Mathematical Foundations of Information and Decisions in Dynamic Cell Signalling
Lead Research Organisation:
University of Warwick
Department Name: Mathematics
Abstract
Because DNA is a linear string of the base pairs A, T, C and G, the nature of information stored in the genome is well-described by classical information theory. However, this information is translated by molecular interactions into dynamical processes in the cell and it is these processes that determine the end-states of the cell such as its final cell type or whether it will kill itself or decide to divide. These processes are modelled mathematically by stochastic dynamical systems. They respond to signals generated both inside and outside the cell and can use the dynamical interactions to pass information in these signals to processing units, such as networks of genes, to be used for cellular decision-making. However, while the notion of information content is clear when one is talking about strings formed from a finite alphabet as in DNA or RNA, there is currently no clear conceptual framework once the genomic information has been passed into the dynamic processes.
A key aim of this project is to develop such a conceptual framework in the context of dynamic signalling systems by providing the mathematical foundations. A key idea behind our approach which is novel is the integration of cellular decision-making with information transmission. In this approach the value of the information in the signalling system is defined by how well it can be used to make the "correct" decisions. Rather than asking how much information is being transmitted, we ask whether the amount and quality of the information is adequate for reliable decision-making either at the single cell level or at the level of populations of cells. Decision-making will be viewed in a context similar to hypothesis testing and discrimination analysis. The basic idea will be that the cell is using the information provided by the signalling system to test multiple hypotheses or discriminate between multiple choices each of which determines a particular cellular outcome.
To do this we study the way that the probability distribution of gene responses changes as the input signal changes. Cells receive many signals informing them about the external environment and their internal state. These signals are communicated by signalling systems made up of interacting proteins into the nucleus of the cell typically by raising the level of a transcription factor (TF) in the nucleus. These transcription factors regulate genes. In this way the input signal S causes a response R by the genes. However, the process is highly stochastic and therefore the response R has a distribution P(R|S) and we are very interested in how this changes as S changes.
Gene networks can be designed so that the response R encodes a decision. For example, R might be the level of a gene that causes the cell to divide or kill itself. We will determine the principles behind such decision making and will understand the general principles governing it. In particular we will develop tools to understand its effectiveness.
To do this we will need to analyse detailed models of signalling systems. We have developed new approaches to this and will be further developing these in the project. These models indicate that the dependence of P(R|S) has a surprising dependence on S when S is multi-dimensional - the response moves in a much lower-dimensional space than the input S which implies that such systems will find complex decision making difficult. We will investigate whether this is behind the commonly observed modifications of the TFs that regulate genes because we hypothesise that while tightly coupled oscillating systems allow more complex decisions than equilibrium systems, the multiplexing is severely limited because of the above low-dimensionality. It can grow greatly when these modification states are included in the model because the ability of the TF to be modified or bound by other proteins that can be dynamically regulated allows the TF to change its function dynamically.
A key aim of this project is to develop such a conceptual framework in the context of dynamic signalling systems by providing the mathematical foundations. A key idea behind our approach which is novel is the integration of cellular decision-making with information transmission. In this approach the value of the information in the signalling system is defined by how well it can be used to make the "correct" decisions. Rather than asking how much information is being transmitted, we ask whether the amount and quality of the information is adequate for reliable decision-making either at the single cell level or at the level of populations of cells. Decision-making will be viewed in a context similar to hypothesis testing and discrimination analysis. The basic idea will be that the cell is using the information provided by the signalling system to test multiple hypotheses or discriminate between multiple choices each of which determines a particular cellular outcome.
To do this we study the way that the probability distribution of gene responses changes as the input signal changes. Cells receive many signals informing them about the external environment and their internal state. These signals are communicated by signalling systems made up of interacting proteins into the nucleus of the cell typically by raising the level of a transcription factor (TF) in the nucleus. These transcription factors regulate genes. In this way the input signal S causes a response R by the genes. However, the process is highly stochastic and therefore the response R has a distribution P(R|S) and we are very interested in how this changes as S changes.
