Emerging accessibility patterns in long telomeric overhangs.

We present single-molecule experimental and computational modeling studies investigating the accessibility of human telomeric overhangs of physiologically relevant lengths. We studied 25 different overhangs that contain 4-28 repeats of GGGTTA (G-Tract) sequence and accommodate one to seven tandem G-quadruplex (GQ) structures. Using the FRET-PAINT method, we probed the distribution of accessible sites via a short imager strand, which is complementary to a G-Tract and transiently binds to available sites. We report accessibility patterns that periodically change with overhang length and interpret these patterns in terms of the underlying folding landscape and folding frustration. Overhangs that have [4n]G-Tracts, (12, 16, 20…) demonstrate the broadest accessibility patterns where the peptide nucleic acid probe accesses G-Tracts throughout the overhang. On the other hand, constructs with [4n+2]G-Tracts, (14, 18, 22…) have narrower patterns where the neighborhood of the junction between single- and double-stranded telomeres is most accessible. We interpret these results as the folding frustration being higher in [4n]G-Tract constructs compared to [4n+2]G-Tract constructs. We also developed a computational model that tests the consistency of different folding stabilities and cooperativities between neighboring GQs with the observed accessibility patterns. Our experimental and computational studies suggest the neighborhood of the junction between single- and double-stranded telomeres is least stable and most accessible, which is significant as this is a potential site where the connection between POT1/TPP1 (bound to single-stranded telomere) and other shelterin proteins (localized on double-stranded telomere) is established.

Coarse-grained molecular simulations of allosteric cooperativity.

Interactions between a protein and a ligand are often accompanied by a redistribution of the population of thermally accessible conformations. This dynamic response of the protein's functional energy landscape enables a protein to modulate binding affinities and control binding sensitivity to ligand concentration. In this paper, we investigate the structural origins of binding affinity and allosteric cooperativity of binding two Ca(2+) ions to each domain of Calmodulin (CaM) through simulations of a simple coarse-grained model. In this model, the protein's conformational transitions between open and closed conformational ensembles are simulated explicitly and ligand binding and unbinding are treated implicitly within the grand canonical ensemble. Ligand binding is cooperative because the binding sites are coupled through a shift in the dominant conformational ensemble upon binding. The classic Monod-Wyman-Changeux model of allostery with appropriate binding free energies to the open and closed ensembles accurately describes the simulated binding thermodynamics. The simulations predict that the two domains of CaM have distinct binding affinity and cooperativity. In particular, the C-terminal domain binds Ca(2+) with higher affinity and greater cooperativity than the N-terminal domain. From a structural point of view, the affinity of an individual binding loop depends sensitively on the loop's structural compatibility with the ligand in the bound ensemble, as well as the conformational flexibility of the binding site in the unbound ensemble.

Comparing allosteric transitions in the domains of calmodulin through coarse-grained simulations.

Calmodulin (CaM) is a ubiquitous Ca(2+)-binding protein consisting of two structurally similar domains with distinct stabilities, binding affinities, and flexibilities. We present coarse grained simulations that suggest that the mechanism for the domain's allosteric transitions between the open and closed conformations depends on subtle differences in the folded state topology of the two domains. Throughout a wide temperature range, the simulated transition mechanism of the N-terminal domain (nCaM) follows a two-state transition mechanism while domain opening in the C-terminal domain (cCaM) involves unfolding and refolding of the tertiary structure. The appearance of the unfolded intermediate occurs at a higher temperature in nCaM than it does in cCaM consistent with nCaM's higher thermal stability. Under approximate physiological conditions, the simulated unfolded state population of cCaM accounts for 10% of the population with nearly all of the sampled transitions (approximately 95%) unfolding and refolding during the conformational change. Transient unfolding significantly slows the domain opening and closing rates of cCaM, which can potentially influence its Ca(2+)-binding mechanism.

Allostery and folding of the N-terminal receiver domain of protein NtrC.

