Cross-disciplinary investigation of pattern formation in Zebrafish using spatially extended mathematical models with volume exclusion
Lead Research Organisation:
University of Bath
Department Name: Biology and Biochemistry
Abstract
Considerable theoretical and experimental investigations-have prompted hypotheses that a Turing-type reaction-diffusion mechanism may be responsible for the striped pigment pattern of zebrafish. However, recent experimental studies suggest that the mechanism uses cell-cell interactions, rather than the classic pre-pattern- generating pair of interacting, diffusible ligands.
Indeed, Yamanaka and Kondo (2014) have suggested that the asymmetric interactions and differential movement rates of xanthophores and melanophores - leading to escape-pursuit behaviour - can induce pattern formation. Recently a third cell type - iridophores - have also been suggested as critically important for zebrafish pattern formation. Finally, we have identified Agouti Signalling Peptide (ASIP) as a further patterning component, likely acting in parallel to the stripe-forming mechanism.
Mathematical modelling has played an important role in the elucidation of zebrafish striping mechanisms. The framework typically employed to represent this phenomenon utilises deterministic continuum partial differential equations (PDEs). These two-species PDE-based models fail to capture the underlying biology appropriately for four main reasons: (i) they do not account for the fluctuations inherent in biological systems; (ii) finite cell size effects are neglected; the crucial role of (iii) iridophores and (iv) ASIP signalling are ignored.
The central goal of this project is to generate a framework to investigate the effects of stochasticity and finite cell size upon pattern formation models which include iridophores and ASIP signalling, and to apply it to the study of zebrafish skin patterning.
I will construct an on-lattice exclusion-process model in which cells interact with neighbours, and move to neighbouring lattice sites. A detailed investigation of the relationship between key length scales in the model, the system size and compartment size, and their impact on the patterns formed, will be carried out. Subsequently hypotheses on pigment cell interactions will be explicitly encoded in this framework to explore the potential of the model to replicate the patterns on both wild-type and mutant fish.
These theoretical studies will alternate with experimental investigations. Guided by the modelling outputs, I will generate data to test the models efficacy. Data will be obtained from the literature and guided experimental studies for which our ongoing collaboration with Rotllant and Cerda-Reverter will be invaluable. Experimental studies will involve direct quantitative measurements of important properties of the pigment cell pattern, e.g. perhaps including dynamic cell-cell distances and density; pair correlation functions; gene expression (e.g. using qRT-PCR on skin samples); and RT-PCR comparing skin samples at different stages.
Indeed, Yamanaka and Kondo (2014) have suggested that the asymmetric interactions and differential movement rates of xanthophores and melanophores - leading to escape-pursuit behaviour - can induce pattern formation. Recently a third cell type - iridophores - have also been suggested as critically important for zebrafish pattern formation. Finally, we have identified Agouti Signalling Peptide (ASIP) as a further patterning component, likely acting in parallel to the stripe-forming mechanism.
Mathematical modelling has played an important role in the elucidation of zebrafish striping mechanisms. The framework typically employed to represent this phenomenon utilises deterministic continuum partial differential equations (PDEs). These two-species PDE-based models fail to capture the underlying biology appropriately for four main reasons: (i) they do not account for the fluctuations inherent in biological systems; (ii) finite cell size effects are neglected; the crucial role of (iii) iridophores and (iv) ASIP signalling are ignored.
The central goal of this project is to generate a framework to investigate the effects of stochasticity and finite cell size upon pattern formation models which include iridophores and ASIP signalling, and to apply it to the study of zebrafish skin patterning.
I will construct an on-lattice exclusion-process model in which cells interact with neighbours, and move to neighbouring lattice sites. A detailed investigation of the relationship between key length scales in the model, the system size and compartment size, and their impact on the patterns formed, will be carried out. Subsequently hypotheses on pigment cell interactions will be explicitly encoded in this framework to explore the potential of the model to replicate the patterns on both wild-type and mutant fish.
These theoretical studies will alternate with experimental investigations. Guided by the modelling outputs, I will generate data to test the models efficacy. Data will be obtained from the literature and guided experimental studies for which our ongoing collaboration with Rotllant and Cerda-Reverter will be invaluable. Experimental studies will involve direct quantitative measurements of important properties of the pigment cell pattern, e.g. perhaps including dynamic cell-cell distances and density; pair correlation functions; gene expression (e.g. using qRT-PCR on skin samples); and RT-PCR comparing skin samples at different stages.
Organisations
People |
ORCID iD |
Robert Kelsh (Primary Supervisor) | |
Jennifer Owen (Student) |
Publications
Gavagnin E
(2018)
Pair correlation functions for identifying spatial correlation in discrete domains
in Physical Review E
Kelsh RN
(2017)
Zebrafish adult pigment stem cells are multipotent and form pigment cells by a progressive fate restriction process: Clonal analysis identifies shared origin of all pigment cell types.
in BioEssays : news and reviews in molecular, cellular and developmental biology
Studentship Projects
Project Reference | Relationship | Related To | Start | End | Student Name |
---|---|---|---|---|---|
BB/M009122/1 | 30/09/2015 | 31/03/2024 | |||
1864779 | Studentship | BB/M009122/1 | 30/09/2016 | 30/03/2021 | Jennifer Owen |
Description | Gained understanding as to what generates striped pattern on zebrafish using mathematical model Generated a function that identifies and quantifies different patterns Progress towards refining anaesthetic procedure for juvenile zebrafish Progress towards understanding dorsal ventral countershading in zebrafish (the phenomena where the top of the body is dark and lower part of the body is light - used for camoflage) |
Exploitation Route | Can use the mathematical model to empirically investigate the causes of other types of mutations in the zebrafish without directly testing on the fish. Future researchers will be able to anaesthetise juvenile fish freely. |
Sectors | Education |
Description | Landahl Travel Grant to attend SMB 2017 |
Amount | $750 (USD) |
Funding ID | Landahl Travel Grant |
Organisation | University of Utah |
Sector | Academic/University |
Country | United States |
Start | 07/2017 |
End | 08/2017 |
Description | Bath Taps into Science |
Form Of Engagement Activity | Participation in an activity, workshop or similar |
Part Of Official Scheme? | No |
Geographic Reach | Local |
Primary Audience | Schools |
Results and Impact | Managed a stall entitled 'Fish, not just pets' for schools in Bath. |
Year(s) Of Engagement Activity | 2017 |
Description | University of Bath 50th Anniversary Festival |
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 | Managed a stall entitled 'Fish, not just pets'. Members of the public came to talk to us at the stand. |
Year(s) Of Engagement Activity | 2017 |