Gene networks can be designed so that the response R encodes a decision. For example, R might be the level of a gene that causes the cell to divide or kill itself. We will determine the principles behind such decision making and will understand the general principles governing it. In particular we will develop tools to understand its effectiveness.
To do this we will need to analyse detailed models of signalling systems. We have developed new approaches to this and will be further developing these in the project. These models indicate that the dependence of P(R|S) has a surprising dependence on S when S is multi-dimensional - the response moves in a much lower-dimensional space than the input S which implies that such systems will find complex decision making difficult. We will investigate whether this is behind the commonly observed modifications of the TFs that regulate genes because we hypothesise that while tightly coupled oscillating systems allow more complex decisions than equilibrium systems, the multiplexing is severely limited because of the above low-dimensionality. It can grow greatly when these modification states are included in the model because the ability of the TF to be modified or bound by other proteins that can be dynamically regulated allows the TF to change its function dynamically.
Planned Impact
(i) Mathematicians interested in analysis and modelling of biological and biomedical systems. The ability to model information flows and decision-making will open up new areas for interaction with biologists. This impact will be felt in the short term (0-5 years).
(ii) Mathematicians and engineers interested in decision-making in noisy environments. While the project orientation is biological and medical, the problems and methodology proposed are likely to be of much broader interest. For example, next-generation cars will have to respond to noisy signals and base decisions on this and the methodology developed here is likely to be useful in such situations. This will be developed through our EPSRC funded MathSys CTD which has JLR as a partner. This impact will be felt in the first 2-5 years.
(iii) Biologists and biomedics who can start to design experiments to directly test cellular decision-making in complex systems. These issues are of great relevance to them but they currently lack to conceptual framework within which to design experiments and formulate deep questions about the decision-making aspects of their systems. The results should enable a more global treatment of inflammation and related diseases by enabling a more coherent integration of the signalling systems involved. While the treatment here directly concerns inflammation it can be applied to other areas where the signals are used to move cells into different states. For example, the can be applied to development and regenerative medicine where signals drive cells from one equilibrium to another or to cancer where the signalling has broken down and where one needs the conceptual framework to discuss this in a more global fashion. Some impact will be from day one (as I am already talking to them) but significantly in the first 2-5 years.
(iv) Health service. The use of new-technology and sensor data to stratify patients according to risk and/or to predict adverse events needs tools for forecasting and these will have to analyse noisy signals similar in principle to those discussed here. The methods developed in this project are likely to impact on such work, in particular that concerned with developing methods for appropriately integrating diverse probabilistic systems, with online updating of information bases including inferential methodologies. This will be developed through established contacts in the health service with who we have established collaborations e.g. clinicians such as Professor Francis Levi and Professor Nick James, hospitals such as University Hospital Birmingham and University Hospitals Coventry & Warwickshire, and international organisations such as INSERM (with which we are one of the Laboratoires Européens et Internationaux Associés) and the International Association for Research in Cancer (IARC) in Lyon. This research will make a significant contribution to this field in the medium term (3-10 years).
(ii) Mathematicians and engineers interested in decision-making in noisy environments. While the project orientation is biological and medical, the problems and methodology proposed are likely to be of much broader interest. For example, next-generation cars will have to respond to noisy signals and base decisions on this and the methodology developed here is likely to be useful in such situations. This will be developed through our EPSRC funded MathSys CTD which has JLR as a partner. This impact will be felt in the first 2-5 years.
(iii) Biologists and biomedics who can start to design experiments to directly test cellular decision-making in complex systems. These issues are of great relevance to them but they currently lack to conceptual framework within which to design experiments and formulate deep questions about the decision-making aspects of their systems. The results should enable a more global treatment of inflammation and related diseases by enabling a more coherent integration of the signalling systems involved. While the treatment here directly concerns inflammation it can be applied to other areas where the signals are used to move cells into different states. For example, the can be applied to development and regenerative medicine where signals drive cells from one equilibrium to another or to cancer where the signalling has broken down and where one needs the conceptual framework to discuss this in a more global fashion. Some impact will be from day one (as I am already talking to them) but significantly in the first 2-5 years.
