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The following report selects and summarises some of the conclusions and recommendations generated throughout a series of workshops and discussions that have lead to the publication of the Science Policy Briefing (SPB) Nr. 35, published by the European Science Foundation. (Large parts of the present text are directly based on the ESF SPB. Detailed recommendations with regard to specific application areas are not given here but can be found in the SPB. Issues related to mathematical modelling, including training and the need for an infrastructure supporting modelling are discussed in greater detail in the present text). The numerous reports and publications about the advances within the rapidly growing field of systems biology have led to a plethora of alternative definitions for key concepts. Here, with 'mathematical modelling' the authors refer to the modelling and simulation of subcellular, cellular and macro-scale phenomena, using primarily methods from dynamical systems theory. The aim of such models is encoding and testing hypotheses about mechanisms underlying the functioning of cells. Typical examples are models for molecular networks, where the behaviour of cells is expressed in terms of quantitative changes in the levels of transcripts and gene products. Bioinformatics provides essential complementary tools, including procedures for pattern recognition, machine learning, statistical modelling (testing for differences, searching for associations and correlations) and secondary data extracted from databases. Dynamical systems theory is the natural language to investigate complex biological systems demonstrating nonlinear spatio-temporal behaviour. However, the generation of experimental data suitable to parameterise, calibrate and validate such models is often time consuming and expensive or not even possible with the technology available today. In our report, we use the term 'computational model' when mathematical models are complemented with information - generated from bioinformatics resources. Hence, 'the model' is, in reality, an integrated collection of data and models from various (possibly heterogeneous) sources. The present report focuses on a selection of topics, which were identified as appropriate case studies for medical systems biology, and adopts a particular perspective which the authors consider important. We strongly believe that mathematical modelling represents a natural language with which to integrate data at various levels and, in doing so, to provide insight into complex diseases: Modelling necessitates the statement of explicit hypotheses, a process which often enhances comprehension of the biological system and can uncover critical points where understanding is lacking. Simulations can reveal hidden patterns and/or counter-intuitive mechanisms in complex systems. Theoretical thinking and mathematical modelling constitute powerful tools to integrate and make sense of the biological and clinical information being generated and, more importantly, to generate new hypotheses that can then be tested in the laboratory. Medical Systems Biology projects carried out recently across Europe have revealed a need for action: While the need for mathematical modelling and interdisciplinary collaborations is becoming widely recognised in the biological sciences, with substantial implications for the training and research funding mechanisms within this area, the medical sciences have yet to follow this lead. To achieve major breakthroughs in Medical Systems Biology, existing academic funding schemes for large-scale projects need to be reconsidered. The hesitant stance of the pharmaceutical industry towards major investment in systems biology research has to be addressed. Leading medical journals should be encouraged to promote mathematical modelling.