Single-molecule fluorescence studies of intrinsically disordered proteins and liquid phase separation

Intrinsically disordered proteins (IDPs) are ubiquitous in proteomes and serve in a range of cellular functions including signaling, regulation, transport and enzyme function. IDP misfunction and aggregation are also associated with several diseases including neurodegenerative diseases and cancer. During the past decade, single-molecule methods have become popular for detailed biophysical and structural studies of these complex proteins. This work has included recent applications to cellular liquid-liquid phase separation (LLPS), relevant for functional dynamics of membraneless organelles such as the nucleolus and stress granules. In this concise review, we cover the conceptual motivations for development and application of single-molecule fluorescence methods for such IDP studies. We follow with a few key examples of systems and biophysical problems that have been addressed, and conclude with thoughts for emerging and future directions

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

Origins of Chevron Rollovers in Non-Two-State Protein Folding Kinetics

Chevron rollovers of some proteins imply that their logarithmic folding rates are nonlinear in native stability. This is predicted by lattice and continuum G\=o models to arise from diminished accessibilities of the ground state from transiently populated compact conformations under strongly native conditions. Despite these models' native-centric interactions, the slowdown is due partly to kinetic trapping caused by some of the folding intermediates' nonnative topologies. Notably, simple two-state folding kinetics of small single-domain proteins are not reproduced by common G\=o-like schemes.Comment: 10 pages, 4 Postscript figures (will appear on PRL

Folding, Design and Determination of Interaction Potentials Using Off-Lattice Dynamics of Model Heteropolymers

We present the results of a self-consistent, unified molecular dynamics study of simple model heteropolymers in the continuum with emphasis on folding, sequence design and the determination of the interaction parameters of the effective potential between the amino acids from the knowledge of the native states of the designed sequences.Comment: 8 pages, 3 Postscript figures, uses RevTeX. Submitted to Physical Review Letter

On the statistical mechanics of prion diseases

We simulate a two-dimensional, lattice based, protein-level statistical mechanical model for prion diseases (e.g., Mad Cow disease) with concommitant prion protein misfolding and aggregation. Our simulations lead us to the hypothesis that the observed broad incubation time distribution in epidemiological data reflect fluctuation dominated growth seeded by a few nanometer scale aggregates, while much narrower incubation time distributions for innoculated lab animals arise from statistical self averaging. We model `species barriers' to prion infection and assess a related treatment protocol.Comment: 5 Pages, 3 eps figures (submitted to Physical Review Letters

Statistical mechanics of secondary structures formed by random RNA sequences

The formation of secondary structures by a random RNA sequence is studied as a model system for the sequence-structure problem omnipresent in biopolymers. Several toy energy models are introduced to allow detailed analytical and numerical studies. First, a two-replica calculation is performed. By mapping the two-replica problem to the denaturation of a single homogeneous RNA in 6-dimensional embedding space, we show that sequence disorder is perturbatively irrelevant, i.e., an RNA molecule with weak sequence disorder is in a molten phase where many secondary structures with comparable total energy coexist. A numerical study of various models at high temperature reproduces behaviors characteristic of the molten phase. On the other hand, a scaling argument based on the extremal statistics of rare regions can be constructed to show that the low temperature phase is unstable to sequence disorder. We performed a detailed numerical study of the low temperature phase using the droplet theory as a guide, and characterized the statistics of large-scale, low-energy excitations of the secondary structures from the ground state structure. We find the excitation energy to grow very slowly (i.e., logarithmically) with the length scale of the excitation, suggesting the existence of a marginal glass phase. The transition between the low temperature glass phase and the high temperature molten phase is also characterized numerically. It is revealed by a change in the coefficient of the logarithmic excitation energy, from being disorder dominated to entropy dominated.Comment: 24 pages, 16 figure

Steric constraints in model proteins

A simple lattice model for proteins that allows for distinct sizes of the amino acids is presented. The model is found to lead to a significant number of conformations that are the unique ground state of one or more sequences or encodable. Furthermore, several of the encodable structures are highly designable and are the non-degenerate ground state of several sequences. Even though the native state conformations are typically compact, not all compact conformations are encodable. The incorporation of the hydrophobic and polar nature of amino acids further enhances the attractive features of the model.Comment: RevTex, 5 pages, 3 postscript figure

Role of Secondary Motifs in Fast Folding Polymers: A Dynamical Variational Principle

A fascinating and open question challenging biochemistry, physics and even geometry is the presence of highly regular motifs such as alpha-helices in the folded state of biopolymers and proteins. Stimulating explanations ranging from chemical propensity to simple geometrical reasoning have been invoked to rationalize the existence of such secondary structures. We formulate a dynamical variational principle for selection in conformation space based on the requirement that the backbone of the native state of biologically viable polymers be rapidly accessible from the denatured state. The variational principle is shown to result in the emergence of helical order in compact structures.Comment: 4 pages, RevTex, 4 eps figure

Protein structures and optimal folding emerging from a geometrical variational principle

Novel numerical techniques, validated by an analysis of barnase and chymotrypsin inhibitor, are used to elucidate the paramount role played by the geometry of the protein backbone in steering the folding to the correct native state. It is found that, irrespective of the sequence, the native state of a protein has exceedingly large number of conformations with a given amount of structural overlap compared to other compact artificial backbones; moreover the conformational entropies of unrelated proteins of the same length are nearly equal at any given stage of folding. These results are suggestive of an extremality principle underlying protein evolution, which, in turn, is shown to be associated with the emergence of secondary structures.Comment: Revtex, 5 pages, 5 postscript figure