Mathematical investigation into the role of cell-cell communication pathways on collective cell migration
Lead Research Organisation:
University of Dundee
Department Name: Mathematics
Abstract
A large number of fundamental processes in development and various diseases (e.g., cancer growth and invasion, wound healing, morphogenesis) are the result of the coordinated movement of cells. Independent of cell types, collective movement usually involves three factors: cell-cell and cell-matrix interactions, polarization of cells into "leaders" and "followers", and chemical and physical signals that allow cells to communicate with each other. There are multiple ways of cell movement, ranging from single cell movement to collective movement (where cells stay connected as they move).
The movement of single cells has been investigated quite in detail over the past decades, and the key aspects of single cell movement (e.g., molecular control of cell protrusions, interactions between cells and their substrate) have been already identified. However, the collective movement of cells is less understood, and there are many open questions regarding the mechanisms involved in this type of movement. For example, it is less understood how cell movement and cell-cell communication interact to create new tissues, or to allow cells to colonise specific areas. Another aspect less understood is how cells interpret and integrate signals from the environment and from other cells to produce specific types of cell aggregations and collective movement. Finally, it is still unknown whether all cells sense guidance signals, or only the leader cells sense these signals and then instruct other cells to follow them.
To formulate hypotheses that could help address these questions, we will derive a class of mechanistic mathematical models that describe cell movement and cell-cell interactions via different communication mechanisms. Using various mathematical techniques (e.g. travelling wave analysis, bifurcation analysis), we will investigate the role of different cell-cell communication mechanisms on the movement and structure of cell aggregations. We will also investigate the effect of parameters on the transitions between different types of cell movement behaviours.
The movement of single cells has been investigated quite in detail over the past decades, and the key aspects of single cell movement (e.g., molecular control of cell protrusions, interactions between cells and their substrate) have been already identified. However, the collective movement of cells is less understood, and there are many open questions regarding the mechanisms involved in this type of movement. For example, it is less understood how cell movement and cell-cell communication interact to create new tissues, or to allow cells to colonise specific areas. Another aspect less understood is how cells interpret and integrate signals from the environment and from other cells to produce specific types of cell aggregations and collective movement. Finally, it is still unknown whether all cells sense guidance signals, or only the leader cells sense these signals and then instruct other cells to follow them.
To formulate hypotheses that could help address these questions, we will derive a class of mechanistic mathematical models that describe cell movement and cell-cell interactions via different communication mechanisms. Using various mathematical techniques (e.g. travelling wave analysis, bifurcation analysis), we will investigate the role of different cell-cell communication mechanisms on the movement and structure of cell aggregations. We will also investigate the effect of parameters on the transitions between different types of cell movement behaviours.
Planned Impact
The proposed research will achieve its impact through the application of modelling and techniques developed here to investigate experimental data on cell-cell signalling and cell migration, and to propose new experimental hypotheses.
At this stage, the research has a predominantly academic impact (with immediate beneficiaries being other researchers in cell biology and applied mathematics). However, the impact will be broadened by the set up of new collaborations and further grant applications that could take these ideas further for business exploitation (especially in the biotechnical industry, where cell migration is becoming very important in the context of artificial tissues and stem cell implants). To this end, in the first year I will be looking to apply for other grants that can take the ideas developed during this grant period further to the market (e.g., the EPSRC Follow On Fund, Technology Strategy Board initiatives, the MRC Developmental Pathway Funding Scheme). Also, during this first grant stage I intend to look at suitable industrial collaborative partners, as my research will develop for longer-term collaborations. Examples of possible industrial partners in Scotland are DySIS Medical or Mode Diagnostics.
In the short term, this research is expected to lower the costs and shorten the time period for basic experiments on cell migration. This could reduce the time for treatments (for cancers and developmental diseases) to go from the bench to the bedside. Also, it could increase the effectiveness of current treatments by better understanding the mechanisms of the diseases.