(iv) Health service. The use of new-technology and sensor data to stratify patients according to risk and/or to predict adverse events needs tools for forecasting and these will have to analyse noisy signals similar in principle to those discussed here. The methods developed in this project are likely to impact on such work, in particular that concerned with developing methods for appropriately integrating diverse probabilistic systems, with online updating of information bases including inferential methodologies. This will be developed through established contacts in the health service with who we have established collaborations e.g. clinicians such as Professor Francis Levi and Professor Nick James, hospitals such as University Hospital Birmingham and University Hospitals Coventry & Warwickshire, and international organisations such as INSERM (with which we are one of the Laboratoires Européens et Internationaux Associés) and the International Association for Research in Cancer (IARC) in Lyon. This research will make a significant contribution to this field in the medium term (3-10 years).
People |
ORCID iD |
David Rand (Principal Investigator) | |
Giorgos Minas (Researcher) |
Publications
Sáez M
(2022)
Dynamical landscapes of cell fate decisions.
in Interface focus
Rand DA
(2021)
Geometry of gene regulatory dynamics.
in Proceedings of the National Academy of Sciences of the United States of America
Minas G
(2017)
Inferring transcriptional logic from multiple dynamic experiments.
in Bioinformatics (Oxford, England)
Minas G
(2017)
Long-time analytic approximation of large stochastic oscillators: Simulation, analysis and inference.
in PLoS computational biology
Minas G
(2020)
Multiplexing information flow through dynamic signalling systems.
in PLoS computational biology
Giorgos Minas
(2019)
Parameter sensitivity analysis for biochemical reaction networks.
in Mathematical Biosciences and Engineering
Minas G
(2019)
Parameter sensitivity analysis for biochemical reaction networks.
in Mathematical biosciences and engineering : MBE
Camacho-Aguilar E
(2021)
Quantifying cell transitions in C. elegans with data-fitted landscape models
in PLOS Computational Biology
Harper CV
(2018)
Temperature regulates NF-?B dynamics and function through timing of A20 transcription.
in Proceedings of the National Academy of Sciences of the United States of America
Description | Many cellular and molecular systems such as the circadian clock and the cell cycle are oscillators that are modelled using nonlinear dynamical systems. Moreover, oscillatory systems are ubiquitous elsewhere in science. There is an extensive theory for perfectly noise-free dynamical systems and very effective algorithms for simulating their temporal behaviour. On the other hand, biological systems are inherently stochastic and the presence of stochastic noise can play a crucial role. Unfortunately, there are far fewer analytical tools and much less understanding for stochastic models especially when they are nonlinear and have lots of state variables and parameters. Moreover simulation is not so effective and can be very slow if the system is large. In this article we describe how to accurately approximate such systems in a way that facilitates fast simulation, parameter estimation and new approaches to analysis, such as calculating probability distributions that describe the system's stochastic behaviour and describing how these distributions change when the parameters of the system are varied. We have also applied ideas from this theory to problems in developmental biology, We use a theory of landscapes that describe the way cells transition between different differentiation states and have discovered a new complex landscape involved in the development of the neural tube. This work has now appeared in three papers which together give a new approach to cellular decision-making that highlights the way in which bifurcations regulate the transition paths by which cells progress from precursor states to more complex ones. They also provides practical tools for the analysis of single cell data. There has been a great amount of interest and an invitation to write a review article. |
Exploitation Route | This work greatly facilitates modelling methods for biological systems. Our current work is with the Crick Institute and this will facilitate integration of any relevant outcomes into medicine. A grant to further the work has bee awarded. We have been approached by multiple groups interested in collaboration. |
Sectors | Creative Economy,Healthcare,Pharmaceuticals and Medical Biotechnology |
