Abstract. Solutions calculated by Evolutionary Algorithms have come to surpass exact methods for solving various problems. The Rubik's Cube multiobjective optimization problem is one such area. In this work we present an evolutionary approach to solve the Rubik's Cube with a low number of moves by building upon the classic Thistlethwaite's approach. We provide a group theoretic analysis of the subproblem complexity induced by Thistlethwaite's group transitions and design an Evolutionary Algorithm from the ground up including detailed derivation of our custom fitness functions. The implementation resulting from these observations is thoroughly tested for integrity and random scrambles, revealing performance that is competitive with exact methods without the need for pre-calculated lookup-tables.

The prediction of essential biological features based on a given protein sequence is a challenging task in computational biology. To limit the amount of in vitro verification, the prediction of essential biological activities gives the opportunity to detect so far unknown sequences with similar properties. Besides the application within the identification of proteins being involved in tumorigenesis, other functional classes of proteins can be predicted. The prediction accuracy depends on the selected machine learning approach and even more on the composition of the descriptor set used. A computational approach based on feedforward neural networks was applied for the prediction of small GTPases. Consequently, this was realized by taking secondary structure and hydrophobicity information as a preprocessing architecture and thus, as descriptors for the neural networks. We developed a neural network cluster, which consists of a filter network and four subfamily networks. The filter network was trained to identify small GTPases and the subfamily networks were trained to assign a small GTPase to one of the subfamilies. The accuracy of the prediction, whether a given sequence represents a small GTPase is very high (98.25%). The classifications of the subfamily networks yield comparable accuracy. The high prediction accuracy of the neural network cluster developed, gives the opportunity to suggest the use of hydrophobicity and secondary structure prediction in combination with a neural network cluster, as a promising method for the prediction of essential biological activities.

As an advanced approach to identify suitable targeting molecules required for various diagnostic and therapeutic interventions, we developed a procedure to devise peptides with customizable features by an iterative computer-assisted optimization strategy. An evolutionary algorithm was utilized to breed peptides in silico and the “fitness” of peptides was determined in an appropriate laboratory in vitro assay. The influence of different evolutional parameters and mechanisms such as mutation rate, crossover probability, gaussian variation and fitness value scaling on the course of this artificial evolutional process was investigated. As a proof of concept peptidic ligands for a model target molecule, the cell surface glycolipid ganglioside GM1, were identified. Consensus sequences describing local fitness optima were reached from diverse sets of L- and proteolytically stable D lead peptides. Ten rounds of evolutional optimization encompassing a total of just 4400 peptides lead to an increase in affinity of the peptides towards fluorescently labeled ganglioside GM1 by a factor of 100 for L- and 400 for D-peptides.

In nature, building block-based biopolymers can adapt to functional and environmental demands by recombination and mutation of the monomer sequence. We present here an analogous, artificial evolutionary optimization process which we have applied to improve the functionality of cell-penetrating peptide molecules. The “evolution” consisted of repeated rounds of in silico peptide sequence alterations using a genetic algorithm followed by in vitro peptide synthesis, experimental analysis, and ranking according to their “fitness” (i.e., their ability to carry the cargo carboxyfluorescein into cultured cells). The genetic algorithm-based optimization method was customized and adapted from former successful applications in the lab to realize an early convergence and a minimum number of in vitro and in silico processing steps by configured settings derived from empirical in silico simulation. We started out with 20 “lead peptides” which we had previously identified as top performers regarding their ability to enter cultured cells. Ten breeding rounds comprising 240 peptides each yielded a peptide population of which the top 10 candidates displayed a 6-fold (median values) increase in its cell-penetration capability compared with the top 10 lead peptides, and two consensus sequences emerged which represent local fitness optima. In addition, the cell-penetrating potential could be proven independently of the carboxyfluorescein cargo in an alternative setting. Our results demonstrate that we have established a powerful optimization technology that can be used to further improve peptides with known functionality and adapt them to specific applications.

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