Stochastic representations of biological systems
Lead Research Organisation:
University of Bath
Department Name: Mathematical Sciences
Abstract
Biological systems exhibit a tremendously wide variety of behaviours at many different spatial scales. The field of mathematical biology, therefore, has seen the development of a plethora of methodologies. More recently, we have seen the introduction of hybrid methods, which combine modelling regimes at different spatial scales in such a way as to exploit both the accuracy of the finer representation, and the computational efficiency of the coarser.
One biological process of interest in this research is the cell-division cycle, being one of the most fundamental processes to the functioning of all multicellular life. While the exact mechanisms driving this cycle can vary considerably between cellular species, the cycle can be broadly divided into four distinct biological phases. In multicellular life, regulation of the length of the cell-division cycle, and therefore the rate of population growth, is critical to the development of organisms, as well as to the maintenance of homeostasis and wound healing. There are many challenges, both mathematical and experimental, associated with the study of the cell-division cycle. Average proliferation rates can be estimated at the population level by examining the growth curves of actively proliferative populations, however inference of the mean length and variance of each phase is impossible from these types of data sets. More complex experimental techniques are therefore required to estimate these parameters. A common technique for modelling the cell cycle is to represent it as a sequence of exponentially distributed waiting times, after which the cell divides into two identical daughter cells. The convolution of these exponential distributions therefore gives the overall distribution of the total length of the cell cycle, which we call the cell cycle distribution time (CCTD). Currently, the impact that different CCTDs have on the invasion speed of proliferative cell populations is not well understood.
This research aims to contribute to this growing body of research by constructing stochastic representations of cellular populations built on more realistic biological principles than those currently used in the literature. Most such representations currently do not consider important biological factors which impact the speed of proliferation, such as inter-relatedness between cells and phenotypic diversity throughout the population. To be precise, this research aims to develop and apply novel hybrid methodologies for modelling a number of real biological problems, such as the growth of malignant tumours, the healing of wounds, and embryonic development. This research has access to a number of data sets, mostly in the form of video files, which track the growth, and in some cases, the migration, of a particular cell line. This research will also construct hybrid methods for more general problems. Cell proliferation and migration are a special case of a broader class of systems, known as reaction-diffusion systems; these arise in many other scientific disciplines, such as physics and chemistry, and generally describe the changing concentration of chemical or biochemical substances over time.
One biological process of interest in this research is the cell-division cycle, being one of the most fundamental processes to the functioning of all multicellular life. While the exact mechanisms driving this cycle can vary considerably between cellular species, the cycle can be broadly divided into four distinct biological phases. In multicellular life, regulation of the length of the cell-division cycle, and therefore the rate of population growth, is critical to the development of organisms, as well as to the maintenance of homeostasis and wound healing. There are many challenges, both mathematical and experimental, associated with the study of the cell-division cycle. Average proliferation rates can be estimated at the population level by examining the growth curves of actively proliferative populations, however inference of the mean length and variance of each phase is impossible from these types of data sets. More complex experimental techniques are therefore required to estimate these parameters. A common technique for modelling the cell cycle is to represent it as a sequence of exponentially distributed waiting times, after which the cell divides into two identical daughter cells. The convolution of these exponential distributions therefore gives the overall distribution of the total length of the cell cycle, which we call the cell cycle distribution time (CCTD). Currently, the impact that different CCTDs have on the invasion speed of proliferative cell populations is not well understood.
This research aims to contribute to this growing body of research by constructing stochastic representations of cellular populations built on more realistic biological principles than those currently used in the literature. Most such representations currently do not consider important biological factors which impact the speed of proliferation, such as inter-relatedness between cells and phenotypic diversity throughout the population. To be precise, this research aims to develop and apply novel hybrid methodologies for modelling a number of real biological problems, such as the growth of malignant tumours, the healing of wounds, and embryonic development. This research has access to a number of data sets, mostly in the form of video files, which track the growth, and in some cases, the migration, of a particular cell line. This research will also construct hybrid methods for more general problems. Cell proliferation and migration are a special case of a broader class of systems, known as reaction-diffusion systems; these arise in many other scientific disciplines, such as physics and chemistry, and generally describe the changing concentration of chemical or biochemical substances over time.
Planned Impact
The impact of the SAMBa CDT will occur principally through the following two pathways:
1. Direct engagement with industrial partners, leading to PhD projects that are collaborative with industry, and that are focussed on topics with direct industrial impact.
2. The production of PhD graduates with
(a) the mathematical, statistical and computational technical skill sets that have been identified as in crucial demand both by EPSRC and by our industrial partners, coupled to
(b) extensive experience of industrial collaboration.
