Computational Systems Biology - Currently inactive areas

Due to our finite bandwidth, we are currently not pursuing these research interests at the moment. However, this does not mean that we are not interested in them. Indeed, we are more than happy to revisit these interests!

Evolutionary dynamics of bacteria

Diversification in the so called core genome of bacteria is governed by the interplay between point mutations that always increase diversity and horizontal gene transfer (HGT) which serves a dual role. If a strain receives HGT from a donor in the population, its genomic distance from its close relatives increases over the transferred region. At the same time, the same region becomes identical between the donor and the recipient. We are interested in understanding how these two factors shape the evolution of genes, genomes, and populations. We have developed theoretical and computational models to systematically study this interplay. We recently studied the evolution of E. coli strains with the help of the model and an in-house bioinformatic pipeline that allowed us to identify the core genome of E. coli and the regions on the core genome that were horizontally transferred.

Publications:

Recombination-driven genome evolution and stability of bacterial species (Genetics 2017), Dixit PD, Pang TY, and Maslov S. Featured on EurekAlert.org and Phys.org
Recombinant transfer in the basic genome of Escherichia coli (PNAS 2015), Dixit PD*, Pang TY*, Studier FW, and Maslov S. Recommended in F1000Prime

Maximum Path Entropy

Biophysical data is usually incomplete and error-prone; not everything of interest can be measured and measurements are usually noisy. As a result, computational biophysics research often requires developing methods to extract meaningful information from data. We keep an active interest in method development in biophysics, specifically, using approaches from statistical physics.

One center of mass of interest is inference of stochastic dynamical models from data. Markov processes are commonly used in modeling dynamics of biological systems. However, quite often, not enough data is available to prescribe all possible rates. For example, you may know the equilibrium distribution over states and a diffusion constant. Can we then guess an "optimal" Markov process from such incomplete data? We invoke the dynamical analog of the maximum entropy principle, the principle of maximum path entropy. We have developed a series of results on Maximum path entropy Markov processes. The applications have been numerous, including understanding structural dynamics of biomolecules, biochemical reaction networks, dimensionality reduction methods, and decision theory.

Publications:

The Maximum Caliber variational principle for dynamical processes (Annual reviews of Physical Chemistry), Ghosh K*, Dixit PD*, Agozzino L, and Dill K
Quantifying spatiotemporal variability and noise in absolute microbiota abundances using replicate sampling (Nature Methods, 2019), Ji B*, Sheth R*, Dixit PD*, Huang Y, Kaufman A, Wang H, and Vitkup D.
Introducing user-prescribed constraints in Markov chains for nonlinear dimensionality reduction (Neural Computation 2019). Dixit PD
Building Markov state models using optimal transport theory (Journal of Chemical Physics 2019), Dixit PD and Dill K
Entropy production rate as a criterion for inconsistency in decision theory (Journal of Statistical Mechanics 2019), Dixit PD
Communication: Introducing prescribed biases in out-of-equilibrium Markov models (Journal of Chemical Physics 2018), Dixit PD. Featured in the JCP editor's choice 2018 collection!
Caliber Corrected Markov Modeling (C2M2): Correcting Equilibrium Markov Models (Journal of Chemical Theory and Computation 2018), Dixit PD and Dill K
Perspective: Maximum caliber is a general variational principle for dynamical systems (Journal of Chemical Physics 2018), Dixit PD, et al.
Stationary properties of maximum-entropy random walks (Physical Review E 2015), Dixit PD
Inferring transition rates of networks from populations in continuous-time Markov processes (Journal of Chemical Theory and Computation 2015), Dixit PD, Jain A, Stock G, and Dill K
Inferring microscopic kinetic rates from stationary state distributions (Journal of Chemical Theory and Computation 2014), Dixit PD, and Dill K

Thermodynamics of small systems

The equilibrium Boltzmann exponential distributions (cannonical ensemble, grand canonical ensemble, etc.) is tremendously successful in describing macroscopically large systems in contact with a bath. Boltzmann distributions are derived from a key assumption: the contact (for example, energy or mass exchange) between the system and its surroundings is weak. This implies that inter-system interactions are much stronger than system-bath interactions. Weak contact is an excellent assumption for large systems because contact interactions are usually subextensive; they scale as ~N^2/3 with system size N. As a result, the equilibrium properties of a system depend on its own Hamiltonian and single parameter (for example, temperature, chemical potential, etc.) for each type of exchange between the system and its surrounding.