In the long term, progress in the design of new treatments is expected to have economic and commercial benefits through exploitation of this research by the large pharmaceutical companies, which contribute significantly to the UK prosperity. It is also expected that the success of this project will enhance the quality of life patients.
The results of this proposed research will be disseminated in leading academic journals, and at conferences in the mathematical biology and applied mathematics fields. Also, the results will be disseminated in the annual Newsletter of the Division of Mathematics, University of Dundee.
Finally, this project creates the opportunity for training a new Postdoctoral Fellow with interdisciplinary relevant skills. The Fellow will acquire knowledge in both applied mathematics and cell biology, and will learn to integrate concepts and methods from these different disciplines. This can prepare the Postdoctoral Fellow for a wider range of employment.
At this stage, the research has a predominantly academic impact (with immediate beneficiaries being other researchers in cell biology and applied mathematics). However, the impact will be broadened by the set up of new collaborations and further grant applications that could take these ideas further for business exploitation (especially in the biotechnical industry, where cell migration is becoming very important in the context of artificial tissues and stem cell implants). To this end, in the first year I will be looking to apply for other grants that can take the ideas developed during this grant period further to the market (e.g., the EPSRC Follow On Fund, Technology Strategy Board initiatives, the MRC Developmental Pathway Funding Scheme). Also, during this first grant stage I intend to look at suitable industrial collaborative partners, as my research will develop for longer-term collaborations. Examples of possible industrial partners in Scotland are DySIS Medical or Mode Diagnostics.
In the short term, this research is expected to lower the costs and shorten the time period for basic experiments on cell migration. This could reduce the time for treatments (for cancers and developmental diseases) to go from the bench to the bedside. Also, it could increase the effectiveness of current treatments by better understanding the mechanisms of the diseases.
In the long term, progress in the design of new treatments is expected to have economic and commercial benefits through exploitation of this research by the large pharmaceutical companies, which contribute significantly to the UK prosperity. It is also expected that the success of this project will enhance the quality of life patients.
The results of this proposed research will be disseminated in leading academic journals, and at conferences in the mathematical biology and applied mathematics fields. Also, the results will be disseminated in the annual Newsletter of the Division of Mathematics, University of Dundee.
Finally, this project creates the opportunity for training a new Postdoctoral Fellow with interdisciplinary relevant skills. The Fellow will acquire knowledge in both applied mathematics and cell biology, and will learn to integrate concepts and methods from these different disciplines. This can prepare the Postdoctoral Fellow for a wider range of employment.
Publications
Buono P
(2014)
Codimension-Two Bifurcations in Animal Aggregation Models with Symmetry
in SIAM Journal on Applied Dynamical Systems
Eftimie R
(2015)
The Role of Avoidance and Learning Behaviours on the Formation and Movement of Biological Aggregations
in Mathematical Modelling of Natural Phenomena
Buono PL
(2015)
Symmetries and pattern formation in hyperbolic versus parabolic models of self-organised aggregation.
in Journal of mathematical biology
Pineda M
(2015)
Modelling cell movement, cell differentiation, cell sorting and proportion regulation in Dictyostelium discoideum aggregations.
in Journal of theoretical biology
Macnamara C
(2015)
Memory versus effector immune responses in oncolytic virotherapies.
in Journal of theoretical biology
Buono P
(2016)
Mathematical Sciences with Multidisciplinary Applications
Eftimie R
(2016)
Mathematical Models for Immunology: Current State of the Art and Future Research Directions.
in Bulletin of mathematical biology
Den Breems NY
(2016)
The re-polarisation of M2 and M1 macrophages and its role on cancer outcomes.