The N-terminal receiver domain of protein NtrC (NtrC(r)) exhibits allosteric transitions between the inactive (unphosphorylated) and active (phosphorylated) state on the microsecond time scale. Using a coarse-grained variational model with coupled energy basins, we illustrate that significant loss of conformational flexibility is the key determinant of the inactive (I) → active (A) state transition mechanism of NtrC(r). In particular, our results reveal that the rearrangements of the native contacts involving the regulatory helix-α4 and the flexible ß3-α3 loop upon activation play a crucial role in the activation mechanism. Interestingly, we find that the ß3-α3 loop exhibits a gradual decrease in flexibility throughout the activation transition, while helix-α4, in contrast, becomes more rigid abruptly near the free energy barrier separating the two states. To gain further insight into role these flexible regions play in the transition mechanism, we consider folding of NtrC(r) to both states using a similar model. Our calculated folding routes suggest that helix-α4 becomes structured later when folding to the I state compared to folding of the A state, a result consistent with it is relative conformational flexibility in the two states. Finally, we find a good qualitative agreement between our predicted I → A transition mechanism and the measured backbone dynamics from nuclear magnetic resonance experiments.

Conformational flexibility and the mechanisms of allosteric transitions in topologically similar proteins.

Conformational flexibility plays a central role in allosteric transition of proteins. In this paper, we extend the analysis of our previous study [S. Tripathi and J. J. Portman, Proc. Natl. Acad. Sci. U.S.A. 106, 2104 (2009)] to investigate how relatively minor structural changes of the meta-stable states can significantly influence the conformational flexibility and allosteric transition mechanism. We use the allosteric transitions of the domains of calmodulin as an example system to highlight the relationship between the transition mechanism and the inter-residue contacts present in the meta-stable states. In particular, we focus on the origin of transient local unfolding (cracking), a mechanism that can lower free energy barriers of allosteric transitions, in terms of the inter-residue contacts of the meta-stable states and the pattern of local strain that develops during the transition. We find that the magnitude of the local strain in the protein is not the sole factor determining whether a region will ultimately crack during the transition. These results emphasize that the residue interactions found exclusively in one of the two meta-stable states is the key in understanding the mechanism of allosteric conformational change.

Cooperativity and protein folding rates.

Despite the large and complex conformational space available to an unfolded protein, many small globular proteins fold with simple two-state cooperative kinetics. Understanding what determines folding rates beyond simple rules summarizing kinetic trends has proved to be more elusive than predicting folding mechanism. Topology-based models with smooth energy landscapes give reasonable predictions of the structure of the transition state ensemble, but do not have the kinetic or thermodynamic cooperativity exhibited by two-state proteins. This review outlines some recent efforts to understand what determines the cooperativity and the diversity of folding rates of two-state folding proteins.

Inherent flexibility determines the transition mechanisms of the EF-hands of calmodulin.

We explore how inherent flexibility of a protein molecule influences the mechanism controlling allosteric transitions by using a variational model inspired from work in protein folding. The striking differences in the predicted transition mechanism for the opening of the two domains of calmodulin (CaM) emphasize that inherent flexibility is key to understanding the complex conformational changes that occur in proteins. In particular, the C-terminal domain of CaM (cCaM), which is inherently less flexible than its N-terminal domain (nCaM), reveals "cracking" or local partial unfolding during the open/closed transition. This result is in harmony with the picture that cracking relieves local stresses caused by conformational deformations of a sufficiently rigid protein. We also compare the conformational transition in a recently studied even-odd paired fragment of CaM. Our results rationalize the different relative binding affinities of the EF-hands in the engineered fragment compared with the intact odd-even paired EF-hands (nCaM and cCaM) in terms of changes in flexibility along the transition route. Aside from elucidating general theoretical ideas about the cracking mechanism, these studies also emphasize how the remarkable intrinsic plasticity of CaM underlies conformational dynamics essential for its diverse functions.

Capillarity-like growth of protein folding nuclei.

