Models of spatio-temporal reaction systems with applications to systems and synthetic biology
Lead Research Organisation:
University of Oxford
Department Name: Mathematical Institute
Abstract
The applicant plans to combine mathematical tools with multi-resolution data to develop models and methods in a framework that considers both space and time. Due to the nonlinear nature of the real-world, understanding behaviors of the physical, biological and social fields require general and widely applicable mathematical frameworks. To do this, the applicant will focus on a particular biological problem of widespread interest: protein interactions and their ability to regulate cellular decision making. This is of paramount importance; for example, in cancer, a cell is unable to transmit a death signal through protein interactions, causing the cell to continue to proliferate when it should arrest. Often these signaling processes involve many agents, all interacting in nontrivial ways, in different locations and at different levels of organization.
The development and analysis of mathematical models describing protein interactions will, crucially, allow us to understand their dynamics, predict molecular mechanisms, reveal their function, and guide cell decisions. This is an ongoing biologically and medically relevant problem of fundamental importance and mathematical/statistical approaches may provide insights into the role and dynamics in spatial organization in cells, but more generally, to other systems. Dynamical approaches will be used for model development since these consider the temporal deterministic evolution of the system and may provide mechanistic information about the system.
Throughout the fellowship, analysis and methods will be developed with chemically resolved data of the protein interaction system. Multi-resolution data of these protein interactions will be collected from Supporting Partners at the Weizmann Institute, Princeton University and University of Tokyo to test our predictions and methods. A range of mathematical/statistical approaches will be used for analysis and method development. One particular problem we will focus on is how to determine which model could describe data generated from a system. This question of model selection, or model discrmination, has led the applicant to work and develop a range of methods to distinguish between models.
Understanding the mechanisms responsible for the behavior of protein signaling in a spatio-temporal framework would advance the fields of mathematics and biology. The Supporting Partners and applicant have already contributed to this arena of studying complex systems; moreover, they share a mutual interest to advance the field through the construction of spatio-temporal models of protein interactions and develop novel mathematical techniques that may be applicable to other inherently spatial systems.
More generally, the research has direct biological implications-the work may provide insights for dysfunction of protein signaling resulting in diseases such as cancer, and we can extend our framework to analyze other biological processes inside living organism. These types of investigations will benefit from the mathematical, statistical and computational protocols that are developed in this project. Furthermore, the nonparametric and statistical methods developed for different types of spatial models can be applied to other contexts.
The development and analysis of mathematical models describing protein interactions will, crucially, allow us to understand their dynamics, predict molecular mechanisms, reveal their function, and guide cell decisions. This is an ongoing biologically and medically relevant problem of fundamental importance and mathematical/statistical approaches may provide insights into the role and dynamics in spatial organization in cells, but more generally, to other systems. Dynamical approaches will be used for model development since these consider the temporal deterministic evolution of the system and may provide mechanistic information about the system.
Throughout the fellowship, analysis and methods will be developed with chemically resolved data of the protein interaction system. Multi-resolution data of these protein interactions will be collected from Supporting Partners at the Weizmann Institute, Princeton University and University of Tokyo to test our predictions and methods. A range of mathematical/statistical approaches will be used for analysis and method development. One particular problem we will focus on is how to determine which model could describe data generated from a system. This question of model selection, or model discrmination, has led the applicant to work and develop a range of methods to distinguish between models.
Understanding the mechanisms responsible for the behavior of protein signaling in a spatio-temporal framework would advance the fields of mathematics and biology. The Supporting Partners and applicant have already contributed to this arena of studying complex systems; moreover, they share a mutual interest to advance the field through the construction of spatio-temporal models of protein interactions and develop novel mathematical techniques that may be applicable to other inherently spatial systems.
More generally, the research has direct biological implications-the work may provide insights for dysfunction of protein signaling resulting in diseases such as cancer, and we can extend our framework to analyze other biological processes inside living organism. These types of investigations will benefit from the mathematical, statistical and computational protocols that are developed in this project. Furthermore, the nonparametric and statistical methods developed for different types of spatial models can be applied to other contexts.
Planned Impact
Spatio-temporal systems are pervasive in the life and physical sciences, in particular, reaction systems are studied in biology and related engineering disciplines. The immediate and mid-term impact of this research is developing an integrative framework of spatio-temporal models and methods with this spatially resolved data. There is a large scope for applying such methods in other systems in computational biology.
Other application areas include:
- pharmacology and predicting behavior to a particular drug
- developmental and stem cell biology
- ecology and species interactions
To maximize short-term impact we will present results at conferences and post them on the preprint server arxiv. The results involving the Bayesian analysis for PDEs will be incorporated into the ABS-SysBio software framework which is freely available online.
