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Mathematical and Computational Biology
The complexity of the problems faced by researchers in the biological sciences is substantial and often difficult to overcome by those trained within a single field. Our commitment to supporting collaboration across departments opens new and exciting avenues of research.
Research Highlights
- A team led by Dr Matteo Degiacomi (Durham, Physics) have developed the open source software Jabberdock which models transmembrane protein docking. Find out more here.
- Dr Ulrik Beierholm (Durham Psychology) and a team of interdisciplinary academics are exploring Bayesian approaches to understand how the nervous system deals with uncertainty. Find out more here.
- An interdisciplinary team including Professor Bernard Piette (Durham Mathematical Sciences) and Professor Jonathan Heddle (Durham Biosciences) have been exploring the geometries of artificial protein cages that exhibit near-miss symmetry. Find out more here.
- A collaboration between Dr Chris Prior (Durham Mathematical Sciences), Halim Kusumaatmaja (Durham Physics) and Dr Jack Panter (Durham Physics) has resulted in a new model of elastic fibre bundles. The model simulates the kind of structural collapse seen in many biological filament bundles including the optic nerve bundle. Find out more here.
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Jabberdock, New Open Source Software to Model Transmembrane Protein Docking
The new, open source transmembrane protein docking software Jabberdock was developed in Durham by the Degiacomi group. It allows users to model the docking interactions of transmembrane proteins, an important class of proteins that make up 50% of all targets in drug design.
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Nearly-symmetrical Convex Polyhedral Cages and the Introduction of a New Mathematical Concept
At first glance the TRAP-cage, a structure made up of 24 hendecagons engineered from TRAP (trp RNA-binding attenuation protein), looks regular, but this is a mathematical impossibility. Tiny variations in the nearly-identical hendecagons allow the structure to “fit” with near-miss symmetry.
Jabberdock, New Open Source Software to Model Transmembrane Protein Docking
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Nearly-symmetrical Convex Polyhedral Cages and the Introduction of a New Mathematical Concept
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Activities
Visual PDE
VisualPDE is an online tool designed by Benjamin Walker (University of Bath), Adam Townsend (Durham Mathematical Sciences) and Andrew Krause (Durham Mathematical Sciences) to visualise partial differential equations, bringing them to life for a wider audience. The picture in the banner at the top of this page is a simulation based on the Schnakenberg model to form Turing patterns on a representation of Alan Turing. These patterns are important in mathematical biology as a way to describe morphogenesis; the way biological organisms develop their structure as they grow.
Biomathematics and Biocomputing Special Interest Group
Members of the BSI, led by Dr Ulrik Beierholm (Durham Psychology) set up the Biomathematics and Biocomputing Special Interest Group in 2018. It brings together people from across the University to connect on these topics, including those who are not regularly part of the BSI community.
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VisualPDE
A snapshot of a Turing Pattern simulation on an earlier version of the Biophysical Sciences Institute logo.
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Biomathematics and Biocomputing Special Interest Group
Attendees gather for the launch of the Biocomputation Special Interest Group held in-person during the summer of 2018 (image courtesy of Durham University).
VisualPDE
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Biomathematics and Biocomputing Special Interest Group
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Highlight Publications
Aston, S., Negen, J., Nardini, M., & Beierholm, U., 2022. Central tendency biases must be accounted for to consistently capture Bayesian cue combination in continuous response data. Behavior Research Methods, 54, 1.
Bale A., Rambo R., Prior C., 2023. The SKMT Algorithm: A method for assessing and comparing underlying protein entanglement. PLoS Computational Biology, 19(11).
Glover, J.D., Sudderick, Z.R., Shih, B.B.-., Batho-Samblas, C., Charlton, L., Krause, A.L., & Headon, D.J., 2023. The developmental basis of fingerprint pattern formation and variation. Cell, 186, 5.
Krause A.L., Gaffney E.A., Jewell T.J., Klika V., Walker B.J., 2024. Turing Instabilities are Not Enough to Ensure Pattern Formation, Bulletin of Mathematical Biology, 86(2), 2.
Krause, A.L., Gaffney, E.A. & Walker, B.J., 2023. Concentration-Dependent Domain Evolution in Reaction–Diffusion Systems. Bull Math Biol, 85, 14.
Piette, B.M.A.G., & Lukács, Á., 2023. Near-Miss Symmetric Polyhedral Cages. Symmetry, 15, 717.
Piette, B.M.A.G., Kowalczyk, A., & Heddle, J.G., 2022 . Characterization of near-miss connectivity-invariant homogeneous convex polyhedral cages. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 478, 2260.