For small systems where N~10-1000, the contact interactions could be as strong as the internal interactions within the system. Notably, it is known that, for small systems, the Boltzmann equilibrium distributions have to be appended by a potential of mean force. The equilibrium properties of the system depend on its Hamiltonian and the microscopic details of its interaction with the surrounding.

Is it possible to generalize the canonical ensemble distribution for small systems while avoiding the detailed description of system-bath interactions? For not-so-large systems, the answer turns out to be yes! I have shown that if we forgo the requirement that the intensive parameters (temperature, chemical potential, etc.) are fixed at a particular value, the phase space behavior of small systems can be accurately captured in the super-statistical picture.

Publications

Mini-grand canonical ensemble: Chemical potential in the solvation shell (Journal of Chemical Physics 2017), Dixit PD, Bansal A, Chapman G, and Asthagiri D. Editor's pick!
Detecting temperature fluctuations at equilibrium (Physical Chemistry Chemical Physics 2015), Dixit PD
A maximum entropy thermodynamics of small systems (Journal of Chemical Physics 2013), Dixit PD

Statistical mechanics of solute solvent interactions

In my doctoral work, I studied interactions of small molecules with proteins and the aqueous solvent medium using tools from statistical physics and quantum chemistry. We developed a thermodynamic framework to understand why proteins prefer one molecule over the others and studied K⁺ selectivity of the KcsA K⁺ channel over the competing Na⁺. We also developed a fully analytical multi-scale theory that incorporated quantum chemical and molecular mechanical details and studied thermodynamics of Zn²⁺ binding and Zn²⁺ selectivity over competing Fe²⁺, Ni²⁺, Co²⁺, and Cd²⁺ to a zinc finger peptide.

Publications:

Separating the Role of Protein Restraints and Local Metal-Site Interaction Chemistry in the Thermodynamics of a Zinc Finger Protein (Biophysical Journal 2011), Dixit PD and Asthagiri D
Ion-water clusters, bulk medium effects, and ion hydration (Journal of Chemical Physics 2011), Merchant S, Dixit PD, Dean K, and Asthagiri D
An Elastic-Network-Based Local Molecular Field Analysis of Zinc Finger Proteins (Journal of Physical Chemistry B 2011), Dixit PD and Asthagiri D
The Role of Bulk Protein in Local Models of Ion-Binding to Proteins: Comparative Study of KcsA, Its Semisynthetic Analog with a Locked-in Binding Site, and Valinomycin (Biophysical Journal 2011), Dixit PD and Asthagiri D
Thermodynamics of ion selectivity in the KcsA K+ channel (Journal of General Physiology 2011), Dixit PD and Asthagiri D
Molecular packing and chemical association in liquid water simulated using ab initio hybrid Monte Carlo and different exchange-correlation functionals (Journal of Chemical Physics 2010), Weber V, Merchant S, Dixit PD, and Asthagiri D
Ion selectivity from local configurations of ligands in solutions and ion channels (Chemical Physics Letters 2010), Asthagiri D, Dixit PD, et al.
Ion Selectivity in the KcsA Potassium Channel from the Perspective of the Ion Binding Site (Biophysical Journal 2009), Dixit PD, Merchant S, and Asthagiri D

Miscellaneous Publications:

A simple measure of native‐state topology and chain connectivity predicts the folding rates of two‐state proteins with and without crosslinks (Proteins 2006), Dixit PD and Weikl T.

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