Chromosome and protein folding: In search for unified principles

Structural biology has traditionally focused on the structures of proteins, short nucleic acids, small molecules, and their complexes. However, it is now widely recognized that the 3D organization of chromosomes should also be included in this list, despite significant differences in scale and complexity of organization. Here we highlight some notable similarities between the folding processes that shape proteins and chromosomes. Both biomolecules are folded by two types of processes: the affinity-mediated interactions, and by active (ATP-dependent) processes. Both chromosome and proteins in vivo can have partially unstructured and non-equilibrium ensembles with yet to be understood functional roles. By analyzing these biological systems in parallel, we can uncover universal principles of biomolecular organization that transcend specific biopolymers.     

Fast tree search for a triangular lattice model of protein folding

Using a triangular lattice model to study the designability of protein folding, we overcame the parity problem of previous cubic lattice model and enumerated all the sequences and compact structures on a simple two-dimensional triangular lattice model of size 4 5 6 5 4. We used two types of amino acids, hydrophobic and polar, to make up the sequences, and achieved 223W212 different sequences excluding the reverse symmetry sequences. The total string number of distinct compact structures was 219,093, excluding reflection symmetry in the self-avoiding path of length 24 triangular lattice model. Based on this model, we applied a fast search algorithm by constructing a cluster tree. The algorithm decreased the computation by computing the objective energy of non-leaf nodes. The parallel experiments proved that the fast tree search algorithm yielded an exponential speed-up in the model of size 4 5 6 5 4. Designability analysis was performed to understand the search result.     

Conformational propagation with prion-like characteristics in a simple model of protein folding

Protein refolding/misfolding to an alternative form plays an aetiologic role in many diseases in humans, including Alzheimer's disease, the systemic amyloidoses, and the prion diseases. Here we have discovered that such refolding can occur readily for a simple lattice model of proteins in a propagatable manner without designing for any particular alternative native state. The model uses a simple contact energy function for interactions between residues and does not consider the peculiarities of polypeptide geometry. In this model, under conditions where the normal (N) native state is marginally stable or unstable, two chains refold from the N native state to an alternative multimeric energetic minimum comprising a single refolded conformation that can then propagate itself to other protein chains. The only requirement for efficient propagation is that a two-faced mode of packing must be in the ground state as a dimer (a higher-energy state for this packing leads to less efficient propagation). For random sequences, these ground-state dimeric configurations tend to have more beta-sheet-like extended structure than almost any other sort of dimeric ground-state assembly. This implies that propagating states (such as for prions) are beta-sheet rich because the only likely propagating forms are beta-sheet rich. We examine the details of our simulations to see to what extent the observed properties of prion propagation can be predicted by a simple protein folding model. The formation of the alternative state in the present model shows several distinct features of amyloidogenesis and of prion propagation. For example, an analog of the phenomenon of conformationally distinct strains in prions is observed. We find a parallel between 'glassy' behavior in liquids and the formation of a propagatable state in proteins. This is the first report of simulation of conformational propagation using any heteropolymer model. The results imply that some (but not most) small protein sequences must maintain a sequence signal that resists refolding to propagatable alternative native states and that the ability to form such states is not limited to polypeptides (or reliant on regular hydrogen bonding per se) but can occur for other protein-like heteropolymers.     

Structural search and retrieval using a tableau representation of protein folding patterns

Comparison and classification of folding patterns from a database of protein structures is crucial to understand the principles of protein architecture, evolution and function. Current search methods for proteins with similar folding patterns are slow and computationally intensive. The sharp growth in the number of known protein structures poses severe challenges for methods of structural comparison. There is a need for methods that can search the database of structures accurately and rapidly. We provide several methods to search for similar folding patterns using a concise tableau representation of proteins that encodes the relative geometry of secondary structural elements. Our first approach allows the extraction of identical and very closely-related protein folding patterns in constant-time (per hit). Next, we address the hard computational problem of extraction of maximally-similar subtableaux, when comparing two tableaux. We solve the problem using Quadratic and Linear integer programming formulations and demonstrate their power to identify subtle structural similarities, especially when protein structures significantly diverge. Finally, we describe a rapid and accurate method for comparing a query structure against a database of protein domains, TableauSearch. TableauSearch is rapid enough to search the entire structural database in seconds on a standard desktop computer. Our analysis of TableauSearch on many queries shows that the method is very accurate in identifying similarities of folding patterns, even between distantly related proteins. AVAILABILITY: A web server implementing the TableauSearch is available from http://hollywood.bx.psu.edu/TabSearch.     

