PhD Studentship: Multimodal Sampling with Ballistic-style Markov Processes: From Atomistic Water to Rapid Simulation of Polymer Folding

Supervisors: Dr Michael Faulkner, Engineering, Prof. David Quigley, Physics
Project Partner: Prof. Gareth Roberts, Statistics

Many major problems in predictive modelling involve multimodal energy landscapes. For example, proteins in a biological cell stabilise in a variety of folded configurations – or modes. Cells function correctly in the low-energy mode, but rare misfolds at higher energy lead to cell malfunction.

Capturing the misfolds is, however, a challenge because simulations jam in certain modes on long timescales. Biasing simulations away from visited configurations should resolve this problem, but convergence is poor due to numerical instabilities of state-of-the-art simulations.

This project leverages the fast yet stable dynamics of ballistic-style Markov processes to produce rapid multimodal sampling of polymer models.

Background

Many of the most challenging problems in predictive modelling involve multimodal energy landscapes. Such systems can get trapped in local energy minima on long simulation timescales, preventing efficient exploration of the state space. Polymer models (of systems such as proteins) create particularly significant challenges due to their long structures. Each mode corresponds to a different polymer folding, and the challenge is to unfold and refold the polymer on short timescales to sample all physical configurations.

Many techniques have attempted to tackle the general problem, with equi-energy sampling offering particular promise. This biases the system away from visited configurations – and samples are re-weighted once the process has converged. The technique essentially amounts, however, to promoting the temperature to an auxiliary variable – leading to poor convergence when integrated into traditional gradient-based simulation methods (e.g., molecular dynamics) as the optimal time step changes with temperature. Metropolis Monte Carlo (MC) is numerically stable and so circumvents the time-step issue, but its diffusive dynamics mix very slowly.

Recent advances in comp-stats and stat-phys have led to state-of-the-art MC sampling algorithms that drive the system through its state space with ballistic-style dynamics. These piecewise deterministic Markov processes (PDMPs) are the optimal candidate for tackling these issues as they combine full numerical stability with efficient gradient-based dynamics – implying the capacity to surpass the state-of-the-art. This project will develop equi-energy sampling within PDMPs. We will integrate the method into existing PDMPs for atomistic water then move on to polymer models. This will bias polymers away from visited foldings. Future integration of machine-learn potentials will accelerate atomistic sampling of physical foldings of polymers in solution and polymer melts. For references see hetsys@warwick.ac.uk 

About HetSys

The EPSRC Centre for Doctoral Training in Modelling of Heterogeneous Systems (HetSys), based at the University of Warwick, is an exceptional environment for students from physical sciences, life sciences, mathematics, statistics, and engineering. HetSys specializes in applying advanced mathematical methods to tackle complex, real-world problems across a variety of research areas.

Our research themes span exciting topics such as nanoscale devices, innovative catalysts, superalloys, smart fluids, space plasmas, and more. HetSys provides:

• A vibrant, interdisciplinary student community.
• Flexible, tailored training opportunities.
• A collaborative environment that fosters creativity and growth.

Interested?

Join HetSys and help shape the future of sustainable technology through groundbreaking research. For more information about this project and how to apply, visit: https://warwick.ac.uk/fac/sci/hetsys/themes/projects2025.

Funding Details

Additional Funding Information

Awards for both UK residents and international applicants pay a stipend to cover maintenance as well as paying the university fees & a research training support. The stipend is at the standard UKRI rate.

For more details visit: https://warwick.ac.uk/fac/sci/hetsys/apply/funding/ 

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