Although there are many definitions of “systems biology,” what is commonly contained in all is the assertion that true (quantitative and predictive) understanding of how complex function arises in biology can only be obtained by building mathematical and computational models which capture some of the underlying biophysics of the system under study. Such models typically consist of mathematical equations and/or computational algorithms describing the interactions between multiple biological components and physical processes which, ideally, synthesise and integrate the vast wealth of biological information generated through experiments, and allow exposition of the way function emerges through the (typically non-linear) interactions between these components. The non-linear nature of the system means that in most circumstances the solution of the equations can only be obtained through computer simulation, and hence most such models are computational in nature.
Research within the SysBio DTC programme is divided into four application areas that span the range of spatial and temporal scales of interest:
- Detailed pathway modelling
- Larger scale network modelling
- Cellular modelling
- Physiome modelling
Cutting across and supporting these modelling themes are experimental research programmes which focus on particular model systems. These experimental programmes range from the level of direct imaging of single protein:protein interactions, right up to the level of the intact organism, and therefore provide the necessary range of modelling and theoretical challenges to allow progress towards our generic goal of developing an underpinning theory for biological systems as a whole. Our goal is to develop theoretical and experimental approaches that will allow us to begin to address the following challenges of Systems Biology research:
- Model selection: for a given data set multiple modelling approaches are generally possible – which is the most useful?
- Abstraction: how should we balance computational tractability with the need to incorporate biological complexity?
- Noise: how should we incorporate both intrinsic and extrinsic noise?
- Incomplete data sets: how can we build accurate, predictive models when interactions have to be inferred?
- Interfaces: what is the best approach to modelling across the stochastic/deterministic and discrete/continuous interfaces?
- Multi-scale: as we build increasingly multi-scale models, when and how should models at different scales be coupled?
- Extension and re-use: In a small number of instances for very specific systems, complete data sets exist where all likely interactions are known; can such models be re-used as a basis when extending to other systems?
- Functionality: what are the design principles in systems biology?
- Composition: can we devise languages for describing components and sub-systems within biological systems that will allow (potentially automatic) composition of those models as complexity and model size increases?
- Granularity: to what extent is coarse graining or homogenisation appropriate as we move to larger spatial and temporal scales and how might this best be done?
- Visualisation: how should we visualise and interrogate complex (high-dimensional) data sets?
| Detailed Pathway Modelling
An example: Bacterial chemotaxis
Bacteria swim by rotating semi-rigid helical flagella. They use motility to move towards optimum environments for growth, which in the case of a pathogen may be the gut wall or a wound and in the case of a symbiont may be its host. As bacteria are too small to sense environmental gradients directly they must use temporal sampling, biasing their overall pattern of swimming in a favourable direction.
Chemotaxis and sensory signalling
Bacteria sense and respond to changes in chemicals, terminal electron acceptors such as oxygen and nitrate, light, temperature, osmolarity, pH; integrating the signals to produce a balanced response. A family of receptor proteins sense the change in an environmental stimulus and signal through a cytoplasmic relay of histidine protein kinases and response regulators to control the rotation of the bacterial flagellum. Rhodobacter sphaeroides is a photosynthetic bacterium with a single flagellum. It has a complex and flexible metabolism and over the past few years it has become apparent that its chemosensory pathway is also more complex than that of E.coli, and probably more representative of bacteria in general. We are using R. sphaeroides to investigate (i) the mechanisms involved in controlling expression of the different chemotaxis genes, (ii) the localisation of the different chemotaxis protein homologues to different sites in the bacterial cell, (iii) the segregation of chemotaxis proteins on cell division, (iv) the integration of the different environmental signals, (v) the mathematical modelling of the signalling pathway from the receptors to the flagellar motor.
We are interested in the mechanics of the flagellar motor in both E. coli and R. sphaeroides. Although the proton gradient is saturating under most conditions, the R. sphaeroides motor changes speed spontaneously, whilst the E. coli motor switches its direction of rotation. We are investigating (i) the copy number and dynamics of individual protein components of the flagellar motor, (ii) the mechanisms involved in driving rotation, (iii) the mechanisms which allow speed change and control stopping or switching of the motor.
| Larger Scale Network Modelling
Oxford Complex Systems and Systems and Signals attempt to understand the structure and dynamics of complex natural systems. We approach this through both theoretical treatments and data analysis and have a focus on networks and signals. We have investigated mathematical models for the growth of complex networks and asked how dense regions in these networks can be created and characterized. Example nets we have considered are cellular protein-protein interactions, networks of cells and social networks. We are also investigating methods for modelling and analysing the structure of natural signals and have analysed signals ranging from heart rhythms, to precipitation levels, to the motion of the bacterial flagellum. We have a particular interest in the fluctuations that occur within cells and in small numbers of cells and thus also work in cellular and subcellular image analysis.
Oxford Complex Systems
Oxford Physics and Biochemistry - Sytems and Signals
An Example: Cellular Hypoxia
Our understanding of cellular processes and how they work together to perform essential functions in the organism, relies on the detailed knowledge of the molecules in the cell and their interactions with each other. With the completion of the sequencing of the human genome we now know that humans only have some 25,000 genes - on the same order of magnitude as many other, less complex organisms. The sheer complexity of molecular networks which underpins higher life forms to function as finely tuned, adaptive systems, is only possible because the number of gene products, the proteins, is far higher.
It is estimated that in humans, differential gene expression, splicing, and post-translational modifications give rise to more than a million different proteins, which interact in multiple ways with each other - thereby adding layers of complexity to the biomolecular 'circuits' and regulatory pathways. The proteome is highly complex and dynamic in both space and time. Post-translational modifications often determine the structure, function and localization of proteins.
One of the key methods for the investigation of protein structure and activity is mass spectrometry, which can be used to identify the presence and amount of specific proteins in cell extracts, but also its various states of modification.
A key challenge for the next decade and beyond is to define the proteome at high resolution, i.e. from the primary through to the quaternary structure, and to quantify the varying amounts present in the different compartments of the cell. This knowledge will then enable us to rationally modify biological processes to alleviate or cure disease.
| Physiome Modelling
If we were to attempt to build a model of every human function we would have to take account of processes that vary on a wide range of length scales and a wide range of length scales.
For example, we would have to take account of the following length scales:
The largest length scale here is 10^9 times the shortest length scale.
The range of time scales is even larger:
The range of time scales here is 10^15.
It is clear that to model a human we need to link between the processes that occur on these widely differing scales. For example, using the example of the heart, regulation of ion concentration within cardiac cells at the genetic level ensures that ion transport mechanisms function correctly via the cell membrane proteins within cardiac cells. This leads eventually to the propagation of an electrical signal across cardiac muscle fibres, causing these fibres to contract to form a heartbeat, pumping oxygen rich blood to the rest of the body. Information also travels in the opposite direction: for example an impact on the chest may be able to stop or re-start the heart due to the presence of stretch-activated ion channels.
The mathematical and computational challenge is to develop techniques that combines information from different scales into a larger coupled model. This usually requires a variety of techniques. For example: a stochastic model may be required at shorter scales, and this usually requires solution via a computational simulation. At larger scales averaging techniques often allow us to describe the system by a deterministic differential equation model. Multiscale techniques are then used to combine the information obtained at these separate scales. This then allows us to investigate the effect of processes that occur at different length scales and time scales on each other.
Academics involved in this research are based in both the Computational Biology Group and the Wolfson Centre for Mathematical Biology.