Malleability of protein folding pathways: a simple reason for complex behaviour

Although the structures of native proteins are generally unique, the pathways by which they form are often free to vary. Some proteins fold by a multitude of different pathways, whereas others seem restricted to only one choice. An explanation for this variation in folding behaviour has recently emerged from studies of transition state changes: the number of accessible pathways is linked to the number of nucleation motifs contained within the native topology. We refer to these nucleation motifs as 'foldons', as they approach the size of an independent cooperative unit. Thus, with respect to pathway malleability and the composition of the folding funnel, proteins can be seen as modular assemblies of competing foldons. For the split beta-alpha-beta fold, these foldons are two-strand-helix motifs coupled by spatial overlap.     

Apparent Debye-Huckel electrostatic effects in the folding of a simple, single domain protein

We have monitored the effects of salts and denaturants on the folding of the simple, two-state protein FynSH3. As predicted by Debye-Huckel limiting law, both the stability and (log) folding rate of FynSH3 increase nearly perfectly linearly (r(2)> 0.99) with the square root of ionic strength upon increasing concentrations of the relatively nonchaotropic salt sodium chloride. The stability of FynSH3 is also linear in square root ionic strength when the relatively nonchaotropic salts sodium bromide, potassium bromide, and potassium chloride are employed. Comparison of the kinetic and equilibrium effects of sodium chloride suggests that the electrostatic interactions formed in the folding transition state are approximately 50% as destabilizing as those formed in the native state, presumably reflecting the more compact nature of the latter. In contrast, the relationship between concentration and folding kinetics is more complex when the highly chaotropic salt guanidine hydrochloride (GuHCl) is employed. At moderate to high GuHCl concentrations the net effect of the linear, presumably chaotrope-induced deceleration and the presumed, square root-dependent ionic strength-induced acceleration is well approximated as linear, thus accounting for the observation of "chevron behavior" (log folding rate linear in denaturant concentration) typically reported for the folding of single domain proteins. At very low GuHCl concentrations, however, significant kinetic rollover is observed. This rollover is reasonably well fitted as a sum of a linear, presumably chaotropic effect and a square root-dependent, presumably electrostatic effect. These results thus not only provide insight into the nature of the folding transition state but also suggest that caution is in order when extrapolating GuHCl-based chevrons to estimate folding rates in the absence of denaturant and in interpreting deviations from chevron linearity as evidence for non-two-state kinetics.     

Complex folding pathways in a simple beta-hairpin

The determination of the folding mechanisms of proteins is critical to understand the topological change that can propagate Alzheimer and Creutzfeld-Jakobs diseases, among others. The computational community has paid considerable attention to this problem; however, the associated time scale, typically on the order of milliseconds or more, represents a formidable challenge. Ab initio protein folding from long molecular dynamics simulations or ensemble dynamics is not feasible with ordinary computing facilities and new techniques must be introduced. Here we present a detailed study of the folding of a 16-residue beta-hairpin, described by a generic energy model and using the activation-relaxation technique. From a total of 90 trajectories at 300 K, three folding pathways emerge. All involve a simultaneous optimization of the complete hydrophobic and hydrogen bonding interactions. The first two pathways follow closely those observed by previous theoretical studies (folding starting at the turn or by interactions between the termini). The third pathway, never observed by previous all-atom folding, unfolding, and equilibrium simulations, can be described as a reptation move of one strand of the beta-sheet with respect to the other. This reptation move indicates that non-native interactions can play a dominant role in the folding of secondary structures. Furthermore, such a mechanism mediated by non-native hydrogen bonds is not available for study by unfolding and Gō model simulations. The exact folding path followed by a given beta-hairpin is likely to be influenced by its sequence and the solvent conditions. Taken together, these results point to a more complex folding picture than expected for a simple beta-hairpin.     

