How optimization of potential functions affects protein folding.

The relationship between the optimization of the potential function and the foldability of theoretical protein models is studied based on investigations of a 27-mer cubic-lattice protein model and a more realistic lattice model for the protein crambin. In both the simple and the more complicated systems, optimization of the energy parameters achieves significant improvements in the statistical-mechanical characteristics of the systems and leads to foldable protein models in simulation experiments. The foldability of the protein models is characterized by their statistical-mechanical properties--e.g., by the density of states and by Monte Carlo folding simulations of the models. With optimized energy parameters, a high level of consistency exists among different interactions in the native structures of the protein models, as revealed by a correlation function between the optimized energy parameters and the native structure of the model proteins. The results of this work are relevant to the design of a general potential function for folding proteins by theoretical simulations.

Recent improvements in prediction of protein structure by global optimization of a potential energy function

Recent improvements of a hierarchical ab initio or de novo approach for predicting both α and β structures of proteins are described. The united-residue energy function used in this procedure includes multibody interactions from a cumulant expansion of the free energy of polypeptide chains, with their relative weights determined by Z-score optimization. The critical initial stage of the hierarchical procedure involves a search of conformational space by the conformational space annealing (CSA) method, followed by optimization of an all-atom model. The procedure was assessed in a recent blind test of protein structure prediction (CASP4). The resulting lowest-energy structures of the target proteins (ranging in size from 70 to 244 residues) agreed with the experimental structures in many respects. The entire experimental structure of a cyclic α-helical protein of 70 residues was predicted to within 4.3 Å α-carbon (Cα) rms deviation (rmsd) whereas, for other α-helical proteins, fragments of roughly 60 residues were predicted to within 6.0 Å Cα rmsd. Whereas β structures can now be predicted with the new procedure, the success rate for α/β- and β-proteins is lower than that for α-proteins at present. For the β portions of α/β structures, the Cα rmsd's are less than 6.0 Å for contiguous fragments of 30–40 residues; for one target, three fragments (of length 10, 23, and 28 residues, respectively) formed a compact part of the tertiary structure with a Cα rmsd less than 6.0 Å. Overall, these results constitute an important step toward the ab initio prediction of protein structure solely from the amino acid sequence.

Changes of Mitochondrial Properties in Maize Seedlings Associated with Selection for Germination at Low Temperature. Fatty Acid Composition, Cytochrome c Oxidase, and Adenine Nucleotide Translocase Activities1

Mitochondria are affected by low temperature during seedling establishment in maize (Zea mays L.). We evaluated the associated changes in the mitochondrial properties of populations selected for high (C4-H) and low (C4-L) germination levels at 9.5°C. When seedlings of the two populations were grown at 14°C (near the lower growth limit), the mitochondrial inner membranes of C4-H showed a higher percentage of 18-carbon unsaturated fatty acids, a higher fluidity, and a higher activity of cytochrome c oxidase. We found a positive relationship between these properties and the activity of a mitochondrial peroxidase, allowing C4-H to reduce lipid peroxidation relative to C4-L. The specific activity of reconstituted ATP/ADP translocase was positively associated with this peroxidase activity, suggesting that translocase activity is also affected by chilling. The level of oxidative stress and defense mechanisms are differently expressed in tolerant and susceptible populations when seedlings are grown at a temperature near the lower growth limit. Thus, the interaction between membrane lipids and cytochrome c oxidase seems to play a key role in maize chilling tolerance. Furthermore, the divergent-recurrent selection procedure apparently affects the allelic frequencies of genes controlling such an interaction.

