Publications: Science Omega Review UK Issue 1

A tissue issue - an article from Professor Mark Chaplain

Protein model
...the goal is now to build a ‘mathematical book of the cell’, composed of individual chapters made from the sentences and paragraphs of the specific models.
Professor Mark Chaplain
The University of Dundee’s Professor Mark Chaplain turns the spotlight on multiscale mathematical modelling of complex biomedical systems...

The past two decades have witnessed enormous advances in our understanding of the molecular basis of cell structure and function. Scientists, as well as the general public, are cognisant of the spectacular success of the human genome project and the consequent burgeoning interest in the related fields of proteomics and metabolomics. Biochemists and cell biologists have made similarly impressive strides in elucidating the mechanisms mediating cell-signalling and its consequences for the control of gene expression, cell proliferation and cell motility. It is, however, abundantly clear that reductionist logic using this impressive ‘sub-cell-level’ information base is not sufficient to deduce an understanding of phenomena operative at the next higher level of biological organisation – the tissue.

Employing a literary analogy, the vast ‘omic’ databases of catalogued genes and proteins, taken together with our growing understanding of the inner workings of individual cells, provide a ‘dictionary’ and a ‘grammatical syntax’ required for the next great challenge, i.e. understanding the ‘sentences’ and ‘paragraphs’ characteristic of emergent tissue-level phenomena. This applies to both ‘normal’ tissue growth and development processes (such as embryo-genesis) and pathological tissue processes (such as wound healing and cancer).

Life scientists and clinicians are recognising the need to integrate data across a range of spatial and temporal scales (from genes to tissues) in order to fully understand the systems they are studying. In this respect, there are three natural, key scales linked to each other which, when considered together, go to make up understanding tissue-level phenomena: the sub-cellular scale, the cellular scale and the tissue scale itself.

The sub-cellular scale refers to activities that take place within the cell or at the cell membrane, e.g. DNA synthesis, gene expression, cell cycle mechanisms, absorption of vital nutrients, activation or inactivation of receptors, and transduction of chemical signals. The cellular scale refers to the main activities of the individual cells, e.g. statistical description of the progression and activation state of the cells, interactions among different types of cells present in the body (e.g. epithelial cells, endothelial cells, macrophages, lymphocytes, neurons), proliferative and destructive interactions, aggregation and disaggregation properties. The tissue scale refers to those phenomena that are typical of continuum systems, e.g. cell migration, diffusion and transport of nutrients and chemical factors, mechanical responses, interactions between different tissues, and tissue remodelling.

Tissue growth and homeostasis, then, is a complicated phenomenon involving many interrelated processes across a wide range of spatial and temporal scales, and as such presents the mathematical modeller with a correspondingly complex set of problems to solve.

However, along with the rapid growth in acquisition of genetic, proteomic and other biochemical and biological data, there has been a parallel development from the ‘theoretical side’. In particular, ‘systems biology’ has emerged as a new field of research over the past decade, applied to a wide range of problems in the biomedical sciences. Systems biology seeks to bring to bear a range of interdisciplinary skills and tools on complex biomedical problems. By adopting a holistic or integrative approach (as opposed to the more traditional reductionist logic), systems biology aims to predict emergent behaviour that will arise from complex biomedical systems, i.e. behaviour that appears over time due to the interactions between genes, proteins, cells and tissues across a range of spatial and temporal scales. Given the complexity of most biomedical systems and the inherent nonlinearities in such systems, without adopting some kind of ‘systems’ approach, it is not possible to make accurate predictions. Indeed, in the last few years, systems biology itself has evolved and further developed – seeking not just to understand events at the separate biological scales in a qualitative manner. There are now mathematical models that are truly multi-scale, leading to the emergence of ‘quantitative systems biology’ or ‘quantitative integrative biology’.

Systems biology was initially mainly concerned with modelling general intracellular events, e.g. signal transduction processes and other molecular systems within cells. Perhaps some of the biggest advances in systems biology have been made in elucidating the complex control mechanisms and interactions involved in what are generically known as gene regulatory networks (GRNs). As its name suggests, this is a network within a cell that controls the function of certain genes. Systems biology has made important steps in the understanding of GRNs through modelling the interactions between the key components, i.e. between mRNA molecules and protein molecules, and the processes of transcription and translation. In some of the most important GRNs, proteins activate other genes, and these are known as transcription factors, which play a major role in controlling important signalling regulatory networks involved in cell proliferation and apoptosis. A range of systems biology approaches has been adopted to model GRNs, including ordinary differential equations, dynamical systems theory, Boolean networks, bifurcation theory, graph theory and stochastic systems. New information has been gained about the precise spatio-temporal dynamics of mRNA and proteins within cells and has yielded fresh insight into a range of cellular diseases such as cancer.

Systems biology has also made important contributions in understanding events at a cellular level. Cell migration is vitally important in a wide variety of biological contexts. It is a very complex process that is controlled by intracellular signalling pathways as well as the cell’s microenvironment. Modelling at the cellular scale has led to the development of a range of individual-based models (e.g. cellular automata, force-based models, Potts models), which, among other things, have investigated the role of adhesion (both cell-cell and cell matrix) and its effect on cell migration. By focusing on adhesion, the significance of the cell’s environment on its migration can be investigated theoretically and this has led to greater insight into and understanding of important biological processes such as embryogenesis (e.g. gastrulation) and pathological processes such as wound healing and cancer (e.g. invasion and metastasis).

The final scale of modelling discussed here, the tissue scale, has been explored theoretically for longer than either intracellular modelling or cell-based modelling, and it is at this scale where the most exciting challenges and new developments lie. Traditionally systems of partial differential equations known as reaction-diffusion systems or reaction-diffusion-taxis systems have been used to model the complex interactions between cells, tissue and various diffusible chemical factors that control cell migration and proliferation. Although providing a certain amount of qualitative insight into such systems, until recently it has been difficult to obtain any real quantitative predictions. However, with the developments of novel mathematical techniques such as homogenisation theory, arising from the necessity to be able to link together different temporal and spatial scales in a rigorous manner, and the increase in computational power available to researchers, real strides forward have been made in creating multiscale tissue models of, for example, the heart, lung and brain.

To use the literary analogy mentioned earlier, the goal is now to build a ‘mathematical book of the cell’, composed of individual chapters made from the sentences and paragraphs of the specific models.

The development of quantitative, predictive multiscale models (integrative systems biology) is now not only providing the first outlines for a sketch of the cell but also shedding light on emergent properties of tissue dynamics. In the longer term, such developments can be expected to have a positive impact on patients suffering from debilitating diseases (e.g. arthritis, diabetes, cancer) through improved clinical treatment.


Professor Mark Chaplain
Chair in Mathematical Biology
Division of Mathematics
University of Dundee

www.maths.dundee.ac.uk



[This article was originally published on 20th March 2013 as part of Science Omega Review UK 01]


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