Description | As a result of this grant I have entered into strong collaborations with internationally leading researchers on projects with medical impact. There are two main areas: (i) molecular mechanisms of vertebrate regeneration and (ii) heart developmental pathologies. The first area is a collaboration with Dr James Briscoe's lab at the Francis Crick Institute and Dr Elly Tanaka at the Mac Planck institute Research Institute of Molecular Pathology (IMP) in Vienna. The work on (ii) is with Dr Tim Saunder's lab at the Warwick Medical School and is supported by a grant from the BHF. The relevant research in this area was started as part of this grant and gives a new way to understand the process of cell decision-making and differentiation and new data analysis techniques to use single cell data to quantify this process. This grant enabled me to develop the collaboration with Briscoe's group and this has grown significantly since then and extended into the collaborations with the Tanaka and Saunders labs. |
First Year Of Impact | 2021 |
Sector | Healthcare,Pharmaceuticals and Medical Biotechnology |
Impact Types | Societal |
Description | Improving Cancer Prognosis Through Circadian Time-Telling |
Amount | £344,837 (GBP) |
Funding ID | C53720/A29468 |
Organisation | Cancer Research UK |
Sector | Charity/Non Profit |
Country | United Kingdom |
Start | 04/2020 |
End | 03/2023 |
Description | Using catastrophes, dynamics & data analysis to uncover how differentiating cells make decisions. |
Amount | £439,130 (GBP) |
Funding ID | EP/T031573/1 |
Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
Sector | Public |
Country | United Kingdom |
Start | 07/2021 |
End | 06/2024 |
Title | TimeTeller |
Description | This is an algorithm that enables one to obtain an assessment of an individual's circadian clock in cells of a particular tissue using a single transcriptomics sample. It will be of use in all areas of circadian medicine. |
Type Of Material | Physiological assessment or outcome measure |
Year Produced | 2022 |
Provided To Others? | Yes |
Impact | Too soon to say. |
Description | Collaboration with Aarti Jagannath, Nuffield Department of Clinical Neurosciences. |
Organisation | University of Oxford |
Department | Nuffield Department of Clinical Neurosciences |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | Expertise in data analysus. Analysis of data for the paper mentioned below. |
Collaborator Contribution | Expertise in light signalling, sleep regulation and circadian rhythms. |
Impact | Involvement in Wellcome grant application Joint paper with CRUK grant group: Taylor L., von Lendenfeld F., Ashton A., Sanghani H., Tam E., Usselmann L., Verennetikova M., Dallmann R., McKeating J., Vasudevan S. & Jagannath A. 2022 Sleep and circadian rhythm disruption alters the lung transcriptome to predispose to viral infection. bioRxiv, doi: 10.1101/2022.02.28.482377. (submitted to Nature Immunology) Multidisciplinary: circadian biology and mathematics |
Start Year | 2018 |
Description | Collaboration with Dr Eric Siggia (Rockefeller) |
Organisation | Rockefeller University |
Country | United States |
Sector | Academic/University |
PI Contribution | Support as Project Partner on grant EPSRC EP/T031573/1 Using catastrophes, dynamics & data analysis to uncover how differentiating cells make decisions. |
Collaborator Contribution | Advice on developmental biology |
Impact | Joint papers |
Start Year | 2020 |
Description | Collaboration with Dr James Briscoe |
Organisation | Francis Crick Institute |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | Analysis of data. Development of new approaches for this. |
Collaborator Contribution | Provision of state-of-the-art single cell data and biological information. |
Impact | This collaboration is multidisciplinary. Outcomes are forthcoming. |
Start Year | 2016 |
Description | Dr Timothy Saunders collaboration on early development of the heart |
Organisation | University of Warwick |
Department | Warwick Medical School |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | To apply my theory recently developed about developmental landscapes to early development of the heart and to understand the regulatory dynamics. I am a collaborator on a recently started BHF grant to saunders. |
Collaborator Contribution | Provision of biological data. Planning of experimental approach. |
Impact | Application to British Heart Foundation. This was successful. |
Start Year | 2022 |
Description | BIOMS Symposium 2018 |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Professional Practitioners |
