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

Rational peptide design for regulating liquid-liquid phase separation on the basis of residue-residue contact energy

Since liquid-liquid phase separation (LLPS) of proteins is governed by their intrinsically disordered regions (IDRs), it can be controlled by LLPS-regulators that bind to the IDRs. The artificial design of LLPS-regulators based on this mechanism can be leveraged in biological and therapeutic applications. However, the fabrication of artificial LLPS-regulators remains challenging. Peptides are promising candidates for artificial LLPS-regulators because of their ability to potentially bind to IDRs complementarily. In this study, we provide a rational peptide design methodology for targeting IDRs based on residue-residue contact energy obtained using molecular dynamics (MD) simulations. This methodology provides rational peptide sequences that function as LLPS regulators. The peptides designed with the MD-based contact energy showed dissociation constants of 35-280 nM for the N-terminal IDR of the tumor suppressor p53, which are significantly lower than the dissociation constants of peptides designed with the conventional 3D structure-based energy, demonstrating the validity of the present peptide design methodology. Importantly, all of the designed peptides enhanced p53 droplet formation. The droplet-forming peptides were converted to droplet-deforming peptides by fusing maltose-binding protein (a soluble tag) to the designed peptides. Thus, the present peptide design methodology for targeting IDRs is useful for regulating droplet formation.

Rational design using sequence information only produces a peptide that binds to the intrinsically disordered region of p53

Intrinsically disordered regions (IDRs) of proteins are involved in many diseases. The rational drug design against disease-mediating proteins is often based on the 3D structure; however, the flexible structure of IDRs hinders the use of such structure-based design methods. Here, we developed a rational design method to obtain a peptide that can bind an IDR using only sequence information based on the statistical contact energy of amino acid pairs. We applied the method to the disordered C-terminal domain of the tumor suppressor p53. Titration experiments revealed that one of the designed peptides, DP6, has a druggable affinity of ~1 μM to the p53 C-terminal domain. NMR spectroscopy and molecular dynamics simulation revealed that DP6 selectively binds to the vicinity of the target sequence in the C-terminal domain of p53. DP6 inhibits the nonspecific DNA binding of a tetrameric form of the p53 C-terminal domain, but does not significantly affect the specific DNA binding of a tetrameric form of the p53 core domain. Single-molecule measurements revealed that DP6 retards the 1D sliding of p53 along DNA, implying modulation of the target searching of p53. Statistical potential-based design may be useful in designing peptides that target IDRs for therapeutic purposes.

Guided macro-mutation in a graded energy based genetic algorithm for protein structure prediction

Protein structure prediction is considered as one of the most challenging and computationally intractable combinatorial problem. Thus, the efficient modeling of convoluted search space, the clever use of energy functions, and more importantly, the use of effective sampling algorithms become crucial to address this problem. For protein structure modeling, an off-lattice model provides limited scopes to exercise and evaluate the algorithmic developments due to its astronomically large set of data-points. In contrast, an on-lattice model widens the scopes and permits studying the relatively larger proteins because of its finite set of data-points. In this work, we took the full advantage of an on-lattice model by using a face-centered-cube lattice that has the highest packing density with the maximum degree of freedom. We proposed a graded energy-strategically mixes the Miyazawa-Jernigan (MJ) energy with the hydrophobic-polar (HP) energy-based genetic algorithm (GA) for conformational search. In our application, we introduced a 2 × 2 HP energy guided macro-mutation operator within the GA to explore the best possible local changes exhaustively. Conversely, the 20 × 20 MJ energy model-the ultimate objective function of our GA that needs to be minimized-considers the impacts amongst the 20 different amino acids and allow searching the globally acceptable conformations. On a set of benchmark proteins, our proposed approach outperformed state-of-the-art approaches in terms of the free energy levels and the root-mean-square deviations.

Efficient conformational space exploration in ab initio protein folding simulation

Ab initio protein folding simulation largely depends on knowledge-based energy functions that are derived from known protein structures using statistical methods. These knowledge-based energy functions provide us with a good approximation of real protein energetics. However, these energy functions are not very informative for search algorithms and fail to distinguish the types of amino acid interactions that contribute largely to the energy function from those that do not. As a result, search algorithms frequently get trapped into the local minima. On the other hand, the hydrophobic-polar (HP) model considers hydrophobic interactions only. The simplified nature of HP energy function makes it limited only to a low-resolution model. In this paper, we present a strategy to derive a non-uniform scaled version of the real 20×20 pairwise energy function. The non-uniform scaling helps tackle the difficulty faced by a real energy function, whereas the integration of 20×20 pairwise information overcomes the limitations faced by the HP energy function. Here, we have applied a derived energy function with a genetic algorithm on discrete lattices. On a standard set of benchmark protein sequences, our approach significantly outperforms the state-of-the-art methods for similar models. Our approach has been able to explore regions of the conformational space which all the previous methods have failed to explore. Effectiveness of the derived energy function is presented by showing qualitative differences and similarities of the sampled structures to the native structures. Number of objective function evaluation in a single run of the algorithm is used as a comparison metric to demonstrate efficiency.

