Global minimization of an off-lattice potential energy function using a chaperone-based refolding method

STUDIES OF FINDING LOW ENERGY CONFIGURATIONS IN OFF-LATTICE PROTEIN MODELS

We studied two three-dimensional off-lattice protein models with two species of monomers, hydrophobic and hydrophilic. Low energy configurations in both models were optimized using the energy landscape paving (ELP) method and subsequent gradient descent. The numerical results show that the proposed methods are very promising for finding the ground states of proteins. For all sequences with lengths 13 ≤ n ≤ 55, the algorithm finds states with lower energy than previously proposed putative ground states.

Reconciling theories of chaperonin accelerated folding with experimental evidence

For the last 20 years, a large volume of experimental and theoretical work has been undertaken to understand how chaperones like GroEL can assist protein folding in the cell. The most accepted explanation appears to be the simplest: GroEL, like most other chaperones, helps proteins fold by preventing aggregation. However, evidence suggests that, under some conditions, GroEL can play a more active role by accelerating protein folding. A large number of models have been proposed to explain how this could occur. Focused experiments have been designed and carried out using different protein substrates with conclusions that support many different mechanisms. In the current article, we attempt to see the forest through the trees. We review all suggested mechanisms for chaperonin-mediated folding and weigh the plausibility of each in light of what we now know about the most stringent, essential, GroEL-dependent protein substrates.

GroEL-mediated protein folding: making the impossible, possible

Protein folding is a spontaneous process that is essential for life, yet the concentrated and complex interior of a cell is an inherently hostile environment for the efficient folding of many proteins. Some proteins-constrained by sequence, topology, size, and function-simply cannot fold by themselves and are instead prone to misfolding and aggregation. This problem is so deeply entrenched that a specialized family of proteins, known as molecular chaperones, evolved to assist in protein folding. Here we examine one essential class of molecular chaperones, the large, oligomeric, and energy utilizing chaperonins or Hsp60s. The bacterial chaperonin GroEL, along with its co-chaperonin GroES, is probably the best-studied example of this family of protein-folding machine. In this review, we examine some of the general properties of proteins that do not fold well in the absence of GroEL and then consider how folding of these proteins is enhanced by GroEL and GroES. Recent experimental and theoretical studies suggest that chaperonins like GroEL and GroES employ a combination of protein isolation, unfolding, and conformational restriction to drive protein folding under conditions where it is otherwise not possible.

Energy optimization for off-lattice protein folding

Two three-dimensional AB off-lattice protein models consisting of hydrophobic and hydrophilic monomers are studied in this paper. By incorporating an extra energy contribution into the original energy function, the protein folding is converted from a constraint optimization problem into an unconstrained one which can be solved by the well-known gradient method. From the initial configurations randomly generated by the heuristic strategy proposed in this paper, our algorithm can find better results than those by nPERM for the four Fibonacci sequences. Based on the initial configurations obtained by energy landscape paving (ELP) routine, some of our results for the lowest energies are better than the best values reported in the literature.

Structure optimization in a three-dimensional off-lattice protein model

We studied a three-dimensional off-lattice AB model with two species of monomers, hydrophobic (A) and hydrophilic (B), and present two optimization algorithms: face-centered-cubic (FCC)-lattice pruned-enriched-Rosenbluth method (PERM) and subsequent conjugate gradient (PERM++) minimization and heuristic conjugate gradient (HCG) simulation based on "off-trap" strategy. In PERM++, we apply the PERM to the FCC-lattice to produce the initial conformation, and conjugate gradient minimization is then used to reach the minimum energy state. Both algorithms have been tested in the three-dimensional AB model for all sequences with lengths 13 < or = n < or = 55. The numerical results show that the proposed methods are very promising for finding the ground states of proteins. In several cases, we renew the putative ground states energy values.

A quasi-physical algorithm for the structure optimization in an off-lattice protein model

In this paper, we study an off-lattice protein AB model with two species of monomers, hydrophobic and hydrophilic, and present a heuristic quasi-physical algorithm. First, by elaborately simulating the movement of the smooth solids in the physical world, we find low-energy conformations for a given monomer chain. A subsequent off-trap strategy is then proposed to trigger a jump for a stuck situation in order to get out of the local minima. The algorithm has been tested in the three-dimensional AB model for all sequences with lengths of 13-55 monomers. In several cases, we renew the putative ground state energy values. The numerical results show that the proposed methods are very promising for finding the ground states of proteins.