The underlying opportunity that SAMBa provides is to train graduates to have the ability to combine complex models with 'big data'. Such people will be uniquely equipped to deliver impact: whether they continue with academic careers or move directly to posts in industry, through quantitative modelling, they will provide the information that gives UK businesses competitive advantages. Our industrial partners make it clear to us that competitiveness in the energy, manufacturing, service, retail and financial sectors is increasingly dependent on who can best and most quickly analyse the huge datasets made available by the present information revolution.
During their training as part of SAMBa, these students will have already gained experience of industrial collaboration, through their PhD projects and/or the Integrated Think Tanks (ITTs) that we propose, that will give all SAMBa students opportunities to develop these transferable skills. PhD projects that involve industrial collaboration, whether arising from ITTs or not, will themselves deliver economic and social benefits to UK through the private companies and public sector organisations with which SAMBa will collaborate.
We emphasise that Bath is at the forefront of knowledge transfer (KT) activities of the kind needed to translate our research into impact. Our KT agenda has recently been supported by KT Accounts and Impact Acceleration Accounts from EPSRC (£4.9M in total) and a current HEFCE HEIF allocation of £2.4M. Bath is at the forefront of UK activity in KTPs, having completed 150 and currently holding 16 KTP contracts worth around £2.5M.
The SAMBa ITTs are an exciting new mechanism through which we will actively look for opportunities to turn industrial links into research partnerships, supported in the design of these projects by the substantial experience available across the University.
More widely, we envisage impact stemming from a range of other activities within SAMBa:
- We will look to feed the results of projects involving ecological or epidemiological data directly into environmental and public health policy. We have done this successfully many times and have three REF Case Studies describing work of this nature.
- Students will be encouraged to make statistical tools available as open source software. This will promote dissemination of their research results, particularly beyond academia. There is plenty of recent evidence that such packages are taken up and used.
- Students will discuss how to use new media to promote the public understanding of science, for example contributing to projects such as Wikipedia.
- Students will be encouraged to engage in at least one outreach activity. Bath is well known for its varied, and EPSRC-supported, public engagement activities that include Royal Institution Masterclasses, coaching the UK Mathematics Olympiad team, and reaching 50 000 people in ten days with an exhibit at the Royal Society's 350th Anniversary Summer Exhibition in 2010.
1. Direct engagement with industrial partners, leading to PhD projects that are collaborative with industry, and that are focussed on topics with direct industrial impact.
2. The production of PhD graduates with
(a) the mathematical, statistical and computational technical skill sets that have been identified as in crucial demand both by EPSRC and by our industrial partners, coupled to
(b) extensive experience of industrial collaboration.
The underlying opportunity that SAMBa provides is to train graduates to have the ability to combine complex models with 'big data'. Such people will be uniquely equipped to deliver impact: whether they continue with academic careers or move directly to posts in industry, through quantitative modelling, they will provide the information that gives UK businesses competitive advantages. Our industrial partners make it clear to us that competitiveness in the energy, manufacturing, service, retail and financial sectors is increasingly dependent on who can best and most quickly analyse the huge datasets made available by the present information revolution.
During their training as part of SAMBa, these students will have already gained experience of industrial collaboration, through their PhD projects and/or the Integrated Think Tanks (ITTs) that we propose, that will give all SAMBa students opportunities to develop these transferable skills. PhD projects that involve industrial collaboration, whether arising from ITTs or not, will themselves deliver economic and social benefits to UK through the private companies and public sector organisations with which SAMBa will collaborate.
We emphasise that Bath is at the forefront of knowledge transfer (KT) activities of the kind needed to translate our research into impact. Our KT agenda has recently been supported by KT Accounts and Impact Acceleration Accounts from EPSRC (£4.9M in total) and a current HEFCE HEIF allocation of £2.4M. Bath is at the forefront of UK activity in KTPs, having completed 150 and currently holding 16 KTP contracts worth around £2.5M.
The SAMBa ITTs are an exciting new mechanism through which we will actively look for opportunities to turn industrial links into research partnerships, supported in the design of these projects by the substantial experience available across the University.
More widely, we envisage impact stemming from a range of other activities within SAMBa:
- We will look to feed the results of projects involving ecological or epidemiological data directly into environmental and public health policy. We have done this successfully many times and have three REF Case Studies describing work of this nature.
- Students will be encouraged to make statistical tools available as open source software. This will promote dissemination of their research results, particularly beyond academia. There is plenty of recent evidence that such packages are taken up and used.
- Students will discuss how to use new media to promote the public understanding of science, for example contributing to projects such as Wikipedia.
- Students will be encouraged to engage in at least one outreach activity. Bath is well known for its varied, and EPSRC-supported, public engagement activities that include Royal Institution Masterclasses, coaching the UK Mathematics Olympiad team, and reaching 50 000 people in ten days with an exhibit at the Royal Society's 350th Anniversary Summer Exhibition in 2010.
Organisations
People |
ORCID iD |
| Christian Yates (Primary Supervisor) | |
| Joshua YOUNG (Student) |