Biophysical Sciences Institute

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.

Mathematical & Computational Biology Academics

VisualPDE.com simulation “Turing on Turing”

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.

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.
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

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.

Image of transmembrane protein interactions

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.

A structure referred to as a TRAP-cage, made out of 24 nearly regular hendecagons of TRAP (trp RNA-binding attenuation protein)

Highlight Publications

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.

VisualPDE

A snapshot of a Turing Pattern simulation on an earlier version of the Biophysical Sciences Institute logo.
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

A snapshot of a Turing Pattern simulation on an earlier version of the Biophysical Sciences Institute logo.

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).

A group of people at the Computational Biology Special Interest Group launch in 2018

Find out more about Our Research

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

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.