Mathematics

The prevalence of intrinsically disordered polypeptides (IDPs) and protein regions in structural biology has prompted the recent development of molecular dynamics (MD) force fields for the more realistic representations of such systems. Using experimental NMR backbone scalar 3J-coupling constants of the intrinsically disordered proteins alpha-synuclein and amyloid-beta in their native aqueous environment as a metric, we compare the performance of four recent MD force fields, namely AMBER ff14SB, CHARMM C36m, AMBER ff99SB-disp, and AMBER ff99SBnmr2, by partitioning the polypeptides into an overlapping series of heptapeptides for which a cumulative total of 276 us MD simulations are performed. The results show substantial differences between the different force fields at the individual residue level. Except for ff99SBnmr2, the force fields systematically underestimate the scalar 3J(HN,Ha) couplings, due to an underrepresentation of beta-conformations and an overrepresentation of either alpha- or PPII conformations. The study demonstrates that the incorporation of coil library information in modern molecular dynamics force fields, as shown here for ff99SBnmr2, provides substantially improved performance and more realistic sampling of local backbone phi,psi dihedral angles of IDPs as reflected in good accuracy of computed scalar 3J(HN,Ha)-couplings with < 0.5 Hz error. Such force fields will enable a better understanding how structural dynamics and thermodynamics influence IDP function. Although the methodology based on heptapeptides used here does not allow the assessment of potential intramolecular long-range interactions, its computational affordability permits well-converged simulations that can be easily parallelized. This should make the quantitative validation of intrinsic disorder observed in MD simulations of polypeptides with experimental scalar J-couplings widely applicable.

We discuss deformation theory of rational curves and Mori’s famous Bend and Break techniques as well as their applications to Geometric Manin’s Conjecture. The lecture series contain introductory components as well as problem sessions and they aim for graduate students and postdocs.

We discuss deformation theory of rational curves and Mori’s famous Bend and Break techniques as well as their applications to Geometric Manin’s Conjecture. The lecture series contain introductory components as well as problem sessions and they aim for graduate students and postdocs.

We discuss deformation theory of rational curves and Mori’s famous Bend and Break techniques as well as their applications to Geometric Manin’s Conjecture. The lecture series contain introductory components as well as problem sessions and they aim for graduate students and postdocs.

During reproduction, viruses manufacture products that diffuse within the host cell. Because a virus does not have exclusive access to its own gene products, coinfection of multiple viruses allows for strategies of cooperation and defection— cooperators produce large amounts of gene product while defectors produce less product but specialize in appropriating a larger share of the common pool. Experimental data shows that, under conditions where coinfection is common, bacteriophage $\Phi$6 becomes trapped in a Prisoner’s dilemma, with defectors spreading to fixation, causing lowered population fitness. However, these experiments did not allow for fluctuation in the density of the external viral population. Here, I’ll discuss a model formulated to see if environmental feedback can free $\Phi$6 from the Prisoner’s dilemma. I’ll also discuss the concept of the Effective Game, which incorporates the frequency and density of different viral types in the environment.