Systems biology: mathematical modeling and model analysis

Liu [21] stated that systems biology

seeks to explain biologic phenomenon, not on a gene-by-gene basis, but through the net interactions of all cellular and biochemical components within a cell or organism. Operationally, systems biology requires the ability to digitalize biological output so that it can be computed, the computational power to analyze comprehensive and massive datasets, and the capacity to integrate heterogeneous data into a usable knowledge format. Thus, systems biology can be described as ‘integrative biology’ with the ultimate goal of being able to predict de novo biological outcomes given the list of the components involved.

In other words, systems biology is a scientific approach aimed at moving away from reductionism (i.e. the investigation of biological mechanisms by dissecting them into ever-smaller components and analysing them in isolation from other parts of the system) and moving towards the decoding of life in a holistic way by viewing it through the lens of complex, dynamic living systems with many interrelations and interactions within the contexts of time, space, and physiology [3,9,14,22,26].

Today, systems biology is a well-established area of research activity which is conducted in an interdisciplinary manner because investigations depend on the knowledge of scientists from various scientific fields including mathematics, bioinformatics, computer science, biostatistics, biology, medicine, physics, and engineering [1,8,11,23]. Current research in systems biology focuses on topics such as cell–cell interactions, pathway-based biomarkers, metabolic and signal networks, and genetic switches [5,6,18,22]. Furthermore, systems biology approaches are used in evolutionary and ecosystems investigations [8,20], ageing research [4], and molecular diagnostics and drug discovery with the ultimate goal to provide personalized patient care [10,19,24]. In recent years, new branches of systems biology have emerged including ‘systems genetics’ [18], ‘systems physiology’ [15], ‘systems microbiology’ [7], and ‘systems oncology’ [16], to name a few.

Methods used in systems biology typically include mathematical calculations and modelling, computer simulations, and probabilistic analyses [2,22,23]. As several researchers pointed out, one of the biggest challenges in systems biology research is to develop required technologies, especially powerful computers and sophisticated software tools for the storage, analysis, and integration of the large and ever-increasing quantities of data being generated [1,2,25]. The good news is, as Bartocci and Liò [2] pointed out: ‘As the amount of biological data in the public domain grows, so does the range of modeling and analysis techniques employed in systems biology’.

I recently came across a book about systems biology, written by Kremling [17], which focuses on the mathematical modelling and model analysis in systems biology. The book is part of the Chapman & Hall/CRC Mathematical and Computational Biology Series, which aim is ‘to capture new developments and summarize what is known over the entire spectrum of mathematical and computational biology and medicine’. I devote the remainder of my essay to reviewing this book.

Kremling [17] divided his book into four parts containing a total of 12 chapters. The first part is entitled ‘Fundamentals’ and contains four chapters. He introduced the reader in the first chapter to two different, but complementary, approaches which can be used in systems biology: the bottom-up (inductive) and the top-down (deductive) approaches. A requirement in systems biology is not only that the biological phenomenon under study can be described mathematically, but also that the developed model can sufficiently explain the presented data. He mentioned that the starting point in systems biology is typically the biological experiment, which can then lead either to the conduct of additional biological experiments or immediately to mathematical modelling, analysis/evaluation, and prediction. The process of problem definition, biological experiment, and modelling is known as the ‘iterative cycle’. This first chapter also includes a description of the role and use of modules (i.e. system components) and motifs (i.e. connections of components that form patterns) in systems biology.

In Chapter 2, Kremling [17] offered the reader an excellent primer on the basics of biology by describing the components of the cell, differences between prokaryotes and eukaryotes, and mechanisms of cell division and growth, as well as metabolic processes in anabolism and catabolism. He also described functions of deoxyribonucleic acid (DNA) and ribonucleic acid (RNA), including replication, transcription, and translation, and reviewed what is known about the regulation of enzyme synthesis and activity, signal transduction, and cell–cell communication. The third chapter is about the fundamentals of mathematical modelling. He distinguished between a system and a mathematical model by pointing out that a system is formed by a certain number of components that can interact with each other, while a model can be seen as an abstract and somewhat simplified representation of ‘reality’ that shows the relationship(s) of inputs and state variables. Kremling [17] provided here an overview of different model classes including unstructured/structured models, unsegregated/segregated models, discrete/continuous models, and deterministic/stochastic models. He also discussed qualitative modelling, which he defined as an analysis of the ‘interactions between components without describing these interactions in detail’. The final chapter (Chapter 4) of Part I is devoted to model calibration and experimental design. Kremling [17] mentioned that the goal of model calibration is to find a good match between experimental data and simulation calculations. He provided guidance for various calibration methods that pertain to the accuracy and quality of the estimated system parameters and the model. I believe that these first four chapters can provide readers with a valuable primer on both the basics of biology and the fundamentals of mathematical modelling.

