Boolean modelling of biochemical networks

The study of biological systems, from cells, to organisms and populations, is becoming increasingly quantitative. In particular, the way that biochemical networks are described is changing from the traditional diagrammatic sketch of possible interactions to a set of mathematical equations that simulate (i.e. model) how the concentration of each molecular species varies with time. A key advantage of mathematical models is that they can be used to predict the response of networks to external perturbations, such as changes in environmental conditions or the addition of pharmacological agents. This reduces the need for large numbers of expensive and time-consuming experiments. However, the more complex a biochemical network model, the greater the range of possible dynamic behaviours it can exhibit. Consequently, extensive computer simulations are necessary for accurate predictions of experimental behaviour to be obtained. For biologically realistic models that can comprise hundreds of molecular species, the number of simulations required far exceeds that which is possible on a practical timescale. It follows that for the predictive power of mathematical models in biology to be fully realised, there is a pressing need for methods that allow their behaviour to be comprehensively explored in a computationally efficient manner.

The proposed project will address this need by developing a new modelling methodology based on representing biochemical networks as digital circuits. In this approach, each species is considered to be either "on" (i.e. present) or "off" (i.e. absent), and changes in concentration are simply treated as transitions between these two states. The significant reduction in computational complexity that this affords has the potential to greatly expand the range of networks that can be usefully modelled. As a test case of the approach, digital circuit models will be constructed of the gene network that generates circadian oscillations in an important plant species, Arabidopsis thaliana. Circadian oscillations regulate many processes critical for plant growth and reproduction, such as photosynthesis and seed germination. As part of this work, the computational tractability of the digital circuit models will be exploited to determine how temperature modifies the plant circadian network. In the long term, this may prove important for predicting how future temperature shifts will affect the viability of important crop species, thereby informing strategies for breeding varieties with increased resistance to climate change.

This basic science proposal seeks to deliver new methods for quantitatively modelling biochemical systems based on Boolean logic. As such, the main beneficiaries will be scientists working in universities and other research institutes. However the project will also impact society through its contribution to systems and synthetic biology, and its potential for public engagement activities.

Scientific Impact

Research Communities: The project will benefit researchers in applied mathematics, computer science and molecular biology. Systems modellers will benefit from the availability of computationally efficient methods to reverse-engineer regulatory networks and construct large-scale dynamic models. These methods have the potential to significantly expand the range of biochemical circuits amenable to quantitative analysis. In addition, the work will impact modellers interested in the complementarity of logic and differential equation modelling, and the possibility of hybrid methods. The evolutionary optimisation community will benefit through access to the complex non-separable objective functions used for model fitting. The functions will provide a challenging new set of test problems, together with a platform for novel optimisation algorithms that exploit the discrete nature of the logic formulation. The project will also benefit circadian biologists by producing plant clock models with greater computational tractability, thereby facilitating hypothesis generation and testing. In particular, the models will help to quantify how the plant circadian network responds to temperature changes, a key current research topic. In order to ensure that each of these groups benefits from the work, all models, numerical algorithms and publications will be made publically available on a dedicated website. Furthermore, scientific findings will be presented at leading international conferences, and also showcased at an interdisciplinary hot-topic workshop held at Exeter.

Education: The work will impact on students with physical sciences backgrounds by showing how their knowledge can be applied to timely and challenging problems in the life sciences. Project results will be incorporated into taught undergraduate and postgraduates courses at Exeter, highlighting the extent to which mathematical techniques are crucial to cutting-edge research in systems and synthetic biology. The students on these courses will further benefit by being alerted to the potential societal and economic impacts of these fields, and the job opportunities that exist in the biomedical and biotechnology sectors for graduates with advanced mathematical and computational skills.

Social Impact

Computational modelling plays a central role in both systems and synthetic biology. For these fields to be successful in using engineering principles to understand and design biological systems, it is critical to develop modelling techniques that can: (i) cope with large numbers of biochemical species; and (ii) integrate the information provided by multiple experimental protocols. The outcomes of the proposed work will therefore impact on the stated aim of systems and synthetic biology to produce technologies that deliver a more sustainable and healthy future. Specifically, the temperature-dependent models of the plant clock developed during the project may help predict how climate shifts will affect the ability of crops to survive, grow and reproduce. Such findings could be important in informing government policies relating to food security and adapting to environmental change. To ensure that the wider public are made aware of the broader implications of the research, material will be added to the project website highlighting the key role played by the mathematical sciences in addressing 21st century challenges. In addition, outreach activities will be organised for local schoolchildren, showcasing the use of mathematics to model natural phenomena.