in Journal of theoretical biology
Bitsouni V
(2017)
Mathematical modelling of cancer invasion: The multiple roles of TGF-ß pathway on tumour proliferation and cell adhesion
in Mathematical Models and Methods in Applied Sciences
Description | The mathematical models used to describe collective behaviour of cells or animals, can exhibit complex spatial and spatio-temporal patterns (that result from nonlocal and nonlinear interactions between members of biological aggregations). My research has been used (so far) to classify some of the complex patterns that occur near bifurcation points (i.e., near parameter values for which the dynamics of the biological system changes), and to explain the mechanisms that lead to transitions between different patterns for biological aggregations. Moreover, the research generated new questions regarding the necessity of investigating more complex transitions between similar types of aggregation patterns (mathematical investigation of these transitions will allow us to gain a better understanding of the types of models used to describe cell-cell and animal-animal interactions via different communication mechanisms). These complex transitions will be investigated in the near future via a new collaboration with University of Bath. |
Exploitation Route | The fact that transitions between different complex spatial and spatio-temporal patterns in biological aggregations might not be always generated by changes in particular parameter values (that describe, for example, the speed of cells/animals) and might actually be intrinsic to the biological system (resulting from complex bifurcation dynamics), suggests that it might be difficult to control certain types of biological aggregations (e.g., the collective movement of cancer cells, or the collective movement of animals/humans). This further suggests the necessity of collaboration between mathematicians and experimentalists (or people in various sectors that might use mathematical models to predict the outcome of treatments for diseases involving cell migration, or to predict the outcome of human aggregations - e.g., for security purposes) to investigate thoroughly the possible dynamics exhibited by the mathematical models. |
Sectors | Healthcare,Security and Diplomacy,Transport |
Description | The results of my research have been presented to the general public during public talks. |
First Year Of Impact | 2017 |
Sector | Education |
Impact Types | Policy & public services |
Description | PhD Studentship (EPSRC DTA funding) |
Amount | £42,000 (GBP) |
Organisation | University of Dundee |
Sector | Academic/University |
Country | United Kingdom |
Start | 09/2014 |
End | 08/2017 |
Title | mathematical & computational models for collective cell movement via cell-cell communication |
Description | Together with my collaborators, I have developed new mathematical models for the collective movement of cells (cancer cells, Dictyostelium cells), and the signalling pathways that control multiple aspects of cell dynamics. The models incorporated ("in vitro" or "in vivo") data available in the literature. |
Type Of Material | Model of mechanisms or symptoms - in vitro |
Year Produced | 2016 |
Provided To Others? | Yes |
Impact | The models that I developed are capable to incorporate directional signalling in cells or direction communication in animals. This (general) approach can be further applied to specific cells/animals, which interact via specific mechanisms. |
Title | Nonlocal models for cell movement which can incorporate directionality of cell-cell interactions |
Description | Over the last few years I have developed (and investigated numerically and analytically) a class of 1D nonlocal models that can describe cell movement as a result of cell-cell interactions. The advantage of using hyperbolic models consists in their capability of describing cell polarisation or cell-cell interactions via directional communication (which is difficult to model with parabolic equations). Moreover, hyperbolic models are more difficult to investigate analytically (e.g., showing centre manifold results), which also makes them very interesting from a mathematical point of view. |
Type Of Material | Computer model/algorithm |
Provided To Others? | No |
Impact | There is no impact yet. This class of models is still in early stages of analytical investigation. Impact can be obtained in a few years. |
Description | Collaboration with Dr. Buono on models for collective cell movement |
Organisation | University of Ontario Institute of Technology (UOIT) |
Country | Canada |
Sector | Academic/University |
PI Contribution | I have started developing new mathematical models for collective movement of cells. The models will then be investigated (in terms of bifurcation and symmetry of patterns) with my collaborator, Dr. P.-L. Buono. |
Collaborator Contribution | Dr. Buono (University of Ontario Institute of Technology) provided the expertise in symmetry theory. |
