Stochastic protein folding simulation in the three-dimensional HP-model

We present results from three-dimensional protein folding simulations in the HP-model on ten benchmark problems. The simulations are executed by a simulated annealing-based algorithm with a time-dependent cooling schedule. The neighbourhood relation is determined by the pull-move set. The results provide experimental evidence that the maximum depth D of local minima of the underlying energy landscape can be upper bounded by D < n(2/3). The local search procedure employs the stopping criterion (In/delta)(D/gamma) where m is an estimation of the average number of neighbouring conformations, gamma relates to the mean of non-zero differences of the objective function for neighbouring conformations, and 1-delta is the confidence that a minimum conformation has been found. The bound complies with the results obtained for the ten benchmark problems. (c) 2008 Elsevier Ltd. All rights reserved.

Population-based local search for protein folding simulation in the MJ energy model and cubic lattices

We present experimental results on benchmark problems in 3D cubic lattice structures with the Miyazawa-Jernigan energy function for two local search procedures that utilise the pull-move set: (i) population-based local search (PLS) that traverses the energy landscape with greedy steps towards (potential) local minima followed by upward steps up to a certain level of the objective function; (ii) simulated annealing with a logarithmic cooling schedule (LSA). The parameter settings for PLS are derived from short LSA-runs executed in pre-processing and the procedure utilises tabu lists generated for each member of the population. In terms of the total number of energy function evaluations both methods perform equally well, however. PLS has the potential of being parallelised with an expected speed-up in the region of the population size. Furthermore, both methods require a significant smaller number of function evaluations when compared to Monte Carlo simulations with kink-jump moves. (C) 2009 Elsevier Ltd. All rights reserved.

General, PDB-based collective variables for protein folding

New, automated forms of data-analysis are required in order to understand the high-dimensional trajectories that are obtained from molecular dynamics simulations on proteins. Dimensionality reduction algorithms are particularly appealing in this regard as they allow one to construct unbiased, low-dimensional representations of the trajectory using only the information encoded in the trajectory. The downside of this approach is that different sets of coordinates are required for each different chemical systems under study precisely because the coordinates are constructed using information from the trajectory. In this paper we show how one can resolve this problem by using the sketch-map algorithm that we recently proposed to construct a low-dimensional representation of the structures contained in the protein data bank (PDB). We show that the resulting coordinates are as useful for analysing trajectory data as coordinates constructed using landmark configurations taken from the trajectory and that these coordinates can thus be used for understanding protein folding across a range of systems.

Metal ions and protein folding: conformational and functional interplay

Dissertation presented to obtain a PhD degree in Biochemistry at Instituto de Tecnologia Química e Biológica, Universidade Nova de Lisboa