Results and Impact | Keynote Lecture. BIOMS Symposium 2018, BioQuant, University of Heidelberg, October, 2018. Title: Multiplexing information flow through dynamic signalling systems |
Year(s) Of Engagement Activity | 2018 |
Description | Colloquium. "The circadian clock: using Maths to understand how a complex dynamical system controls our health and survival." University of Porto, Portugal. January 2020. |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Professional Practitioners |
Results and Impact | A talk for a broad audience on the health implications associated with the circadian clock. |
Year(s) Of Engagement Activity | 2020 |
Description | Contributed Lecture. "TimeTeller: a New Tool for Precision Circadian Medicine and Cancer" XVI European Biological Rhythms Society Congress, Lyon, August 2019. |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Professional Practitioners |
Results and Impact | A talk to a primarily medical and biomedical audience about the way maths has been used to find a new breast cancer prognostic factor. |
Year(s) Of Engagement Activity | 2019 |
Description | Geometry and genetics |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Professional Practitioners |
Results and Impact | Invited lecture. Geometry & Genetics. Meeting of minds on the mathematics of cell programming. London Institute Mathematical Sciences. Royal Institution. March, 2022. |
Year(s) Of Engagement Activity | 2022 |
URL | https://lims.ac.uk/event/meeting-of-minds-on-the-mathematics-of-cell-programming/ |
Description | IMA Lighthill Lecture |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Professional Practitioners |
Results and Impact | Keynote Lecture, IMA Lighthill Lecture. Geometry, information and genetics. British Mathematical Colloquium/ British Applied Mathematical Colloquium Joint Meeting, May 2021. |
Year(s) Of Engagement Activity | 2021 |
URL | https://ima.org.uk/support/lectures/ima-lighthill-lecture/ |
Description | Invited Lecture, Oberwolfach Meeting June, 2017. |
Form Of Engagement Activity | Participation in an activity, workshop or similar |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Study participants or study members |
Results and Impact | Invited Lecture, Oberwolfach Meeting on Reaction Networks and Population Dynamics, June, 2017. |
Year(s) Of Engagement Activity | 2017 |
Description | Invited Spring School Lectures at CompSysBio Spring School. Aussois, France. March 2017 |
Form Of Engagement Activity | Participation in an activity, workshop or similar |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Postgraduate students |
Results and Impact | Two Invited Spring School Lectures. Information and Decision-Making in Dynamic Cell Signalling. |
Year(s) Of Engagement Activity | 2017 |
URL | https://project.inria.fr/compsysbio2017/ |
Description | Lecture to UK Plant and Algal Clocks workshop, 16-17 April 2018 Edinburgh |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | National |
Primary Audience | Professional Practitioners |
Results and Impact | Lecture to UK Plant and Algal Clocks workshop, 16-17 April 2018 Edinburgh. Title: Modelling & measuring the stochasticity in circadian clocks: information theory, new methodology & measuring clock function |
Year(s) Of Engagement Activity | 2018 |
Description | Mini-symposium on Multi-scale Mathematical Models in Endocrinology. |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Professional Practitioners |
Results and Impact | Invited Lecture, ECMTB 2018 Stochastic transcriptional dynamics and spatial signalling for the prolactin gene in single cells and tissue. Mini-symposium on Multi-scale Mathematical Models in Endocrinology. |
Year(s) Of Engagement Activity | 2018 |
Description | Workshop: Modelling and measuring the landscapes of early embryonic development |
Form Of Engagement Activity | Participation in an activity, workshop or similar |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Professional Practitioners |
Results and Impact | MiR@W Day: Modelling and measuring the landscapes of early embryonic development Speakers: Dr. James Briscoe, The Francis Crick Institute, UK: Dynamics of gene regulatory networks and the precision of developmental patterning Dr. Geneviève Dupont, Université Libre de Bruxelles, Belgium: Model of cell fate decision in the early mouse embryo Dr. Paul François, McGill University, Canada: Clock, waves, evolution: geometry of vertebrae patterning Dr. Meritxell Saez, The Francis Crick Institute, UK: Gene-free landscape models for development Dr. Eric Siggia, The Rockefeller University, US: Embryology: Real and Imagined |
Year(s) Of Engagement Activity | 2021 |
URL | https://warwick.ac.uk/fac/sci/maths/research/events/2019-20/ucdm/ |