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

Bilinear optimization of protein structure prediction: An exact approach via AB off-lattice model

Protein structure prediction (PSP) remains a central challenge in computational biology due to its inherent complexity and high dimensionality. While numerous heuristic approaches have appeared in the literature, their success varies. The AB off-lattice model, which characterizes proteins as sequences of A (hydrophobic) and B (hydrophilic) beads, presents a simplified perspective on PSP. This work presents a mathematical optimization-based methodology capitalizing on the off-lattice AB model. Dissecting the inherent non-linearities of the energy landscape of protein folding allowed for formulating the PSP as a bilinear optimization problem. This formulation was achieved by introducing auxiliary variables and constraints that encapsulate the nuanced relationship between the protein's conformational space and its energy landscape. The proposed bilinear model exhibited notable accuracy in pinpointing the global minimum energy conformations on a benchmark dataset presented by the Protein Data Bank (PDB). Compared to traditional heuristic-based methods, this bilinear approach yielded exact solutions, reducing the likelihood of local minima entrapment. This research highlights the potential of reframing the traditionally non-linear protein structure prediction problem into a bilinear optimization problem through the off-lattice AB model. Such a transformation offers a route toward methodologies that can determine the global solution, challenging current PSP paradigms. Exploration into hybrid models, merging bilinear optimization and heuristic components, might present an avenue for balancing accuracy with computational efficiency.

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.