Protein Folding Simulations: Confinement, External Fields and Sequence Design

The present Thesis looks at the problem of protein folding using Monte Carlo and Langevin simulations, three topics in protein folding have been studied: 1) the effect of confining potential barriers, 2) the effect of a static external field and 3) the design of amino acid sequences which fold in a short time and which have a stable native state (global minimum). Regarding the first topic, we studied the confinement of a small protein of 16 amino acids known as 1NJ0 (PDB code) which has a beta-sheet structure as a native state. The confinement of proteins occurs frequently in the cell environment. Some molecules called Chaperones, present in the cytoplasm, capture the unfolded proteins in their interior and avoid the formation of aggregates and misfolded proteins. This mechanism of confinement mediated by Chaperones is not yet well understood. In the present work we considered two kinds of potential barriers which try to mimic the confinement induced by a Chaperon molecule. The first kind of potential was a purely repulsive barrier whose only effect is to create a cavity where the protein folds up correctly. The second kind of potential was a barrier which includes both attractive and repulsive effects. We performed Wang-Landau simulations to calculate the thermodynamical properties of 1NJ0. From the free energy landscape plot we found that 1NJ0 has two intermediate states in the bulk (without confinement) which are clearly separated from the native and the unfolded states. For the case of the purely repulsive barrier we found that the intermediate states get closer to each other in the free energy landscape plot and eventually they collapse into a single intermediate state. The unfolded state is more compact, compared to that in the bulk, as the size of the barrier decreases. For an attractive barrier modifications of the states (native, unfolded and intermediates) are observed depending on the degree of attraction between the protein and the walls of the barrier. The strength of the attraction is measured by the parameter $\epsilon$. A purely repulsive barrier is obtained for $\epsilon=0$ and a purely attractive barrier for $\epsilon=1$. The states are changed slightly for magnitudes of the attraction up to $\epsilon=0.4$. The disappearance of the intermediate states of 1NJ0 is already observed for $\epsilon =0.6$. A very high attractive barrier ($\epsilon \sim 1.0$) produces a completely denatured state. In the second topic of this Thesis we dealt with the interaction of a protein with an external electric field. We demonstrated by means of computer simulations, specifically by using the Wang-Landau algorithm, that the folded, unfolded, and intermediate states can be modified by means of a field. We have found that an external field can induce several modifications in the thermodynamics of these states: for relatively low magnitudes of the field ($<2.06 \times 10^8$ V/m) no major changes in the states are observed. However, for higher magnitudes than ($6.19 \times 10^8$ V/m) one observes the appearance of a new native state which exhibits a helix-like structure. In contrast, the original native state is a $\beta$-sheet structure. In the new native state all the dipoles in the backbone structure are aligned parallel to the field. The design of amino acid sequences constitutes the third topic of the present work. We have tested the Rate of Convergence criterion proposed by D. Gridnev and M. Garcia ({\it work unpublished}). We applied it to the study of off-lattice models. The Rate of Convergence criterion is used to decide if a certain sequence will fold up correctly within a relatively short time. Before the present work, the common way to decide if a certain sequence was a good/bad folder was by performing the whole dynamics until the sequence got its native state (if it existed), or by studying the curvature of the potential energy surface. There are some difficulties in the last two approaches. In the first approach, performing the complete dynamics for hundreds of sequences is a rather challenging task because of the CPU time needed. In the second approach, calculating the curvature of the potential energy surface is possible only for very smooth surfaces. The Rate of Convergence criterion seems to avoid the previous difficulties. With this criterion one does not need to perform the complete dynamics to find the good and bad sequences. Also, the criterion does not depend on the kind of force field used and therefore it can be used even for very rugged energy surfaces.

Green fluorescent protein as a reporter of prion protein folding

Background: The amino terminal half of the cellular prion protein PrPc is implicated in both the binding of copper ions and the conformational changes that lead to disease but has no defined structure. However, as some structure is likely to exist we have investigated the use of an established protein refolding technology, fusion to green fluorescence protein (GFP), as a method to examine the refolding of the amino terminal domain of mouse prion protein. Results: Fusion proteins of PrPc and GFP were expressed at high level in E. coli and could be purified to near homogeneity as insoluble inclusion bodies. Following denaturation, proteins were diluted into a refolding buffer whereupon GFP fluorescence recovered with time. Using several truncations of PrPc the rate of refolding was shown to depend on the prion sequence expressed. In a variation of the format, direct observation in E. coli, mutations introduced randomly in the PrPc protein sequence that affected folding could be selected directly by recovery of GFP fluorescence. Conclusion: Use of GFP as a measure of refolding of PrPc fusion proteins in vitro and in vivo proved informative. Refolding in vitro suggested a local structure within the amino terminal domain while direct selection via fluorescence showed that as little as one amino acid change could significantly alter folding. These assay formats, not previously used to study PrP folding, may be generally useful for investigating PrPc structure and PrPc-ligand interaction.

