Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials

Recent progress in understanding the topological properties of condensed matter has led to the discovery of time-reversal invariant topological insulators. Because of limitations imposed by nature, topologically non-trivial electronic order seems to be uncommon except in small-band-gap semiconductors with strong spin-orbit interactions. In this Article we show that artificial electromagnetic structures, known as metamaterials, provide an attractive platform for designing photonic analogues of topological insulators. We demonstrate that a judicious choice of the metamaterial parameters can create photonic phases that support a pair of helical edge states, and that these edge states enable one-way photonic transport that is robust against disorder.Comment: 13 pages, 3 figure

Biophysical models of evolution

The recent emergence of quantitative high-throughput experimental technology and new biophysical knowledge may finally enable significant empirical and quantitative understanding of adaptive evolution, which has been elusive for almost a century. The modern aim is to unite classical population genetics with biophysical molecular models, and to connect physical properties of biological molecules such as DNA, RNA and proteins with evolutionary parameters. In this vein, I have studied such population models theoretically, and applied one such model to yeast evolution. In Chapters 2 and 3, I will discuss “universality” in population genetics, in particular the universal applicability of a formula for the steady state distribution of phenotypes in a population evolving in the “monomorphic regime”, which describes most organisms. I show that this formula applies far outside the “weak selection” context it was originally developed in, and that it is a universal feature of evolution in this regime. Such universal features will be important components of any grand theory of adaptive evolution, and are essential for studies of real populations where the microscopic population dynamics are generally unknown. I then apply this model to a particular molecular system in yeast, Transcription Factor binding sites, which are short DNA sequences which play an important role in iigene regulation. Using the functional relationship between evolutionary fitness and the phenotypic steady state distribution, I infer the form of the selective pressure the sites experience, and find it is consistent with a simple thermodynamic model of two-state TF-DNA binding. I also show that the selection pressure a site experiences is decoupled from the selection pressure on the gene it regulates. This suggests that binding sites for a given TF evolve over a universal fitness landscape derived from simple physical interactions.Ph. D.Includes bibliographical referencesby Allan M. Haldan

Limits to detecting epistasis in the fitness landscape of HIV.

The rapid evolution of HIV is constrained by interactions between mutations which affect viral fitness. In this work, we explore the role of epistasis in determining the mutational fitness landscape of HIV for multiple drug target proteins, including Protease, Reverse Transcriptase, and Integrase. Epistatic interactions between residues modulate the mutation patterns involved in drug resistance, with unambiguous signatures of epistasis best seen in the comparison of the Potts model predicted and experimental HIV sequence "prevalences" expressed as higher-order marginals (beyond triplets) of the sequence probability distribution. In contrast, experimental measures of fitness such as viral replicative capacities generally probe fitness effects of point mutations in a single background, providing weak evidence for epistasis in viral systems. The detectable effects of epistasis are obscured by higher evolutionary conservation at sites. While double mutant cycles in principle, provide one of the best ways to probe epistatic interactions experimentally without reference to a particular background, we show that the analysis is complicated by the small dynamic range of measurements. Overall, we show that global pairwise interaction Potts models are necessary for predicting the mutational landscape of viral proteins

Evolutionary divergence in the conformational landscapes of tyrosine vs serine/threonine kinases

