Guided simulated annealing method for optimization problems

Using convolutional neural network denoising to reduce ambiguity in X-ray coherent diffraction imaging

The inherent ambiguity in reconstructed images from coherent diffraction imaging (CDI) poses an intrinsic challenge, as images derived from the same dataset under varying initial conditions often display inconsistencies. This study introduces a method that employs the Noise2Noise approach combined with neural networks to effectively mitigate these ambiguities. We applied this methodology to hundreds of ambiguous reconstructed images retrieved from a single diffraction pattern using a conventional retrieval algorithm. Our results demonstrate that ambiguous features in these reconstructions are effectively treated as inter-reconstruction noise and are significantly reduced. The post-Noise2Noise treated images closely approximate the average and singular value decomposition analysis of various reconstructions, providing consistent and reliable reconstructions.

On the characterization and software implementation of general protein lattice models

models of proteins have been widely used as a practical means to computationally investigate general properties of the system. In lattice models any sterically feasible conformation is represented as a self-avoiding walk on a lattice, and residue types are limited in number. So far, only two- or three-dimensional lattices have been used. The inspection of the neighborhood of alpha carbons in the core of real proteins reveals that also lattices with higher coordination numbers, possibly in higher dimensional spaces, can be adopted. In this paper, a new general parametric lattice model for simplified protein conformations is proposed and investigated. It is shown how the supporting software can be consistently designed to let algorithms that operate on protein structures be implemented in a lattice-agnostic way. The necessary theoretical foundations are developed and organically presented, pinpointing the role of the concept of main directions in lattice-agnostic model handling. Subsequently, the model features across dimensions and lattice types are explored in tests performed on benchmark protein sequences, using a Python implementation. Simulations give insights on the use of square and triangular lattices in a range of dimensions. The trend of potential minimum for sequences of different lengths, varying the lattice dimension, is uncovered. Moreover, an extensive quantitative characterization of the usage of the so-called "move types" is reported for the first time. The proposed general framework for the development of lattice models is simple yet complete, and an object-oriented architecture can be proficiently employed for the supporting software, by designing ad-hoc classes. The proposed framework represents a new general viewpoint that potentially subsumes a number of solutions previously studied. The adoption of the described model pushes to look at protein structure issues from a more general and essential perspective, making computational investigations over simplified models more straightforward as well.

Inference of gene regulatory networks using time-series data: a survey

The advent of high-throughput technology like microarrays has provided the platform for studying how different cellular components work together, thus created an enormous interest in mathematically modeling biological network, particularly gene regulatory network (GRN). Of particular interest is the modeling and inference on time-series data, which capture a more thorough picture of the system than non-temporal data do. We have given an extensive review of methodologies that have been used on time-series data. In realizing that validation is an impartible part of the inference paradigm, we have also presented a discussion on the principles and challenges in performance evaluation of different methods. This survey gives a panoramic view on these topics, with anticipation that the readers will be inspired to improve and/or expand GRN inference and validation tool repository.

Structure optimization and folding mechanisms of off-lattice protein models using statistical temperature molecular dynamics simulation: Statistical temperature annealing

The recently proposed statistical temperature molecular dynamics (STMD) algorithm [Kim, Phys. Rev. Lett. 97, 050601 (2006)] is used as the core of an optimization algorithm, statistical temperature annealing (STA), for finding low-lying energy minima of complex potential energy landscapes. Since STMD realizes a random walk in energy, the idea is simply to initiate repeated minimizations from configurations in the low-energy segments of STMD trajectories. STA is tested in structural optimization of various off-lattice AB and extended AB protein models in two and three dimensions with different chain lengths. New putative ground states were found for the two- and three-dimensional AB 55-mer, and for the three-dimensional extended AB 21-mer and 55-mer. The distinct folding features of the models are analyzed in terms of the statistical temperature and other representations of the structure of the potential energy landscape. It is shown that the characteristic behavior of the statistical temperature undergoes a qualitative change with the inclusion of a torsional potential in the extended AB model, as the more rigid backbone makes the potential energy landscape more funnel-like.

Biopolymer structure simulation and optimization via fragment regrowth Monte Carlo

An efficient exploration of the configuration space of a biopolymer is essential for its structure modeling and prediction. In this study, the authors propose a new Monte Carlo method, fragment regrowth via energy-guided sequential sampling (FRESS), which incorporates the idea of multigrid Monte Carlo into the framework of configurational-bias Monte Carlo and is suitable for chain polymer simulations. As a by-product, the authors also found a novel extension of the Metropolis Monte Carlo framework applicable to all Monte Carlo computations. They tested FRESS on hydrophobic-hydrophilic (HP) protein folding models in both two and three dimensions. For the benchmark sequences, FRESS not only found all the minimum energies obtained by previous studies with substantially less computation time but also found new lower energies for all the three-dimensional HP models with sequence length longer than 80 residues.

Coexistence of ferroelectricity and ferromagnetism in tantalum clusters

The atomic and electronic structures of Ta(N) (N=2-23) clusters have been determined in the framework of pseudopotential density-functional calculations, based upon an unbiased global search with guided simulated annealing to an empirical potential. It is found that the ground-state structures of Ta(N) are very similar to those of Nb(N), showing no preference for the icosahedral growth. Also, a size- and structure-dependent ferroelectricity is found in these tantalum clusters. More importantly, it is found that the ferroelectricity and ferromagnetism can coexist in the homogeneous transition-metal cluster, offering a possibility to obtain a new type of "multiferroic" materials composed of the clusters. Finally, the far-infrared spectroscopy is suggested to be an efficient tool to distinguish the ferroelectric clusters.

A branch and bound algorithm for the protein folding problem in the HP lattice model

A branch and bound algorithm is proposed for the two-dimensional protein folding problem in the HP lattice model. In this algorithm, the benefit of each possible location of hydrophobic monomers is evaluated and only promising nodes are kept for further branching at each level. The proposed algorithm is compared with other well-known methods for 10 benchmark sequences with lengths ranging from 20 to 100 monomers. The results indicate that our method is a very efficient and promising tool for the protein folding problem.

Possible ground-state structure of Au26: A highly symmetric tubelike cage

The stable tubelike Au(N) (N=26-28) has been found using the scalar relativistic all-electron density functional theory calculations, which becomes another powerful candidate for the lowest-energy Au(N), competing in energy with those space-filled structures suggested previously. Unlike the icosahedral "golden" fullerene Au32, these tubelike gold clusters may be closely related to the synthesized single-wall gold nanotubes (SWGNTs). The ground-state Au26 has a hollow tubelike structure constructed from the (6, 0) SWGNT, yielding a high-symmetry D6d cage, based upon which the most stable Au27 and Au28 can be obtained by adding one and two more capped atoms on its one end, respectively.