Changes of protein stiffness during folding detect protein folding intermediates

Single-molecule force-quench atomic force microscopy (FQ-AFM) is used to detect folding intermediates of a simple protein by detecting changes of molecular stiffness of the protein during its folding process. Those stiffness changes are obtained from shape and peaks of an autocorrelation of fluctuations in end-to-end length of the folding molecule. The results are supported by predictions of the equipartition theorem and agree with existing Langevin dynamics simulations of a simplified model of a protein folding. In the light of the Langevin simulations the experimental data probe an ensemble of random-coiled collapsed states of the protein, which are present both in the force-quench and thermal-quench folding pathways.     

Cotranslational protein folding

The review analyzes the research concerning the folding of proteins in the course of their synthesis on ribosomes. The experimental data obtained for various proteins using various methods give grounds for concluding that a nascent protein largely acquires its spatial structure while still attached to the ribosome, and final folding into the biologically active conformation takes place as soon as the completed protein is released therefrom. Cotranslational folding is characteristic of both bacterial and eukaryotic cells, and appears to be the universal and the most evolutionarily ancient mechanism.     

Pro-sequence-assisted protein folding

Many proteins, including proteases and growth factors, are synthesized as precursors in the form of prepro-proteins. Whereas the pre-sequences usually act as signal peptides for transport, the pro-sequences of an increasing number of these proteins have been found to be essential for the correct folding of their associated proteins. In contrast to the action of molecular chaperones, pro-sequences appear to catalyse the protein-folding reaction directly. The similarity between the pro-sequence-assisted folding mechanisms of different proteases supports the hypothesis that a common folding mechanism has developed through convergent evolution. Further, the frequent requirement of the pro-sequences for both folding and intracellular transport or secretion suggests that these two functionalities are intimately related.     

Membrane protein folding

Investigating the in vitro refolding of proteins that naturally reside in biological membranes is a notoriously difficult task. Biophysical studies on model systems are beginning to provide a sound physical basis for membrane protein folding that should help to alleviate this problem. Highlights of these studies include insights into the interaction of transmembrane alpha helices, as well as into the important role that membrane lipids play in folding.     

Sub-microsecond protein folding

We have investigated the structure, equilibria, and folding kinetics of an engineered 35-residue subdomain of the chicken villin headpiece, an ultrafast-folding protein. Substitution of two buried lysine residues by norleucine residues stabilizes the protein by 1 kcal/mol and increases the folding rate sixfold, as measured by nanosecond laser T-jump. The folding rate at 300 K is (0.7 micros)(-1) with little or no temperature dependence, making this protein the first sub-microsecond folder, with a rate only twofold slower than the theoretically predicted speed limit. Using the 70 ns process to obtain the effective diffusion coefficient, the free energy barrier height is estimated from Kramers theory to be less than approximately 1 kcal/mol. X-ray crystallographic determination at 1A resolution shows no significant change in structure compared to the single-norleucine-substituted molecule and suggests that the increased stability is electrostatic in origin. The ultrafast folding rate, very accurate X-ray structure, and small size make this engineered villin subdomain an ideal system for simulation by atomistic molecular dynamics with explicit solvent.     

Zinc-dependent protein folding

Studies of classic zinc-finger peptides over the past 15 years have offered insights into the coupled processes of metal binding and protein folding. Within the past two years, this insight has been used to increase our understanding of the importance of first and second shell contributions (i.e. contributions from direct and indirect metal ligands) to metal binding and protein-folding stability, and led to advances in de novo protein design and protein redesign.     

Early events in protein folding

Recent advances have significantly increased the time and spectroscopic resolution of protein folding experiments. We can now study the timescale and nature of polypeptide collapse, and how this correlates with secondary and tertiary structure formation. Studies on ultrafast folding proteins and peptides provide experimental benchmarks on a timescale that overlaps directly with that of molecular dynamics simulations. This makes possible direct tests of both simulations and current models of protein folding.