Part II of the book is entitled ‘Modeling of Cellular Processes’. This part contains three chapters. Kremling [17] discussed in Chapter 5 various issues that relate to enzymatic conversion. More specifically, he discussed enzyme kinetics with a focus on enzyme activators and inhibitors, transport processes, enzyme reaction rates, and thermodynamic influences. Polymerization processes leading to macromolecules within a cell are the topic of Chapter 6. Kremling [17] distinguished between the macroscopic view (e.g. the identification of variables for the number and speed of polymerases) and the microscopic view (here: the reaction mechanisms of the linkage of transcription and translation). In other words, he showed that polymerization models can be deduced from macroscopic observations. Chapter 7 is about signal transduction and genetically regulated systems. He stated that ‘Cellular systems [need to] quickly respond to changing environmental conditions. The response is achieved through activation and deactivation of metabolic pathways or chemotactical movements of the cells’. He described in this chapter the mathematical representation of various schemes of signal transduction (e.g. models of activation, adaptation, and feedback) as well as of the genetic regulation of networks and signalling pathways.

Kremling [17] continued the discussion about the dynamics of biological systems in the third part of the book. His primary focus is here on the analysis of modules and motifs. He started out in Chapter 8 by explaining terms such as time hierarchies, sensitivity, robustness, and variables for metabolic control. Furthermore, he talked about the biochemical systems theory and approaches to structured kinetic modelling. Chapter 9 is about control theory. Kremling [17] reminded the reader of the importance of the property of observability and the ability to accurately deduct/reconstruct mathematically state and output variables. He discussed the behaviour of monotone (i.e. relatively stable) and non-monotone systems, and described feedback that can be studied, for example, in (bacterial) chemotactic behaviour. He then continued in Chapter 10 with the discussion of motifs (here: recurrent patterns) in regulatory networks of cells, including the role of feed-forward loops in the transcription network of the complex and dynamic bacterial system of Escherichia (E.) coli. Furthermore, he looked at signalling motifs such as those that describe quorum sensing behaviour, which has been linked, for example, to the process of biofilm formation of microorganisms in a given environment.

Up to this point, Kremling [17] had explained the analysis of smaller networks within biological systems. In the final part (Part IV) of the book, he shifted his description of mathematical modelling and model analysis from subcellular to cellular systems. More specifically, Kremling [17] discussed in the final two chapters issues that pertain to metabolic engineering (Chapter 11) and to topological characteristics (Chapter 12). He described the reconstruction of a metabolic network as ‘a systematic record of information on the network's components and its interactions’. He pointed out that systems biology researchers have today various tools at their disposal that are useful for the collection and analysis of data. An example of such a tool is ‘EcoCyc’, which is a freely accessible and openly available, comprehensive, bioinformatics database on the biology (genes, metabolism, regulatory networks, etc.) of E. coli [12]. This database is regularly updated to reflect both newly gained knowledge about the biology of E. coli (e.g. new transcription factors and changes in the transporter classification system) and improvements to the EcoCyc website and pathway tools software (e.g. updates to the genome browser and expansions of SmartTables tools) [13].

What I like most about Kremling's book [17] is that he found a suitable balance between the presentation of mathematical approaches to modelling and the description of biological information. After all, systems biology research is difficult to conduct without sufficient knowledge in both of these fields. Helpful to the reader are also other features of this book such as (a) the numerous exercises presented at the end of most chapters, (b) a bibliography and suggestions for further reading [some resources are annotated by Kremling (17)], (c) well-selected figures and tables that sufficiently complement the text, and (d) an appendix, which contains a collection of mathematical approaches such as rules for vector derivatives and statistics/probability theory, among others.

I consider a pitfall of Kremling's [17] book the lack of a glossary, which I believe is particularly important for a book that seeks to attract scientists from an interdisciplinary audience. Also, I found that the index is a bit short with only three pages, but it is functional as I have tested several entries such as ‘Entner-Doudoroff pathway’, Gillespie algorithm’, and ‘Robust control’. Despite some shortcomings, I think that Kremling's [17] book is well structured (the collection and order of chapters is excellent), provides comprehensive material of fundamentals, theory, and applications of methods used in systems biology. It is a user-friendly guide that I believe can serve as a tutorial for students specializing in systems biology as well as a reference work for established researchers in the field. I highly recommend this book to the reader.