Inactive conformations of protein kinase catalytic domains where the DFG motif has a “DFG-out” orientation and the activation loop is folded present a druggable binding pocket that is targeted by FDA-approved ‘type-II inhibitors’ in the treatment of cancers. Tyrosine kinases (TKs) typically show strong binding affinity with a wide spectrum of type-II inhibitors while serine/threonine kinases (STKs) usually bind more weakly which we suggest here is due to differences in the folded to extended conformational equilibrium of the activation loop between TKs vs. STKs. To investigate this, we use sequence covariation analysis with a Potts Hamiltonian statistical energy model to guide absolute binding free-energy molecular dynamics simulations of 74 protein-ligand complexes. Using the calculated binding free energies together with experimental values, we estimated free-energy costs for the large-scale (~17–20 Å) conformational change of the activation loop by an indirect approach, circumventing the very challenging problem of simulating the conformational change directly. We also used the Potts statistical potential to thread large sequence ensembles over active and inactive kinase states. The structure-based and sequence-based analyses are consistent; together they suggest TKs evolved to have free-energy penalties for the classical ‘folded activation loop’ DFG-out conformation relative to the active conformation, that is, on average, 4–6 kcal/mol smaller than the corresponding values for STKs. Potts statistical energy analysis suggests a molecular basis for this observation, wherein the activation loops of TKs are more weakly ‘anchored’ against the catalytic loop motif in the active conformation and form more stable substrate-mimicking interactions in the inactive conformation. These results provide insights into the molecular basis for the divergent functional properties of TKs and STKs, and have pharmacological implications for the target selectivity of type-II inhibitors

Contingency and Entrenchment of Drug-Resistance Mutations in HIV Viral Proteins

The ability of HIV-1 to rapidly mutate leads to antiretroviral therapy (ART) failure among infected patients. Drug-resistance mutations (DRMs), which cause a fitness penalty to intrinsic viral fitness, are compensated by accessory mutations with favorable epistatic interactions which cause an evolutionary trapping effect, but the kinetics of this overall process has not been well characterized. Here, using a Potts Hamiltonian model describing epistasis combined with kinetic Monte Carlo simulations of evolutionary trajectories, we explore how epistasis modulates the evolutionary dynamics of HIV DRMs. We show how the occurrence of a drug-resistance mutation is contingent on favorable epistatic interactions with many other residues of the sequence background and that subsequent mutations entrench DRMs. We measure the time-autocorrelation of fluctuations in the likelihood of DRMs due to epistatic coupling with the sequence background, which reveals the presence of two evolutionary processes controlling DRM kinetics with two distinct time scales. Further analysis of waiting times for the evolutionary trapping effect to reverse reveals that the sequences which entrench (trap) a DRM are responsible for the slower time scale. We also quantify the overall strength of epistatic effects on the evolutionary kinetics for different mutations and show these are much larger for DRM positions than polymorphic positions, and we also show that trapping of a DRM is often caused by the collective effect of many accessory mutations, rather than a few strongly coupled ones, suggesting the importance of multiresidue sequence variations in HIV evolution. The analysis presented here provides a framework to explore the kinetic pathways through which viral proteins like HIV evolve under drug-selection pressure

Contingency and Entrenchment of Drug-Resistance Mutations in HIV Viral Proteins

The ability of HIV-1 to rapidly mutate leads to antiretroviral therapy (ART) failure among infected patients. Drug-resistance mutations (DRMs), which cause a fitness penalty to intrinsic viral fitness, are compensated by accessory mutations with favorable epistatic interactions which cause an evolutionary trapping effect, but the kinetics of this overall process has not been well characterized. Here, using a Potts Hamiltonian model describing epistasis combined with kinetic Monte Carlo simulations of evolutionary trajectories, we explore how epistasis modulates the evolutionary dynamics of HIV DRMs. We show how the occurrence of a drug-resistance mutation is contingent on favorable epistatic interactions with many other residues of the sequence background and that subsequent mutations entrench DRMs. We measure the time-autocorrelation of fluctuations in the likelihood of DRMs due to epistatic coupling with the sequence background, which reveals the presence of two evolutionary processes controlling DRM kinetics with two distinct time scales. Further analysis of waiting times for the evolutionary trapping effect to reverse reveals that the sequences which entrench (trap) a DRM are responsible for the slower time scale. We also quantify the overall strength of epistatic effects on the evolutionary kinetics for different mutations and show these are much larger for DRM positions than polymorphic positions, and we also show that trapping of a DRM is often caused by the collective effect of many accessory mutations, rather than a few strongly coupled ones, suggesting the importance of multiresidue sequence variations in HIV evolution. The analysis presented here provides a framework to explore the kinetic pathways through which viral proteins like HIV evolve under drug-selection pressure