework for future research in our understanding of brain evolution and novel behavioural traits.