Effects of confinement in chaperonin assisted protein folding: rate enhancement by decreasing the roughness of the folding energy landscape

Chaperonins, such as the GroE complex of the bacteria Escherichia coli, assist the folding of proteins under non-permissive folding conditions by providing a cavity in which the newly translated or translocated protein can be encapsulated. Whether the chaperonin cage plays a passive role in protecting the protein from aggregation, or an active role in accelerating folding rates, remains a matter of debate. Here, we investigate the role of confinement in chaperonin mediated folding through molecular dynamics simulations. We designed a substrate protein with an alpha/beta sandwich fold, a common structural motif found in GroE substrate proteins and confined it to a spherical hydrophilic cage which mimicked the interior of the GroEL/ES cavity. The thermodynamics and kinetics of folding were studied over a wide range of temperature and cage radii. Confinement was seen to significantly raise the collapse temperature, T(c), as a result of the associated entropy loss of the unfolded state. The folding temperature, T(f), on the other hand, remained unaffected by encapsulation, a consequence of the folding mechanism of this protein that involves an initial collapse to a compact misfolded state prior to rearranging to the native state. Folding rates were observed to be either accelerated or retarded compared to bulk folding rates, depending on the temperature of the simulation. Rate enhancements due to confinement were observed only at temperatures above the temperature T(m), which corresponds to the temperature at which the protein folds fastest. For this protein, T(m) lies above the folding temperature, T(f), implying that encapsulation alone will not lead to a rate enhancement under conditions where the native state is stable (T<T(f)). For confinement to positively impact folding rates under physiological conditions, it is hence necessary for the protein to exhibit a folding transition above the temperature at which it exhibits its fastest folding rate (T(m)<T(f)). We designed a protein with this property by reducing the energetic frustration in the original alpha/beta sandwich substrate protein. The modified protein exhibited a twofold acceleration in folding rates upon encapsulation. This rate enhancement is due to a mechanistic change in folding involving the elimination, upon encapsulation, of accessible local energy minima corresponding to structures with large radii of gyration. For this protein, confinement hence plays more than the role of a passive cage, but rather adopts an active role, accelerating folding rates by decreasing the roughness of the energy landscape of the protein.

Structure optimization in an off-lattice protein model

We study an off-lattice protein toy model with two species of monomers interacting through modified Lennard-Jones interactions. Low energy configurations are optimized using the pruned-enriched-Rosenbluth method (PERM), hitherto employed to native state searches only for off-lattice models. For two dimensions we found states with lower energy than previously proposed putative ground states for all chain lengths >/=13. This indicates that PERM has the potential to produce native states also for more realistic protein models. For d=3, where no published ground states exist, we present some putative lowest energy states for future comparison with other methods.

Application of a chaperone-based refolding method to two- and three-dimensional off-lattice protein models

A model of protein-chaperone interaction as a two-phase (unfolding/refolding) iterative annealing mechanism able to promote structural segregation of hydrophobic and hydrophilic monomers and thereby facilitate access to nativelike states has recently been applied successfully to two 22-mers of the Honeycutt and Thirumalai BLN (hydrophobic, hydrophilic, neutral) heteropolymer model. This technique is here applied to a much wider data set: 94 8-mers of the off-lattice protein model originally presented in two dimensions by Stillinger and Head-Gordon, and later extended into three dimensions by Irbäck and Potthast; the model chaperone is shown to be equally successful, and by progressive elaboration of the chaperone model as in the earlier BLN model work, to be utilizing very similar underlying mechanisms. It is demonstrated that on average, contacts with the model chaperone give rise to a consistent movement in structure space in the direction of more nativelike structures; this method of global minimization does not therefore rely fundamentally on random search. Insofar as the responses to the chaperone of the two- and three-dimensional forms of the substrate model do differ, this can be interpreted as reflecting the different handling of hydrophilic monomers in the models-in particular, whether there is active repulsion between these and monomers of hydrophobic character. The chaperone-induced refolding method is also tested on a set of 220 9-mer chains of each version of the substrate model, where it is seen that the two-dimensional model, with its more clearly distinguished roles for the hydrophobic and hydrophilic monomers, shows a more favorable scaling behavior.