ß-hairpin forms by rolling up from C-terminal: topological guidance of early folding dynamics.

That protein folding is a non-random, guided process has been known even prior to Levinthal's paradox; yet, guided searches, attendant mechanisms and their relation to primary sequence remain obscure. Using extensive molecular dynamics simulations of a ß-hairpin with key sequence features similar to those of >13,000 ß-hairpins in full proteins, we provide significant insights on the entire pre-folding dynamics at single-residue levels and describe a single, highly coordinated roll-up folding mechanism, with clearly identifiable stages, directing structural progression toward native state. Additional simulations of single-site mutants illustrate the role of three key residues in facilitating this roll-up mechanism. Given the many ß-hairpins in full proteins with similar residue arrangements and since ß-hairpins are believed to act as nucleation sites in early-stage folding dynamics of full proteins, the topologically guided mechanism seen here may represent one of Nature's strategies for reducing early-stage folding complexity.

Crowding alters the folding kinetics of a ß-hairpin by modulating the stability of intermediates.

Crowded environments inside cells exert significant effects on protein structure, stability, and function, but their effects on (pre)folding dynamics and kinetics, especially at molecular levels, remain ill-understood. Here, we examine the latter for, as an initial candidate, a small de novo ß-hairpin using extensive all-atom molecular dynamics simulations for crowder volume fractions φ up to 40%. We find that crowding does not introduce new folding intermediates or misfolded structures, although, as expected, it promotes compact structures and reduces the accessible conformational space. Furthermore, while hydrophobic-collapse-mediated folding is slightly enhanced, the turn-directed zipper mechanism (dominant in crowder-free situations) increases many-fold, becoming even more dominant. Interestingly, φ influences the stability of the folding intermediates (FI(1) and FI(2)) in an apparently counterintuitive manner, which can be understood only by considering specific intrachain interactions and intermediate (and hierarchical) structural transitions. For φ values <20%, native-turn formation is enhanced, and FI(1), characterized by a hairpin structure but slightly mismatched hydrophobic contacts, increases in frequency, thus enhancing eventual folding. However, higher φ values impede native-turn formation, and FI(2), which lacks native turns, re-emerges and increasingly acts as a kinetic trap. The change in the stability of these intermediates with φ strongly correlates with the hierarchical folding stages and their kinetics. The results show that crowding assists intermediate structural changes more by impeding backward transitions than by promoting forward transitions and that a delicate competition between reduction in configuration space and introduction of kinetic traps along the folding route is key to understanding folding kinetics under crowded conditions.

Turn-directed folding dynamics of ß-hairpin-forming de novo decapeptide Chignolin.

Realistic mechanistic pictures of ß-hairpin formation, offering valuable insights into some of the key early events in protein folding, are accessible through short designed polypeptides as they allow atomic-level scrutiny through simulations. Here, we present a detailed picture of the dynamics and mechanism of ß-hairpin formation of Chignolin, a de novo decapeptide, using extensive, unbiased molecular dynamics simulations. The results provide clear evidence for turn-directed broken-zipper folding and reveal details of turn nucleation and cooperative progression of turn growth, hydrogen-bond formations, and eventual packing of the hydrophobic core. Further, we show that, rather than driving folding through hydrophobic collapse, cross-strand side-chain packing could in fact be rate-limiting as packing frustrations can delay formation of the native hydrophobic core prior to or during folding and even cause relatively long-living misfolded or partially folded states that may nucleate aggregative events in more complex situations. The results support the increasing evidence for turn-centric folding mechanisms for ß-hairpin formation suggested recently for GB1 and Peptide 1 based on experiments and simulations but also point to the need for similar examinations of polypeptides with larger numbers of cross-strand hydrophobic residues.

The role of structure in the nonlinear mechanics of cross-linked semiflexible polymer networks.

The microstructural basis of the characteristic nonlinear mechanics of biopolymer networks remains unclear. We present a 3D network model of realistic, cross-linked semiflexible fibers to study strain-stiffening and the effect of fiber volume-occupancy. We identify two structural parameters, namely, network connectivity and fiber entanglements, that fully govern the nonlinear response from small to large strains. The results also reveal distinct deformation mechanisms at different length scales and, in particular, the contributions of heterogeneity at short length scales.

Mechanical model of the tubulin dimer based on molecular dynamics simulations.

The basic unit in microtubules is alphabeta-tubulin, a heterodimer consisting of an alpha- and a beta-tubulin monomer. The mechanical characteristics of the dimer as well as of the individual monomers may be used to obtain new insight into the microtubule tensile properties. In the present work, we evaluate the elastic constants of each monomer and the interaction force between them by means of molecular dynamics simulations. Molecular models of alpha-, beta-, and alphabeta-tubulins were developed starting from the 1TUB.pdb structure from the RCSB database. Simulations were carried out in a solvated environment by using explicit water molecules. In order to measure the monomers' elastic constants, simulations were performed by mimicking experiments carried out with atomic force microscopy. A different approach was used to determine the interaction force between the alpha- and beta-monomers by using 16 different monomer configurations based on different intermonomer distances. The obtained results show an elastic constant value for alpha-tubulin of 3.8-3.9 Nm, while for the beta-tubulin, the elastic constant was measured to be 3.3-3.6 Nm. The maximum interaction force between the monomers was estimated to be 11.9 nN. A mechanical model of the tubulin dimer was then constructed and, using the results from MD simulations, Young's modulus was estimated to be 0.6 GPa. A fine agreement with Young's modulus values from literature (0.1-2.5 GPa) is found, thus validating this approach for obtaining molecular scale mechanical characteristics. In perspective, these outcomes will allow exchanging atomic level description with key mechanical features enabling microtubule characterization by continuum mechanics approach.

Response variability in balanced cortical networks.

We study the spike statistics of neurons in a network with dynamically balanced excitation and inhibition. Our model, intended to represent a generic cortical column, comprises randomly connected excitatory and inhibitory leaky integrate-and-fire neurons, driven by excitatory input from an external population. The high connectivity permits a mean field description in which synaptic currents can be treated as gaussian noise, the mean and autocorrelation function of which are calculated self-consistently from the firing statistics of single model neurons. Within this description, a wide range of Fano factors is possible. We find that the irregularity of spike trains is controlled mainly by the strength of the synapses relative to the difference between the firing threshold and the postfiring reset level of the membrane potential. For moderately strong synapses, we find spike statistics very similar to those observed in primary visual cortex.