A Parallel Framework for Multipoint Spiral Search in ab Initio Protein Structure Prediction

Protein structure prediction is computationally a very challenging problem. A large number of existing search algorithms attempt to solve the problem by exploring possible structures and finding the one with the minimum free energy. However, these algorithms perform poorly on large sized proteins due to an astronomically wide search space. In this paper, we present a multipoint spiral search framework that uses parallel processing techniques to expedite exploration by starting from different points. In our approach, a set of random initial solutions are generated and distributed to different threads. We allow each thread to run for a predefined period of time. The improved solutions are stored threadwise. When the threads finish, the solutions are merged together and the duplicates are removed. A selected distinct set of solutions are then split to different threads again. In our ab initio protein structure prediction method, we use the three-dimensional face-centred-cubic lattice for structure-backbone mapping. We use both the low resolution hydrophobic-polar energy model and the high-resolution 20 × 20 energy model for search guiding. The experimental results show that our new parallel framework significantly improves the results obtained by the state-of-the-art single-point search approaches for both energy models on three-dimensional face-centred-cubic lattice. We also experimentally show the effectiveness of mixing energy models within parallel threads.

A firefly-inspired method for protein structure prediction in lattice models

We introduce a Firefly-inspired algorithmic approach for protein structure prediction over two different lattice models in three-dimensional space. In particular, we consider three-dimensional cubic and three-dimensional face-centred-cubic (FCC) lattices. The underlying energy models are the Hydrophobic-Polar (H-P) model, the Miyazawa–Jernigan (M-J) model and a related matrix model. The implementation of our approach is tested on ten H-P benchmark problems of a length of 48 and ten M-J benchmark problems of a length ranging from 48 until 61. The key complexity parameter we investigate is the total number of objective function evaluations required to achieve the optimum energy values for the H-P model or competitive results in comparison to published values for the M-J model. For H-P instances and cubic lattices, where data for comparison are available, we obtain an average speed-up over eight instances of 2.1, leaving out two extreme values (otherwise, 8.8). For six M-J instances, data for comparison are available for cubic lattices and runs with a population size of 100, where, a priori, the minimum free energy is a termination criterion. The average speed-up over four instances is 1.2 (leaving out two extreme values, otherwise 1.1), which is achieved for a population size of only eight instances. The present study is a test case with initial results for ad hoc parameter settings, with the aim of justifying future research on larger instances within lattice model settings, eventually leading to the ultimate goal of implementations for off-lattice models.

Mixing energy models in genetic algorithms for on-lattice protein structure prediction

Protein structure prediction (PSP) is computationally a very challenging problem. The challenge largely comes from the fact that the energy function that needs to be minimised in order to obtain the native structure of a given protein is not clearly known. A high resolution 20 × 20 energy model could better capture the behaviour of the actual energy function than a low resolution energy model such as hydrophobic polar. However, the fine grained details of the high resolution interaction energy matrix are often not very informative for guiding the search. In contrast, a low resolution energy model could effectively bias the search towards certain promising directions. In this paper, we develop a genetic algorithm that mainly uses a high resolution energy model for protein structure evaluation but uses a low resolution HP energy model in focussing the search towards exploring structures that have hydrophobic cores. We experimentally show that this mixing of energy models leads to significant lower energy structures compared to the state-of-the-art results.

The road not taken: retreat and diverge in local search for simplified protein structure prediction

BACKGROUND

Given a protein's amino acid sequence, the protein structure prediction problem is to find a three dimensional structure that has the native energy level. For many decades, it has been one of the most challenging problems in computational biology. A simplified version of the problem is to find an on-lattice self-avoiding walk that minimizes the interaction energy among the amino acids. Local search methods have been preferably used in solving the protein structure prediction problem for their efficiency in finding very good solutions quickly. However, they suffer mainly from two problems: re-visitation and stagnancy.

RESULTS

In this paper, we present an efficient local search algorithm that deals with these two problems. During search, we select the best candidate at each iteration, but store the unexplored second best candidates in a set of elite conformations, and explore them whenever the search faces stagnation. Moreover, we propose a new non-isomorphic encoding for the protein conformations to store the conformations and to check similarity when applied with a memory based search. This new encoding helps eliminate conformations that are equivalent under rotation and translation, and thus results in better prevention of re-visitation.

CONCLUSION

On standard benchmark proteins, our algorithm significantly outperforms the state-of-the art approaches for Hydrophobic-Polar energy models and Face Centered Cubic Lattice.