Impact | 3 articles (in collaboration with Dr. P.-L. Buono) have been published since 2013. 2 of these articles have been supported by the EPSRC First Grant. 2 new articles on a new research topic will be submitted in the first few months of 2015. These new articles are also supported by the EPSRC First Grant. |
Start Year | 2012 |
Description | Collaboration with Prof. Carrillo on kinetic models for collective behaviour |
Organisation | Imperial College London |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | I contribute with my expertise in nonlocal hyperbolic models for self-organised biological aggregations. These models incorporate also various types of signalling/communication mechanisms between members of the biological aggregation. |
Collaborator Contribution | Prof. Carrillo contributes with his expertise on kinetic models for collective movement, and various analytical and numerical methods to investigate these models. |
Impact | One article submitted for publication. The article is currently under review. The collaboration is not multi-disciplinary. Article: J.A. Carrillo, R. Eftimie, F.K.O. Hoffmann, 2014, Non-local kinetic and macroscopic models for self-organised animal aggregations. Submitted. |
Start Year | 2013 |
Description | Collaboration with Prof. Weijer on models for collective movement of cells |
Organisation | University of Dundee |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | I have developed and started investigating new (nonlocal) mathematical models to describe the collective movement of cells (Dictyostelium Discoideum cells). |
Collaborator Contribution | Prof. Weijer brought the biological and experimental expertise on the subject of collective movement of cells. |
Impact | One research article has been submitted for publication. The collaboration is multi-disciplinary (between Mathematics and Developmental Biology). Article: M. Pineda, C.J. Weijer, R. Eftimie, 2014. Modelling cell movement, cell differentiation, cell sorting and proportion regulation in Dictyostelium discoideum aggregations. Submitted. |
Start Year | 2013 |
Description | Collaboration with Students from INSA Rouen |
Organisation | University of Rouen |
Country | France |
Sector | Academic/University |
PI Contribution | I am developing and investigating analytically mathematical models for the collective movement of animals and cells (and the communication mechanisms/signalling pathways that control collective movement) |
Collaborator Contribution | The summer research students from Rouen perform numerical investigations of these models (thus applying the theoretical knowledge gained during the undergrad years to a very applied mathematical problem). |
Impact | I have published a research article with Mr. Adrien Coulier (summer research student June-August 2013). Another research article will be submitted for peer-review publication by Spring/Summer 2016. |
Start Year | 2013 |
Description | Dr. den Breems: Collaboration on macrophages-tumour interactions |
Organisation | University of Dundee |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | I have helped Dr. Den Breems with the development and analytical investigation of a mathematical model for the interactions between macrophages and tumour cells (part of the collective dynamics of tumour cells). This project aimed to take the resea |
Collaborator Contribution | Dr. Nicoline den Breems, developed in collaboration with me a mathematical model for the interaction between macrophages and tumour cells (part of the collective dynamics of tumour cells). Dr. den Breems investigated the model numerically (i.e., "in silico") and compared the results with available experimental data. |
Impact | We have published a paper on the biological mechanisms for the interactions between macrophages and melanoma cancer cells. |
Start Year | 2013 |
Description | 9th European Conference on Mathematical and Theoretical Biology, Gotheburg, Sweden |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Other audiences |
Results and Impact | Invited talk on my research on the mathematical modelling & investigation (analytical and numerical) of pattern formation in collective dynamics in animals and cells |
Year(s) Of Engagement Activity | 2014 |
Description | AIMS Conference Series on Dynamical Systems and Differential Equations, Madrid, Spain |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Other audiences |
Results and Impact | Invited talk on my research on the investigation (numerical and analytical) of collective movement of animals. |
Year(s) Of Engagement Activity | 2014 |
Description | Collective behaviour: Macroscopic versus Kinetic Descriptions, Imperial College, London |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Other audiences |
Results and Impact | Invited talk on my research on pattern formation in collective movement of cells and animals. |
Year(s) Of Engagement Activity | 2014 |
Description | Conference talk at 3rd International Conference on Engineering and Computational Mathematics, Hong Kong |
Form Of Engagement Activity | A formal working group, expert panel or dialogue |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Postgraduate students |
