How native state topology affects the folding of Dihydrofolate Reductase and Interleukin-1beta

The overall structure of the transition state and intermediate ensembles experimentally observed for Dihydrofolate Reductase and Interleukin-1beta can be obtained utilizing simplified models which have almost no energetic frustration. The predictive power of these models suggest that, even for these very large proteins with completely different folding mechanisms and functions, real protein sequences are sufficiently well designed and much of the structural heterogeneity observed in the intermediates and the transition state ensembles is determined by topological effects.Comment: Proc. Natl. Acad. Sci. USA, in press (11 pages, 4 color PS figures) Higher resolution PS files can be found at http://www-physics.ucsd.edu/~cecilia/pub_list.htm

Diffusive Dynamics of the Reaction Coordinate for Protein Folding Funnels

The quantitative description of model protein folding kinetics using a diffusive collective reaction coordinate is examined. Direct folding kinetics, diffusional coefficients and free energy profiles are determined from Monte Carlo simulations of a 27-mer, 3 letter code lattice model, which corresponds roughly to a small helical protein. Analytic folding calculations, using simple diffusive rate theory, agree extremely well with the full simulation results. Folding in this system is best seen as a diffusive, funnel-like process.Comment: LaTeX 12 pages, figures include

Investigation of routes and funnels in protein folding by free energy functional methods

We use a free energy functional theory to elucidate general properties of heterogeneously ordering, fast folding proteins, and we test our conclusions with lattice simulations. We find that both structural and energetic heterogeneity can lower the free energy barrier to folding. Correlating stronger contact energies with entropically likely contacts of a given native structure lowers the barrier, and anticorrelating the energies has the reverse effect. Designing in relatively mild energetic heterogeneity can eliminate the barrier completely at the transition temperature. Sequences with native energies tuned to fold uniformly, as well as sequences tuned to fold by a single or a few routes, are rare. Sequences with weak native energetic heterogeneity are more common; their folding kinetics is more strongly determined by properties of the native structure. Sequences with different distributions of stability throughout the protein may still be good folders to the same structure. A measure of folding route narrowness is introduced which correlates with rate, and which can give information about the intrinsic biases in ordering due to native topology. This theoretical framework allows us to systematically investigate the coupled effects of energy and topology in protein folding, and to interpret recent experiments which investigate these effects.Comment: 12 pages, 1 figure, to appear in Proc. Natl. Acad. Sc

Mechanical control of the directional stepping dynamics of the kinesin motor

Among the multiple steps constituting the kinesin's mechanochemical cycle, one of the most interesting events is observed when kinesins move an 8-nm step from one microtubule (MT)-binding site to another. The stepping motion that occurs within a relatively short time scale (~100 microsec) is, however, beyond the resolution of current experiments, therefore a basic understanding to the real-time dynamics within the 8-nm step is still lacking. For instance, the rate of power stroke (or conformational change), that leads to the undocked-to-docked transition of neck-linker, is not known, and the existence of a substep during the 8-nm step still remains a controversial issue in the kinesin community. By using explicit structures of the kinesin dimer and the MT consisting of 13 protofilaments (PFs), we study the stepping dynamics with varying rates of power stroke (kp). We estimate that 1/kp <~ 20 microsec to avoid a substep in an averaged time trace. For a slow power stroke with 1/kp>20 microsec, the averaged time trace shows a substep that implies the existence of a transient intermediate, which is reminiscent of a recent single molecule experiment at high resolution. We identify the intermediate as a conformation in which the tethered head is trapped in the sideway binding site of the neighboring PF. We also find a partial unfolding (cracking) of the binding motifs occurring at the transition state ensemble along the pathways prior to binding between the kinesin and MT.Comment: 26 pages, 10 figure

Mean first passage time analysis reveals rate-limiting steps, parallel pathways and dead ends in a simple model of protein folding

We have analyzed dynamics on the complex free energy landscape of protein folding in the FOLD-X model, by calculating for each state of the system the mean first passage time to the folded state. The resulting kinetic map of the folding process shows that it proceeds in jumps between well-defined, local free energy minima. Closer analysis of the different local minima allows us to reveal secondary, parallel pathways as well as dead ends.Comment: 7 page

Dodging the crisis of folding proteins with knots

Proteins with nontrivial topology, containing knots and slipknots, have the ability to fold to their native states without any additional external forces invoked. A mechanism is suggested for folding of these proteins, such as YibK and YbeA, which involves an intermediate configuration with a slipknot. It elucidates the role of topological barriers and backtracking during the folding event. It also illustrates that native contacts are sufficient to guarantee folding in around 1-2% of the simulations, and how slipknot intermediates are needed to reduce the topological bottlenecks. As expected, simulations of proteins with similar structure but with knot removed fold much more efficiently, clearly demonstrating the origin of these topological barriers. Although these studies are based on a simple coarse-grained model, they are already able to extract some of the underlying principles governing folding in such complex topologies.Comment: 29 pages, 11 figures, 1 tabl

Non-Markovian Configurational Diffusion and Reaction Coordinates for Protein Folding

The non-Markovian nature of polymer motions is accounted for in folding kinetics, using frequency-dependent friction. Folding, like many other problems in the physics of disordered systems, involves barrier crossing on a correlated energy landscape. A variational transition state theory (VTST) that reduces to the usual Bryngelson-Wolynes Kramers approach when the non-Markovian aspects are neglected is used to obtain the rate, without making any assumptions regarding the size of the barrier, or the memory time of the friction. The transformation to collective variables dependent on the dynamics of the system allows the theory to address the controversial issue of what are ``good'' reaction coordinates for folding.Comment: 9 pages RevTeX, 3 eps-figures included, submitted to PR