A full structural description of transition state ensembles in protein folding includes the specificity of the ordered residues composing the folding nucleus as well as spatial density. To our knowledge, the spatial properties of the folding nucleus and interface of specific nuclei have yet to receive significant attention. We analyze folding routes predicted by a variational model in terms of a generalized formalism of the capillarity scaling theory that assumes the volume of the folded core of the nucleus grows with chain length as V(f) approximately N(3nu). For 27 two-state proteins studied, the scaling exponent nu ranges from 0.2 to 0.45 with an average of 0.33. This average value corresponds to packing of rigid objects, although generally the effective monomer size in the folded core is larger than the corresponding volume per particle in the native-state ensemble. That is, on average, the folded core of the nucleus is found to be relatively diffuse. We also study the growth of the folding nucleus and interface along the folding route in terms of the density or packing fraction. The evolution of the folded core and interface regions can be classified into three patterns of growth depending on how the growth of the folded core is balanced by changes in density of the interface. Finally, we quantify the diffuse versus polarized structure of the critical nucleus through direct calculation of the packing fraction of the folded core and interface regions. Our results support the general picture of describing protein folding as the capillarity-like growth of folding nuclei.

Inherent flexibility and protein function: The open/closed conformational transition in the N-terminal domain of calmodulin.

The key to understand a protein's function often lies in its conformational dynamics. We develop a coarse-grained variational model to investigate the interplay between structural transitions, conformational flexibility, and function of the N-terminal calmodulin domain (nCaM). In this model, two energy basins corresponding to the "closed" apo conformation and "open" holo conformation of nCaM are coupled by a uniform interpolation parameter. The resulting detailed transition route from our model is largely consistent with the recently proposed EFbeta-scaffold mechanism in EF-hand family proteins. We find that the N-terminal parts of the calcium binding loops shows higher flexibility than the C-terminal parts which form this EFbeta-scaffold structure. The structural transition of binding loops I and II are compared in detail. Our model predicts that binding loop II, with higher flexibility and earlier structural change than binding loop I, dominates the open/closed conformational transition in nCaM.

Variationally determined free energy profiles for structural models of proteins: characteristic temperatures for folding and trapping.

Characterizing the phase diagram for proteins is important both for laboratory studies and for the development of structure prediction algorithms. Using a variational scheme, we calculated the generic features of the protein thermostability over a large range of temperatures for a set of more than 50 different proteins using a model based on native structure alone. Focusing on a specific system, protein G, we further examined, using a more realistic model that includes the nonnative interaction, the thermostability of both the native state and a collection of trap structures. By surveying the native structures for many proteins and by paying closer attention to the various trap structures of protein G, we obtained an overall understanding of the folding dynamics far from the conditions usually focused on; namely, those near the folding temperature alone. Two characteristic temperatures (shown to scale with folding temperature in general) signal drastic changes in the folding mechanism. The variational calculations suggest that most proteins would, indeed, fold in a barrierless manner below a critical temperature analogous to a spinodal in crystallization. For fixed interaction strengths, this temperature, however, seems to be generally very low, approximately 50% of the equilibrium folding temperature. Likewise, native proteins, in general, would unfold in a completely barrierless way at a temperature 25% above folding temperature according to these variational calculations. We also studied the distribution of free energy profiles for escape from a set of trap structures generated by simulations.

Excluded volume, local structural cooperativity, and the polymer physics of protein folding rates.

A coarse-grained variational model is used to investigate the polymer dynamics of barrier crossing for a diverse set of two-state folding proteins. The model gives reliable folding rate predictions provided excluded volume terms that induce minor structural cooperativity are included in the interaction potential. In general, the cooperative folding routes have sharper interfaces between folded and unfolded regions of the folding nucleus and higher free energy barriers. The calculated free energy barriers are strongly correlated with native topology as characterized by contact order. Increasing the rigidity of the folding nucleus changes the local structure of the transition state ensemble nonuniformly across the set of proteins studied. Nevertheless, the calculated prefactors k(0) are found to be relatively uniform across the protein set, with variation in 1/k(0) less than a factor of 5. This direct calculation justifies the common assumption that the prefactor is roughly the same for all small two-state folding proteins. Using the barrier heights obtained from the model and the best-fit monomer relaxation time 30 ns, we find that 1/k(0) approximately 1-5 mus (with average 1/k(0) approximately 4 micros). This model can be extended to study subtle aspects of folding such as the variation of the folding rate with stability or solvent viscosity and the onset of downhill folding.