Enumeration and comprehensive in-silico modeling of three-helix bundle structures composed of typical αα-hairpins

Background The design of protein structures from scratch requires special attention to the combination of the types and lengths of the secondary structures and the loops required to build highly designable backbone structure models. However, it is difficult to predict the combinations that result in globular and protein-like conformations without simulations. In this study, we used single-chain three-helix bundles as simple models of protein tertiary structures and sought to thoroughly investigate the conditions required to construct them, starting from the identification of the typical αα-hairpin motifs. Results First, by statistical analysis of naturally occurring protein structures, we identified three αα-hairpins motifs that were specifically related to the left- and right-handedness of helix-helix packing. Second, specifying these αα-hairpins motifs as junctions, we performed sequence-independent backbone-building simulations to comparatively build single-chain three-helix bundle structures and identified the promising combinations of the length of the α-helix and αα-hairpins types that results in tight packing between the first and third α-helices. Third, using those single-chain three-helix bundle backbone structures as template structures, we designed amino acid sequences that were predicted to fold into the target topologies, which supports that the compact single-chain three-helix bundles structures that we sampled show sufficient quality to allow amino-acid sequence design. Conclusion The enumeration of the dominant subsets of possible backbone structures for small single-chain three-helical bundle topologies revealed that the compact foldable structures are discontinuously and sparsely distributed in the conformational space. Additionally, although the designs have not been experimentally validated in the present research, the comprehensive set of computational structural models generated also offers protein designers the opportunity to skip building similar structures by themselves and enables them to quickly focus on building specialized designs using the prebuilt structure models. The backbone and best design models in this study are publicly accessible from the following URL: https://doi.org/10.5281/zenodo.4321632.

Bioinspired Origami: Case Studies Using a Keyword Search Algorithm

Numerous folding patterns, structures, and behaviors exist in nature that may provide design solutions to engineering problems. While applying biological solutions to engineering design is evidently valuable, the retrieval of useful design inspiration remains a primary challenge preventing the transfer of knowledge from biology to the engineering domain. In prior research, information retrieval techniques are employed to retrieve useful biological design solutions and a text-based search algorithm is developed to return passages where folding in nature is observed. The search algorithm, called FoldSearch, integrates tailored biological keywords and filtering methods to retrieve passages from an extensive biological corpus. The objective of this paper is two-fold — 1) to demonstrate the functionality of FoldSearch, and 2) to create abstract models of the retrieved biological systems from FoldSearch which can be used for the development of novel origami crease patterns and foldable structures. In this paper, the utility of FoldSearch is demonstrated through two case studies where the retrieved biological examples undergo a design abstraction process that leads to the development of bioinspired origami crease patterns and novel foldable structures. The abstraction process is presented as a systematic design methodology for bioinspired origami for the growing research field of origami engineering.

Foldable Hexagonal Structures Based on the Threefold-Symmetric Bricard Linkage

The threefold-symmetric Bricard linkage, a special type of Bricard linkage, is able to generate spatial motion in 3D space with well-defined threefold rotational symmetries and three symmetric planes, which makes it a robust base linkage in designing many one-degrees-of-freedom (DOF) foldable structures. However, its practical applications are limited, as the design method with the consideration of the actual assembly is still an ambiguous area. In this paper, a foldable hexagonal structure based on the alternative form of the threefold-symmetric Bricard linkage is designed and manufactured. Geometric conditions for achieving the desired deployment are analyzed at first. Then the relationship among kinematic variables of the linkage and the geometric parameters of physical bars with a regular triangular cross-section are set up. Finally, an intuitive approach is presented to detect two types of physical blockages in the motion paths of deployment. The proposed method supplies a convenient way to design foldable hexagonal structures for potential practical applications.

Designing Fractal Origami Tessellations Through Eigen Analysis

This article investigates a method of designing fractal origami tessellations through eigen analysis. Foldable structures with hierarchical geometric features could be beneficial in applications where a graded functionality is desired. A representative unit in an origami tessellation is modeled as networked truss elements with torsional springs at fold lines. Eigen analysis and nonlinear mechanics analysis of the representative unit with fractal boundary conditions reveal the foldability of a given fractal origami crease pattern out of its flat state. This configuration can be used to construct a folded fractal origami tessellation with a desired number of fractal levels, which can then be used to evaluate its functional merit. The design process is demonstrated for the design of a fractal origami tessellation with tailored boundary shape change (from rectangular to trapezoidal) through folding, that could be used as an enabling mechanism for an adaptive wing section.

Rigid Foldability of Generalized Triangle Twist Origami Pattern and Its Derived 6R Linkages

Rigid origami is a restrictive form of origami that permits continuous motion between folded and unfolded states along the predetermined creases without stretching or bending of the facets. It has great potential in engineering applications, such as foldable structures that consist of rigid materials. The rigid foldability is an important characteristic of an origami pattern, which is determined by both the geometrical parameters and the mountain-valley crease (M-V) assignments. In this paper, we present a systematic method to analyze the rigid foldability and motion of the generalized triangle twist origami pattern using the kinematic equivalence between the rigid origami and the spherical linkages. All schemes of M-V assignment are derived based on the flat-foldable conditions among which rigidly foldable ones are identified. Moreover, a new type of overconstrained 6R linkage and a variation of doubly collapsible octahedral Bricard are developed by applying kirigami technique to the rigidly foldable pattern without changing its degree-of-freedom. The proposed method opens up a new way to generate spatial overconstrained linkages from the network of spherical linkages. It can be readily extended to other types of origami patterns.