Use of a novel Hill-climbing genetic algorithm in protein folding simulations

We have developed a novel Hill-climbing genetic algorithm (GA) for simulation of protein folding. The program (written in C) builds a set of Cartesian points to represent an unfolded polypeptide's backbone. The dihedral angles determining the chain's configuration are stored in an array of chromosome structures that is copied and then mutated. The fitness of the mutated chain's configuration is determined by its radius of gyration. A four-helix bundle was used to optimise simulation conditions, and the program was compared with other, larger, genetic algorithms on a variety of structures. The program ran 50% faster than other GA programs. Overall, tests on 100 non-redundant structures gave comparable results to other genetic algorithms, with the Hill-climbing program running from between 20 and 50% faster. Examples including crambin, cytochrome c, cytochrome B and hemerythrin gave good secondary structure fits with overall alpha carbon atom rms deviations of between 5 and 5.6 Angstrom with an optimised hydrophobic term in the fitness function. (C) 2003 Elsevier Ltd. All rights reserved.

Grid computing solutions for distributed repositories of protein folding and unfolding simulations

The P-found protein folding and unfolding simulation repository is designed to allow scientists to perform analyses across large, distributed simulation data sets. There are two storage components in P-found: a primary repository of simulation data and a data warehouse. Here we demonstrate how grid technologies can support multiple, distributed P-found installations. In particular we look at two aspects, first how grid data management technologies can be used to access the distributed data warehouses; and secondly, how the grid can be used to transfer analysis programs to the primary repositories --- this is an important and challenging aspect of P-found because the data volumes involved are too large to be centralised. The grid technologies we are developing with the P-found system will allow new large data sets of protein folding simulations to be accessed and analysed in novel ways, with significant potential for enabling new scientific discoveries.

P-found: grid-enabling distributed repositories of protein folding and unfolding simulations for data mining

The P-found protein folding and unfolding simulation repository is designed to allow scientists to perform data mining and other analyses across large, distributed simulation data sets. There are two storage components in P-found: a primary repository of simulation data that is used to populate the second component, and a data warehouse that contains important molecular properties. These properties may be used for data mining studies. Here we demonstrate how grid technologies can support multiple, distributed P-found installations. In particular, we look at two aspects: firstly, how grid data management technologies can be used to access the distributed data warehouses; and secondly, how the grid can be used to transfer analysis programs to the primary repositories — this is an important and challenging aspect of P-found, due to the large data volumes involved and the desire of scientists to maintain control of their own data. The grid technologies we are developing with the P-found system will allow new large data sets of protein folding simulations to be accessed and analysed in novel ways, with significant potential for enabling scientific discovery.

The Xanthomonas citri effector protein PthA interacts with citrus proteins involved in nuclear transport, protein folding and ubiquitination associated with DNA repair

P>Xanthomonas axonopodis pv. citri utilizes the type III effector protein PthA to modulate host transcription to promote citrus canker. PthA proteins belong to the AvrBs3/PthA family and carry a domain comprising tandem repeats of 34 amino acids that mediates protein-protein and protein-DNA interactions. We show here that variants of PthAs from a single bacterial strain localize to the nucleus of plant cells and form homo- and heterodimers through the association of their repeat regions. We hypothesize that the PthA variants might also interact with distinct host targets. Here, in addition to the interaction with alpha-importin, known to mediate the nuclear import of AvrBs3, we describe new interactions of PthAs with citrus proteins involved in protein folding and K63-linked ubiquitination. PthAs 2 and 3 preferentially interact with a citrus cyclophilin (Cyp) and with TDX, a tetratricopeptide domain-containing thioredoxin. In addition, PthAs 2 and 3, but not 1 and 4, interact with the ubiquitin-conjugating enzyme complex formed by Ubc13 and ubiquitin-conjugating enzyme variant (Uev), required for K63-linked ubiquitination and DNA repair. We show that Cyp, TDX and Uev interact with each other, and that Cyp and Uev localize to the nucleus of plant cells. Furthermore, the citrus Ubc13 and Uev proteins complement the DNA repair phenotype of the yeast Delta ubc13 and Delta mms2/uev1a mutants, strongly indicating that they are also involved in K63-linked ubiquitination and DNA repair. Notably, PthA 2 affects the growth of yeast cells in the presence of a DNA damage agent, suggesting that it inhibits K63-linked ubiquitination required for DNA repair.