Native Basin Research Articles

Thermal denaturation and folding rates of single domain proteins: size matters

We analyze the dependence of thermal denaturation transition and folding rates of globular proteins on the number of amino acid residues, N. Using lattice Go models we show that Δ T/ T F∼ N −1, where T F is the folding transition temperature and Δ T is the transition width computed using the temperature dependence of the order parameter that distinguishes between the unfolded state and the native basin of attraction. This finding is consistent with finite size effects expected for the systems undergoing a phase transition from a disordered to an ordered phase. The dependence of the folding rates on N for lattice models and the dataset of 57 proteins and peptides shows that k F≃k F 0 exp(−CN β) with 0< β≤2/3 provides a good fit, where C is a β-dependent constant. We find that k F ≃k F 0 exp(−1.1N 1/2) with an average (over the dataset of proteins) k F 0≈(0.4 μs) −1, can estimate optimal protein folding rates, to within an order of magnitude in most cases. By using this fit for a set of proteins with β-sheet topology we find that k F 0≈ k U 0, the prefactor for unfolding. The maximum ratio of k U 0/ k F 0≈10 for this class of proteins.

Ab initio folding of helix bundle proteins using molecular dynamics simulations.

We have demonstrated that ab initio fast folding simulations at 400 K using a GB implicit solvent model with an all-atom based force field can describe the spontaneous formation of nativelike structures for the 36-residue villin headpiece and the 46-residue fragment B of Staphylococcal protein A. An implicit solvent model combined with high-temperature MD makes it possible to perform direct folding simulations of small- to medium-sized proteins by reducing the computational requirements tremendously. In the early stage of folding of the villin headpiece and protein A, initial hydrophobic collapse and rapid formation of helices were found to play important roles. For protein A, the third helix forms first in the early stage of folding and exhibits higher stability. The free energy profiles calculated from the folding simulations suggested that both of the helix-bundle proteins show a two-state thermodynamic behavior and protein A exhibits rather broad native basins.

Comparative anatomical analysis of the cotyledonary region in three Mediterranean Basin Quercus (Fagaceae)

Anatomical changes at the cotyledonary node from the embryo to the seedling stage in Quercus coccifera, Q. ilex, and Q. humilis were investigated by light and scanning electron microscopy techniques. Mature embryos of Q. humilis possess 2-3 pairs of leaf primordia and a pair of cotyledonary buds, whereas in Q. coccifera and Q. ilex there are two incipient primordia, and cotyledonary buds are not observed until 1 wk after germination. In all three species the cotyledonary buds multiply, forming bud clusters, and a vascular connection is well established within 5-6 wk after germination. As development proceeds, the cotyledonary region becomes woody, but buds, which are exogenous in origin, never become embedded in the periderm. In comparison with Q. suber, another native Mediterranean Basin oak, the cotyledonary node is short and axillary buds are not present below the insertion of cotyledons. In addition, starch accumulation in the cotyledonary region is not observed from histological analysis in the three oaks. Therefore, in Q. coccifera, Q. ilex, and Q. humilis seedlings the cotyledonary node can be considered to be an important regenerative structure enabling them to resprout after the elimination of the shoot above the cotyledons, despite the absence of a lignotuberous structure.

Effects of agricultural activities and best management practices on water quality of seasonal prairie pothole wetlands

Long-term effects of within-basin tillage can constrain condition andfunction of prairie wetlands even after uplands are restored. Runoff wassignificantly greater to replicate wetlands within tilled basins with orwithoutvegetated buffer strips as compared to Conservation Reserve Program restorationcontrols with revegetated uplands (REST). However, mean water levels for nativeprairie reference sites were higher than for REST controls, becauseinfiltrationrates were lower for native prairie basins, which had no prior history oftillage. Nutrient dynamics changed more in response to changes in water leveland vegetation structure than to increased nutrient inputs in watershed runoff.Dissolved oxygen increased between dry and wet years except in basins or zoneswith dense vegetation. As sediment redox dropped, water-column phosphatedeclined as phosphate likely co-precipitated with iron on the sediment surfacewithin open-water or sparsely vegetated zones. In response, N:P ratios shiftedfrom a region indicating N limitation to P limitation. REST sites, with densevegetation and low DO, also maintained high DOC, which maintains phosphate insolution through chelation of iron and catalysis of photoreduction. Referencesites in native prairie and restored uplands diverged over the course of thewet-dry cycle, emphasizing the importance of considering climatic variation inplanning restoration efforts.