Prior, C., Panter, J., & Kusumaatmaja, H., 2022. A minimal model of elastic instabilities in biological filament bundles. Journal of the Royal Society Interface, 19, 194.
Vali, M., Mohammadi, M., Zarei, N., Samadi, M., Atapour-Abarghouei, A., Supakontanasan, W., Suwan, Y., Subramanian, P.S., Miller, N.R., Kafieh, R., & Fard, M.A., 2023. Differentiating Glaucomatous Optic Neuropathy from Non-Glaucomatous Optic Neuropathies Using Deep Learning Algorithms. American Journal of Ophthalmology.
Yaghoubi N., Masumi H., Fatehi M.H., Ashtari F., Kafieh R., 2023. Deep learning and classic machine learning models in the automatic diagnosis of multiple sclerosis using retinal vessels. Multimedia Tools and Applications. doi:10.1007/s11042-023-16812-w
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Mathematical & Computational Biology Academics
Dr Ulrik Beierholm, Department of Psychology
Areas of Expertise: Computational Neuroscience
Research Interests: How the nervous system deals with uncertainty, whether in perception, decision making or learning.
Dr Alessandro Borghi, Department of Engineering
Area of Expertise: Biomedical Engineering, Biomechanics
Research Interests
- Biomechanics
- Finite Element Analysis
- Biological Tissue Characterisation
- Biomaterials
- Medical Image Processing
- Surgical planning
- Medical Devices
- Machine Learning
Dr Matteo T. Degiacomi, Department of Physics
Areas of Expertise: Molecular Dynamics, Machine Learning, Computational Biophysics
Research Interests: The development of protein-protein docking methods, and techniques combining machine learning and molecular dynamics simulations to sample protein conformational spaces.
Dr Lian Gan, Department of Engineering
Areas of Expertise: Fluid Mechanics, Vortex Dynamics
Research Interests
- Pulsatile and periodic flows
- Vortex dynamics in cardiovascular system
- Flow structure interaction in cardiovascular system
- 4D flow MR
Dr Ostap Hryniv, Department of Mathematical Sciences
Areas of Expertise: Probability and Stochastic Processes
Research Interests
- Phase transitions
- Interacting particle systems
- Large deviations
- Stochastic modelling
Dr Rahele Kafieh, Department of Engineering
Areas of Expertise: Biomedical image and signal processing, Artificial Intelligence
Research Interests
- Medical Data Analysis
- Machine learning / Deep Learning
- Image Processing and Computer Vision
- Data Acquisition and Management
- Time-frequency methods
- Dictionary learning
- Data Quality Assessment
Professor Ashraf Khir, Department of Engineering
Areas of Expertise: Physiological Fluid Mechanics, Artificial Hearts/ Ventricular Assist Devices (VAD).
Research Interests
- Arterial waves
- Arterial stiffness – wave speed - PWV
- Non-invasive physiological hemodynamic ultrasound measurements
- Wave intensity analysis (WIA)
- Arterial wall mechanics
- Intra-Aortic Balloon Pump (IABP)
- Design of continuous and pulsatile flow blood pumps
- Mock circulatory loops
Dr Andrew Krause, Department of Mathematical Sciences
Areas of Expertise: Mathematical and Computational Modelling
Research Interests
- Pattern formation in developmental biology
- Reaction-diffusion systems
- Spatial population dynamics
- Nonlinear dynamical systems
Professor Bernard Piette, Department of Mathematical Sciences
Areas of Expertise: Mathematical Physics and Biophysics
Research Interests
- Mathematical modelling of biological systems
- Geometries of nano-bio-materials
- Electron-phonon interaction in nano-systems
Dr Christopher Prior, Department of Mathematical Sciences
Areas of Expertise: Magnetohydrodynamics, Topological Constraints
Research Interests
- Magnetohydrodynamics
- Solar physics
- Protein dynamics
- Biological filament elasticity and topological constraints
Professor Anne Taormina, Department of Mathematical Sciences
Areas of Expertise: Biological Applications of Mathematics
Research Interests
- Group theory and applications to mathematical biology
- String and conformal field theory
Dr Adam Townsend, Department of Mathematical Sciences
Areas of Expertise: Applied & Computational Mathematics, Mathematical Biology
Research Interests
- Development of mathematical and computational techniques to investigate complex fluids
- Non-Newtonian fluid mechanics
Dr Chris Willcocks, Department of Computer Science
Areas of Expertise: Computer Science
Research Interests: Deep generative modelling, such as diffusion probabilistic models and normalising flows, with applications in unpaired domain translation, anomaly detection, physics, biology and chemistry.