Jeremy Schofield

Professor -- Theoretical Chemical Physics

Lash Miller Chemical Laboratories
80 St. George St.
University of Toronto
Toronto, Ontario, Canada   M5S 1A1

Phone: (416)-978-4376
Fax: (416)-978-8775
Office: Lash Miller, Room 239

  • A.B. (Amherst College,1988)
  • Ph.D. (M.I.T.,1993)
  • Postdoctoral Fellow (University of Chicago, Northwestern University,1993-1997)
  • Research Interests:

    My research interests in theoretical physical chemistry are primarily concerned with the structure, phases and dynamics of complex liquid and biological systems. Although the static and transport properties of simple liquid systems are fairly well understood, much less is known about complex liquid systems of great importance in biochemistry and materials chemistry. The unifying theme of our research is the judicious application of analytic theory, computer simulation and computational chemistry to elucidate the molecular foundations of the structure and macroscopic behavior of complex chemical systems. In addition to previous work on the statistical mechanics of time-dependent properties of equilibrium and steady-state fluids, there are currently several projects of particular interest.


    The first project focuses mainly on the role of charge and aquation state in the determination of macromolecular structure in biological systems. There has been very little theoretical work on how the conformation of an isolated macromolecule depends on the number of excess charges bound to it, in spite of the fact that many protein and polypeptide molecules contain ions and are present in a variety of charge states at biological pH conditions. We are working on new molecular dynamics and Monte-Carlo simulation methods which are designed to reproduce the correct statics and dynamics of charged polypeptides and other molecules in which proton transfer is important. The goal of the work is to probe how the transitions between folded and extended conformers depend on temperature, aqueous solvation and charge state of the molecule.

    Another project being pursues concerns the folding dynamics of simple models of protein systems. In protein chains, the competition between energy (or enthalpy) and entropy (energy density of conformational states) leads to transitions between denatured, non-native configurations and compact folded structures that play a specific function in biological systems. These competing interactions can also give rise to a wealth of other structural transitions among meta-stable states. This project is concerned with understanding the factors that influence the rate of conformational transitions and how the temperature behavior of the rates and the folding profile relate to features of the free energy surface, such as funnels.

    The use of a discontinuous model of residue interactions has characteristics that may be exploited to probe the connection between the free energy surface and the folding dynamics. The interactions, tailored to produce secondary structural elements observed in real proteins such as alpha-helices and beta-sheets, may be used to unambiguously define conformations of the protein and permit temperature-independent entropic differences between states to be computed thereby allowing the free energies of all states to be computed at any temperature. Furthermore, if monomers in the protein-like chain experience rapid collisions with an effective solvent that leads to rapid decay of bead velocity autocorrelation functions, monomer dynamics may be described by the Smoluchowski equation. From the Smoluchowski equation, projection operator methods can be used to define expressions for transition rates between configurations in a Markov limit where bead correlations are short-lived on the time scale of transitions between states. Under conditions in which bead correlations are short-lived on the time scale of transitions between states, rate constants can be calculated from spectral analysis of a projected Smoluchowski evolution operator in terms of temperature-independent, one-dimensional integrals of probability densities for bonding distances that can be constructed using analytical fits to estimated cumulative distribution functions. The cumulative distribution functions and relative entropies for bonding can be efficiently computed using parallel tempering algorithms adapted to preferentially sample connected states that differ by a single bond to minimize statistical uncertainties of the computed rates. The forward and reverse rate constants for transitions between states can be expressed as a temperature-dependent linear combination of two effective rates that are temperature independent.

    Although the resulting system of equations is equivalent to Markov models of proteins with continuous interaction potentials, here the Markov model is actually constructed from a physical system. Furthermore, unlike in standard systems, the discontinuous interaction potentials enable configurations to be identified without resorting to carrying out simulations and allow the computation of rate constants at any temperature. The resulting linear system can be readily solved to characterize the relaxation profile of an ensemble of unfolded configurations to the folded state as a function of temperature. The multi-exponential nature of the profile can be characterized by looking at the relative weights of eigenvectors of the linear system to distinguish between stretched and compressed-exponential kinetics.

    The Schofield group is working towards developing discontinuous potential models of protein-like chains by treating some of the system, such as alpha-helices, as rigid objects that are linked together by flexible regions of the system. The interactions of residues and fragments can be constructed using discretizations of continuous potential interactions, while the dynamics of the rigid fragments can simulated using rigid body discontinuous molecular dynamics. By eliminating small-scale motions of rigid components of the biomolecule, one can focus on important motions of domains of the protein system at long times, such as hinge-bending, partial-refolding or shear domain motion.

    Specific questions that will be addressed in this project include: How does the overall complexity of the connectivity map of available states influence the multi-exponential relaxation to the equilibrium population? What is the range of validity of the expressions for the rate constants? When are non-Markovian effects important? Do what extent are motions in the folding process of proteins diffusive?

    The Group
    * Group composition
    * Our beowulf cluster racaille: Photos and description
    * Positions available in the Schofield group


    * Polypeptide Structure
    * Proton transfer dynamics
    * Nonadiabatic MD
    * Stochastic models of complex systems
    * Dynamics in glassy systems
    * Rigid body dynamics

    Class Notes

    * Chem1485: Dynamics in Liquids
    * Chem1464: Foundations of Molecular Simulation
    * CHM427 and CHM1480: Statistical Mechanics