Learning effective amino acid interactions through iterative stochastic techniques

The prediction of the three-dimensional structures of the native states of proteins from the sequences of their amino acids is one of the most important challenges in molecular biology. An essential task for solving this problem within coarse-grained models is the deduction of effective interaction potentials between the amino acids. Over the years, several techniques have been developed to extract potentials that are able to discriminate satisfactorily between the native and nonnative folds of a preassigned protein sequence. In general, when these potentials are used in actual dynamical folding simulations, they lead to a drift of the native structure outside the quasinative basin. In this article, we present and validate an approach to overcome this difficulty. By exploiting several numerical and analytical tools, we set up a rigorous iterative scheme to extract potentials satisfying a prerequisite of any viable potential: the stabilization of proteins within their native basin (less than 3-4 A RMSD). The scheme is flexible and is demonstrated to be applicable to a variety of parameterizations of the energy function, and it provides in each case the optimal potentials.

Folding Free Energy Surface of a Three-Stranded β-Sheet Protein

We present a molecular dynamics (MD) simulation study of the folding thermodynamics of the three-stranded β-sheet protein Betanova. The protein and solvent are explicitly described by employing all atom models. An umbrella sampling technique was employed to probe thermodynamically relevant states at different stages of folding. A database for the sampling was generated by conducting four high-temperature simulations. The initial conditions for the umbrella sampling were selected from this database of structures by employing hierarchical clustering. Sampling of conformational space was then carried out at 275 K and the generated data were combined with the weighted histogram method to produce the two-dimensional folding free energy landscape. We found that the folding of the protein Betanova occurs in two collapse stages. The first collapse brings the protein into a basin that contains various structures differing in their size and elements of secondary structure. At the transition state from this basin of collapsed states to the native basin, the protein adopts a native-like fold and size and forms ≈60% of native contacts. Thus the formation of native-like structure is concurrent with the secondary collapse. The overall stability of protein Betanova is found to be about 1 kcal/mol, in agreement with the experimental estimate. We found that the native side chain contacts are the primary factor in driving Betanova folding and stabilizing its native three-stranded β-sheet conformation. By contrast, hydrogen bonding is found to play a minor role in the folding of Betanova. Solvent is observed to be present in the protein core until late in folding.

Delineation of the native basin in continuum models of proteins

We propose two approaches for determining the native basins in off-lattice models of proteins. The first of them is based on exploring the saddle points on selected trajectories emerging from the native state. In the second approach, the basin size can be determined by monitoring random distortions in the shape of the protein around the native state. Both techniques yield the similar results. As a byproduct, a simple method to determine the folding temperature is obtained.

Linking rates of folding in lattice models of proteins with underlying thermodynamic characteristics

We investigate the sequence-dependent properties of proteins that determine the dual requirements of stability of the native state and its kinetic accessibility using simple cubic lattice models. Three interaction schemes are used to describe the potentials between nearest neighbor nonbonded beads. We show that, under the simulation conditions when the native basin of attraction (NBA) is the most stable, there is an excellent correlation between folding times τF and the dimensionless parameter σT=(Tθ−TF)/Tθ, where Tθ is the collapse temperature and TF is the folding transition temperature. There is also a significant correlation between τF and another dimensionless quantity Z=(EN−Ems)/δ, where EN is the energy of the native state, Ems is the average energy of the ensemble of misfolded structures, and δ is the dispersion in the contact energies. In contrast, there is no significant correlation between τF and the Z-score gap ΔZ=EN−Ems. An approximate relationship between σT and the Z-score is derived, which explains the superior correlation seen between τF and σT. For two state folders τF is linked to the free energy difference (not simply energy gap, however it is defined) between the unfolded states and the NBA.

Kinetic partitioning mechanism as a unifying theme in the folding of biomolecules

We present a unified framework for folding kinetics of proteins and RNA. The basis for this framework relies on the notion of topological frustration, which gives rise to several competing basins of attraction (CBA) in addition to the native basin of attraction (NBA) on the free energy surface. A rough free energy surface results in direct and indirect pathways to the NBA, i.e., a kinetic partitioning mechanism (KPM). The unified framework for folding kinetics allows us to propose a foldability principle, according to which fast folding sequences are characterized by the folding transition temperature $T_{F}$ being close to the collapse transition temperature $T_{\theta }$. Biomolecules, for which foldability principle is satisfied, such as small proteins and tRNAs, are expected to fold rapidly with two-state kinetics. Estimates for the multiple time scales in KPM are also given.