In the medium term we will also discuss the application of the signaling findings as potential drug targets and the often-overlooked effects of space in the system.
In addition there is a lack of individuals conversant in both computational and laboratory techniques, the need for such individuals in academia and industry is likely to increase. The proposed program is an intradisciplinary project, at the wet/dry interface of systems biology. I believe the format of this science proposed in this research project will form an important milestone in my career progression.
Other application areas include:
- pharmacology and predicting behavior to a particular drug
- developmental and stem cell biology
- ecology and species interactions
To maximize short-term impact we will present results at conferences and post them on the preprint server arxiv. The results involving the Bayesian analysis for PDEs will be incorporated into the ABS-SysBio software framework which is freely available online.
In the medium term we will also discuss the application of the signaling findings as potential drug targets and the often-overlooked effects of space in the system.
In addition there is a lack of individuals conversant in both computational and laboratory techniques, the need for such individuals in academia and industry is likely to increase. The proposed program is an intradisciplinary project, at the wet/dry interface of systems biology. I believe the format of this science proposed in this research project will form an important milestone in my career progression.
Organisations
- University of Oxford (Fellow, Lead Research Organisation)
- Princeton University (Collaboration)
- Merrimack Pharmaceuticals (Collaboration)
- Weizmann Institute of Science (Collaboration)
- University of Tokyo (Project Partner)
- Weizmann Institute of Science (Project Partner)
- Princeton University (Project Partner)
People |
ORCID iD |
Heather Harrington (Principal Investigator / Fellow) |
Publications
Adamer MF
(2017)
Graph-facilitated resonant mode counting in stochastic interaction networks.
in Journal of the Royal Society, Interface
Drellich E
(2017)
Algebraic and Geometric Methods in Discrete Mathematics
Dufresne E
(2016)
The geometry of sloppiness
Gross E
(2016)
Algebraic Systems Biology: A Case Study for the Wnt Pathway.
in Bulletin of mathematical biology
Gross E
(2019)
Linear Compartmental Models: Input-Output Equations and Operations That Preserve Identifiability
in SIAM Journal on Applied Mathematics
Gross E
(2016)
Numerical algebraic geometry for model selection and its application to the life sciences.
in Journal of the Royal Society, Interface
Gross E
(2018)
Joining and decomposing reaction networks
Gross E
(2020)
Joining and decomposing reaction networks.
in Journal of mathematical biology
Harrington H
(2019)
Stratifying Multiparameter Persistent Homology
in SIAM Journal on Applied Algebra and Geometry
Harrington H
(2015)
Reduction of dimension for nonlinear dynamical systems
Harrington H
(2019)
A Parameter-Free Model Comparison Test Using Differential Algebra
in Complexity
Harrington H
(2017)
Stratifying multiparameter persistent homology
Harrington H
(2016)
Reduction of dimension for nonlinear dynamical systems
in Nonlinear Dynamics
Jovanovic G
(2015)
Phosphorelay of non-orthodox two component systems functions through a bi-molecular mechanism in vivo: the case of ArcB.
in Molecular bioSystems
Kay SK
(2017)
The role of the Hes1 crosstalk hub in Notch-Wnt interactions of the intestinal crypt.
in PLoS computational biology
Levy D
(2016)
Role of seasonality on predator-prey-subsidy population dynamics.
in Journal of theoretical biology
MacLean AL
(2016)
Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study.
in Methods in molecular biology (Clifton, N.J.)