Results and Impact | Talk on my research on the collective movement of cells in response to various signalling pathways. |
Year(s) Of Engagement Activity | 2017 |
Description | Organised the "Women in Mathematics" event, part of Women in Science festival, Dundee, 7-28 March, 2015 |
Form Of Engagement Activity | Participation in an activity, workshop or similar |
Part Of Official Scheme? | No |
Geographic Reach | Local |
Primary Audience | Public/other audiences |
Results and Impact | Talks with public sparked questions about the use of mathematics. With the help of the public, I have also created a level-2 MegaMenger fractal cube. Some public participants enquired about the existence of an website where they can periodically check updates on our research. |
Year(s) Of Engagement Activity | 2015 |
URL | http://dundeesciencecentre.org.uk/event/show/219.html |
Description | Participated in the 2013 Dundee Science festival |
Form Of Engagement Activity | Participation in an open day or visit at my research institution |
Part Of Official Scheme? | No |
Geographic Reach | Local |
Primary Audience | Public/other audiences |
Results and Impact | Discussion with public sparked questions about research. No notable impacts. |
Year(s) Of Engagement Activity | 2013 |
Description | Plenary talk in Postgraduate Summer School |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Postgraduate students |
Results and Impact | I was invited to give a series of talks based on my own research at the annual IGTC Summit, in Jasper, Alberta (for postgraduate students from different universities in western Canada) |
Year(s) Of Engagement Activity | 2017 |
Description | Public talk: "The beauty of mathematics: from the collective movement of cells to the collective movement of animals" |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | Regional |
Primary Audience | Public/other audiences |
Results and Impact | This was a public talk that gave the audience a brief overview of my research (and focused on the research performed while holding the EPSRC grant) |
Year(s) Of Engagement Activity | 2017 |
Description | SIAM Conference on Analysis of Partial Differential Equations (PD13), Orlando, USA |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Other audiences |
Results and Impact | Invited talk on my research on pattern formation in nonlocal hyperbolic models for collective movement in biology. |
Year(s) Of Engagement Activity | 2013 |
Description | Society for Mathematical Biology Annual Conference, Atlanta |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Other audiences |
Results and Impact | Gave presentation on my research on collective cells movement in Dictyostelium cells, via dual-feedback signalling pathways. |
Year(s) Of Engagement Activity | 2015 |
Description | Workshop Cancer and Immune System, Mathematical Biosciences Institute (MBI), Ohio, USA |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Other audiences |
Results and Impact | Invited presentation in an workshop aimed at researchers interested in mathematical investigation of interactions between cancer and immune cells. Following this workshop (which sparked questions and discussions, and interest for further collaboration), I became more aware of specific signalling pathways that influence the collective movement of cancer cells. |
Year(s) Of Engagement Activity | 2014 |
Description | Workshop on "Mathematical models for cancer cell migration", Oberwolfach, Germany |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Other audiences |
Results and Impact | Invited presentation on my research on collective movement of cells, as controlled by various signalling pathways. |
Year(s) Of Engagement Activity | 2014 |
Description | Workshop on "Nonlocal nonlinear partial differential equations and applications", Anacapri, Italy |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Postgraduate students |
Results and Impact | Invited presentation of my research on nonlocal models for collective movement of cells and animals (via different communication mechanisms). The workshop aimed to stimulate interactions between researchers interested in analytical and numerical methods to investigate nonlocal and nonlinear mathematical models (described by partial differential equations). |
Year(s) Of Engagement Activity | 2015 |
Description | article popularising my research |
Form Of Engagement Activity | A magazine, newsletter or online publication |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Public/other audiences |
Results and Impact | I have written an article and submitted it for publication in 'Snapshots of modern mathematics form Oberwolfach'. The targeted readership consists of mathematics teachers, science journalists, undergraduate and advanced high school students, etc. Article: R. Eftimie, 2014 Modelling communication and movement: from cells to animals and humans. Snapshots of modern mathematics from Oberwolfach. No. 21. The article is still to be published (although it was accepted for publication). Hence, impact might come next years. |
Year(s) Of Engagement Activity | 2014 |