Comparison of Binding Properties and Early Biological Effects of Elicitins in Tobacco Cells1

Elicitins are a family of small proteins secreted by Phytophthora species that have a high degree of homology and elicit defense reactions in tobacco (Nicotiana tabacum). They display acidic or basic characteristics, the acidic elicitins being less efficient in inducing plant necrosis. In this study we compared the binding properties of four elicitins (two basic and two acidic) and early-induced signal transduction events (Ca2+ influx, extracellular medium alkalinization, and active oxygen species production). The affinity for tobacco plasma membrane-binding sites and the number of binding sites were similar for all four elicitins. Furthermore, elicitins compete with one another for binding sites, suggesting that they interact with the same receptor. The four elicitins induced Ca2+ influx, extracellular medium alkalinization, and the production of active oxygen species in tobacco cell suspensions, but the intensity and kinetics of these effects were different from one elicitin to another. As a general observation the concentrations that induce similar levels of biological activities were lower for basic elicitins (with the exception of cinnamomin-induced Ca2+ uptake). The qualitative similarity of early events induced by elicitins indicates a common transduction scheme, whereas fine signal transduction tuning is different in each elicitin.

Chaperonin-facilitated protein folding: optimization of rate and yield by an iterative annealing mechanism.

We develop a heuristic model for chaperonin-facilitated protein folding, the iterative annealing mechanism, based on theoretical descriptions of "rugged" conformational free energy landscapes for protein folding, and on experimental evidence that (i) folding proceeds by a nucleation mechanism whereby correct and incorrect nucleation lead to fast and slow folding kinetics, respectively, and (ii) chaperonins optimize the rate and yield of protein folding by an active ATP-dependent process. The chaperonins GroEL and GroES catalyze the folding of ribulose bisphosphate carboxylase at a rate proportional to the GroEL concentration. Kinetically trapped folding-incompetent conformers of ribulose bisphosphate carboxylase are converted to the native state in a reaction involving multiple rounds of quantized ATP hydrolysis by GroEL. We propose that chaperonins optimize protein folding by an iterative annealing mechanism; they repeatedly bind kinetically trapped conformers, randomly disrupt their structure, and release them in less folded states, allowing substrate proteins multiple opportunities to find pathways leading to the most thermodynamically stable state. By this mechanism, chaperonins greatly expand the range of environmental conditions in which folding to the native state is possible. We suggest that the development of this device for optimizing protein folding was an early and significant evolutionary event.

Optimization of rates of protein folding: the nucleation-condensation mechanism and its implications.

Small, single-module proteins that fold in a single cooperative step may be paradigms for understanding early events in protein-folding pathways generally. Recent experimental studies of the 64-residue chymotrypsin inhibitor 2 (CI2) support a nucleation mechanism for folding, as do some computer stimulations. CI2 has a nucleation site that develops only in the transition state for folding. The nucleus is composed of a set of adjacent residues (an alpha-helix), stabilized by long-range interactions that are formed as the rest of the protein collapses around it. A simple analysis of the optimization of the rate of protein folding predicts that rates are highest when the denatured state has little residual structure under physiological conditions and no intermediates accumulate. This implies that any potential nucleation site that is composed mainly of adjacent residues should be just weakly populated in the denatured state and become structured only in a high-energy intermediate or transition state when it is stabilized by interactions elsewhere in the protein. Hierarchical mechanisms of folding in which stable elements of structure accrete are unfavorable. The nucleation-condensation mechanism of CI2 fulfills the criteria for fast folding. On the other hand, stable intermediates do form in the folding of more complex proteins, and this may be an unavoidable consequence of increasing size and nucleation at more than one site.

Modeling and optimization of populations subject to time-dependent mutation.

It has become clear that many organisms possess the ability to regulate their mutation rate in response to environmental conditions. So the question of finding an optimal mutation rate must be replaced by that of finding an optimal mutation schedule. We show that this task cannot be accomplished with standard population-dynamic models. We then develop a "hybrid" model for populations experiencing time-dependent mutation that treats population growth as deterministic but the time of first appearance of new variants as stochastic. We show that the hybrid model agrees well with a Monte Carlo simulation. From this model, we derive a deterministic approximation, a "threshold" model, that is similar to standard population dynamic models but differs in the initial rate of generation of new mutants. We use these techniques to model antibody affinity maturation by somatic hypermutation. We had previously shown that the optimal mutation schedule for the deterministic threshold model is phasic, with periods of mutation between intervals of mutation-free growth. To establish the validity of this schedule, we now show that the phasic schedule that optimizes the deterministic threshold model significantly improves upon the best constant-rate schedule for the hybrid and Monte Carlo models.