Description | We have developed new mathematical methods for studying biological data using computational algebraic geometry. |
Exploitation Route | The mathematical methods are widely versatile for studying nonlinear models with data, and could be used in many different problems that are inherently nonlinear. |
Sectors | Chemicals,Government, Democracy and Justice,Pharmaceuticals and Medical Biotechnology |
URL | http://people.maths.ox.ac.uk/harrington/code.html |
Description | The aim of this proposal was developing methods to analyse spatio-temporal reaction systems for systems and synthetic biology. While we considered many different types of models and data, many of them were dynamic, but algebraic approaches for spatio-temporal analysis was more difficult. The methods for analysing these biological systems used ideas from computational algebra and statistics, with project partners from Princeton and Weizmann. The strength of these algebraic approaches is the ability to analyse the global behaviour of the system (implicitly) over all model parameters or generically. We collaborated with a pharmaceutical company and proposed tensors as a way to integrate data and algebraic clustering for encoding biological constraints of the data (Seigal et al, 2019). The results of this paper led to a collaboration with clinicians and geneticists to join a data integration team to analyse COVID-19 data during the pandemic (well-after the end date of this fellowship), and led to a publication in Cell. Furthermore, these methods motivated us to apply for a ``New Approaches to Data Science" grant, focusing on invariants in algebraic topology for data analysis. Near the end of this EPSRC fellowship, we partnered with Roche (which has since materialised with a Roche-Turing partnership) as well as finally, the ability to analyse spatio-temporal data. This aim was not achieved during the fellowship, but possible through follow-up funding and collaboration through a Roche studentship and researchers in Oxford oncology. |
First Year Of Impact | 2019 |
Sector | Healthcare,Pharmaceuticals and Medical Biotechnology |
Description | Royal Society International Exchange |
Amount | £12,000 (GBP) |
Organisation | The Royal Society |
Sector | Charity/Non Profit |
Country | United Kingdom |
Start | 07/2014 |
End | 07/2016 |
Description | Royal Society URF |
Amount | £400,000 (GBP) |
Organisation | The Royal Society |
Sector | Charity/Non Profit |
Country | United Kingdom |
Start | 01/2017 |
End | 12/2021 |
Title | parameter-free coplanarity model discrimination using matroids |
Description | The method enables a modeller to reject mechanistic models using steady-state data without the knowledge of kinetic parameter values. Furthermore we introduce matroids to systems biology: by computing the matroid of the competing models, we can provide minimal sets of species that should be measured to perform the coplanarity test. |
Type Of Material | Improvements to research infrastructure |
Year Produced | 2014 |
Provided To Others? | Yes |
Impact | We used this method to test different Wnt models (e.g., nuclear beta-catenin and cytoplasmic beta-catenin from mammalian cells) and demonstrate that certain models can be rejected if the data originates from a different mechanistic model. |
URL | http://arxiv.org/abs/1409.0269 |
Title | Parameter-free model comparison tests |
Description | We have developed a suite of techniques to compare models describing processes in systems and synthetic biology with data. Using computational algebra (and differential algebra) with statistics, we rule out hypothesized mechanisms that are incompatible with the data. |
Type Of Material | Data analysis technique |
Year Produced | 2016 |
Provided To Others? | Yes |
Impact | We applied this technique to study data from the Wnt signalling pathway. |
URL | http://people.maths.ox.ac.uk/harrington/code.html |
Description | Merrimack Pharmaceuticals |
Organisation | Merrimack Pharmaceuticals |
Country | United States |
Sector | Private |
PI Contribution | We were able to develop a new method to analyze their complete data set. |
Collaborator Contribution | The partnership provided me with experimental data. |
Impact | In progress manuscript. |
Start Year | 2014 |
Description | Stanislav Shvartsman |
Organisation | Princeton University |
Country | United States |
Sector | Academic/University |
PI Contribution | We applied mathematical and statistical approaches (Bayesian inference, differential algebra model identification) and later topological data analysis to reduce and analyse models of ERK/MEK. |
Collaborator Contribution | Stas Shvartsman provided data and a stimulating mathematical problem for distinguishing distinguishing different MEK mutants. |
Impact | Publication in Current Biology as well as a follow-up mathematical study https://arxiv.org/pdf/2112.00688 |
Start Year | 2014 |
Description | Weizmann Institute |
Organisation | Weizmann Institute of Science |
Country | Israel |
Sector | Academic/University |
PI Contribution | We developed a spatio-temporal mathematical model of ERK and corroborated it by experimental evidence. |
Collaborator Contribution | The Weizmann Institute performed the experiments. |
Impact | We have published the following paper (multidisciplinary: mathematics, developmental and molecular biology) Nuclear-cytoplasmic shuttling of ERK provides a switch-like transition between proliferation and differentiation of muscle progenitors Michailovici I,Harrington HA, Azogui HH, Yahalom-Ronen Y, Plotnikov A, Ching S, Stumpf MPH, Klein OD, Seger R, Tzahor E. Development 2014 Jul;141(13):2611-20. |
Start Year | 2013 |
Description | Network Science outreach |
Form Of Engagement Activity | Participation in an activity, workshop or similar |
Part Of Official Scheme? | No |
Geographic Reach | Regional |
Primary Audience | Schools |
Results and Impact | Performed outreach with school age children to educate them about networks and mathematics involved in them (e.g., Facebook, twitter, food webs, vaccine strategies etc). The goal is to engage with GCSE to take A levels, we believe from communication with College, some of these kids have considered applying to Oxford. We published a paper in Network Science. I also received recognition at an outreach events ceremony held at Oxford. |
Year(s) Of Engagement Activity | 2012,2013,2014 |
URL | http://arxiv.org/abs/1302.6567%22 |