Lecture 12: Andrei Kucharavy (Rong Li Lab)

Cellular Adaptation Under Stress

Diagram for a cell population adaptation.

Whether the products of human activity, or naturally occurring social, economic or biological, complex systems share the same properties. Composed of a large number of individual components, their components do not have a straightforward relation to their properties and often interact one with another in unexpected ways. Because of that, different instances of the same complex systems are built from slightly different components. Such differences give rise to heterogeneity within a population, which in turn raises significant difficulties for their study. From the biological perspective, such events have been formalized as Fisher’s geometric model, that has been formalized in the thirties of the last century and has been independently re-discovered in unrelated domains as algorithms for ergodic explorations of multi-dimensional spaces for an optimal value function point. 

Andrei Kucharavy and Dr. Rong Li from Johns Hopkins Medicine propose an enhancement of Fisher’s geometric model, allowing to explain a range of previously unexplained observations in biology. Mathematical analysis of their enhancement provides a set of rules applicable to the optimization of a large class of ergodic exploration algorithms.

Related Journal Articles:
1. H. A. Orr, The genetic theory of adaptation: a brief history. Nat. Rev. Genet. 6, 119–127 (2005) 
2. H. A. Orr, R. L. Unckless, The Population Genetics of Evolutionary Rescue. PLoS Genet. 10, e1004551 (2014). 
3. P. S. Pennings, Standing genetic variation and the evolution of drug resistance in HIV. PLoS Comput. Biol. 8 (2012).
_________________________________________________________________________________

Andrei Kucharavy received his Engineer’s Degree in Physics, Mathematics, Programming and Bioinformatics from Ecole Polytechnique, France in 2011. After graduation, he did masters in computational biology at Ecole Polytechnique Fédérale de Lausanne, Switzerland. Currently, Andrei is a Ph.D. student under the joint direction of Dr. Rong Li from Johns Hopkins and Dr. Gilles Fischer, exploring molecular mechanisms of aneuploidy-enabled stress adaptation and drug resistance it enables in yeast and cancer. He works on developing computational methods enabling systematic analysis of molecular mechanisms underlying complex traits. The interface of biological network analysis and evolution theory is his particular interest.

Lecture 11: Dr. Ana Damjanović

Simulating with the right pH.

Schematic representation of a constant-pH simulation
with the two-dimensional EDS-HREM method.

Solution pH is one of the most important environmental factors that affects the structure and dynamics of proteins. Almost all biologically relevant properties of proteins are affected by pH: stability, folding and assembly, interactions with ligands and other biological molecules, solubility, aggregation properties, and enzymatic activity. A change in pH may induce a change in the protonation state of ionizable groups, which in turn can cause structural changes in proteins. Structural changes triggered by protonation/deprotonation can be exploited for function, such as in the case of ATP synthase, bacteriorhodopsin, cytochrome c oxidase, or the photoactive yellow protein.

Superimposed 1 ns trajectories of snake cardiotoxin
from the (A) 2D and (B) 1D constant-pH
EDS-HREM simulations at pH = 2.

Ana Damjanovic from Johns Hopkins Biophysics and her colleagues from NIH present a new method for enhanced sampling for constant-pH simulations in explicit water based on a two-dimensional (2D) replica exchange scheme. The new method is a significant extension of a previously developed constant-pH simulation method, which is based on enveloping distribution sampling (EDS) coupled with a one-dimensional (1D) Hamiltonian exchange method (HREM). EDS constructs a hybrid Hamiltonian from multiple discrete end state Hamiltonians that, in this case, represent different protonation states of the system. The ruggedness and heights of the hybrid Hamiltonian’s energy barriers can be tuned by the smoothness parameter. Within the context of the 1D EDS-HREM method, exchanges are performed between replicas with different smoothness parameters, allowing frequent protonation-state transitions and sampling of conformations that are favored by the end-state Hamiltonians. In this work, the 1D method is extended to 2D with an additional dimension, external pH. Within the context of the 2D method (2D EDS-HREM), exchanges are performed on a lattice of Hamiltonians with different pH conditions and smoothness parameters. The research team demonstrates that both the 1D and 2D methods exactly reproduce the thermodynamic properties of the semi-grand canonical (SGC) ensemble of a system at a given pH. They have tested the new 2D method on aspartic acid, glutamic acid, lysine, a four-residue peptide (sequence KAAE), and snake cardiotoxin. In all cases, the 2D method converges faster and without loss of precision; the only limitation is a loss of flexibility in how CPU time is employed. The results for snake cardiotoxin demonstrate that the 2D method enhances protonation-state transitions, samples a wider conformational space with the same amount of computational resources, and converges significantly faster overall than the original 1D method.

_________________________________________________________________________________

Ana Damjanovic received her B.Sc. in Physics from Belgrade University (1995), and a Ph.D. in Physics from University of Illinois at Urbana-Champaign (2001). For her Ph.D. she worked with Prof. Klaus Schulten on QM description of energy transfer in light-harvesting complexes in various photosynthetic organisms. She did postdocs at UC Berkeley and Johns Hopkins University. At JHU she worked on understanding hydration and conformational changes in proteins through molecular dynamics simulations. She is presently an Associate Research Scientist and Lecturer in the Dept. of Biophysics at Johns Hopkins University. Her current research interests are in the area of development and applications of molecular dynamics simulations at constant pH.