CGRAP: A Web Server for Coarse-Grained Rigidity Analysis of Proteins

Elucidating protein rigidity offers insights about protein conformational changes. An understanding of protein motion can help speed drug development, and provide general insights into the dynamic behaviors of biomolecules. Existing rigidity analysis techniques employ fine-grained, all-atom modeling, which has a costly run-time, particularly for proteins made up of more than 500 residues. In this work, we introduce coarse-grained rigidity analysis, and showcase that it provides flexibility information about a protein that is similar in accuracy to an all-atom modeling approach. We assess the accuracy of the coarse-grained method relative to an all-atom approach via a comparison metric that reasons about the largest rigid clusters of the two methods. The apparent symmetry between the all-atom and coarse-grained methods yields very similar results, but the coarse-grained method routinely exhibits 40% reduced run-times. The CGRAP web server outputs rigid cluster information, and provides data visualization capabilities, including a interactive protein visualizer.

Structure and in silico simulations of a cold-active esterase reveals its prime cold-adaptation mechanism

Here we determined the structure of a cold active family IV esterase (EstN7) cloned from Bacillus cohnii strain N1. EstN7 is a dimer with a classical α/β hydrolase fold. It has an acidic surface that is thought to play a role in cold-adaption by retaining solvation under changed water solvent entropy at lower temperatures. The conformation of the functionally important cap region is significantly different to EstN7's closest relatives, forming a bridge-like structure with reduced helical content providing greater access to the active site through more than one substrate access tunnel. However, dynamics do not appear to play a major role in cold adaption. Molecular dynamics at different temperatures, rigidity analysis, normal mode analysis and geometric simulations of motion confirm the flexibility of the cap region but suggest that the rest of the protein is largely rigid. Rigidity analysis indicates the distribution of hydrophobic tethers is appropriate to colder conditions, where the hydrophobic effect is weaker than in mesophilic conditions due to reduced water entropy. Thus, it is likely that increased substrate accessibility and tolerance to changes in water entropy are important for of EstN7's cold adaptation rather than changes in dynamics.

Integrating Rigidity Analysis into the Exploration of Protein Conformational Pathways Using RRT* and MC

To understand how proteins function on a cellular level, it is of paramount importance to understand their structures and dynamics, including the conformational changes they undergo to carry out their function. For the aforementioned reasons, the study of large conformational changes in proteins has been an interest to researchers for years. However, since some proteins experience rapid and transient conformational changes, it is hard to experimentally capture the intermediate structures. Additionally, computational brute force methods are computationally intractable, which makes it impossible to find these pathways which require a search in a high-dimensional, complex space. In our previous work, we implemented a hybrid algorithm that combines Monte-Carlo (MC) sampling and RRT*, a version of the Rapidly Exploring Random Trees (RRT) robotics-based method, to make the conformational exploration more accurate and efficient, and produce smooth conformational pathways. In this work, we integrated the rigidity analysis of proteins into our algorithm to guide the search to explore flexible regions. We demonstrate that rigidity analysis dramatically reduces the run time and accelerates convergence.

Integrating Rigidity Analysis into the Exploration of Protein Conformational Pathways using RRT* and MC

To understand how proteins function on a cellular level, it is of paramount importance to understand their structures and dynamics, including the conformational changes they undergo to carry out their function. For the aforementioned reasons, the study of large conformational changes in proteins has been an interest to researchers for years. However, since some proteins experience rapid and transient conformational changes, it is hard to experimentally capture the intermediate structures. Additionally, computational brute force methods are computationally intractable, which makes it impossible to find these pathways which require a search in a high-dimensional, complex space. In our previous work, we implemented a hybrid algorithm that combines Monte-Carlo (MC) sampling and RRT*, a version of the Rapidly Exploring Random Trees (RRT) robotics-based method, to make the conformational exploration more accurate and efficient, and produce smooth conformational pathways. In this work, we integrated the rigidity analysis of proteins into our algorithm to guide the search to explore flexible regions. We demonstrate that rigidity analysis dramatically reduces the run time and accelerates convergence.

Structure and dynamics of a cold-active esterase reveals water entropy and active site accessibility as the likely drivers for cold-adaptation

Cold-active esterases hold great potential for undertaking useful biotransformations at low temperatures. Here, we determined the structure of a cold active family IV esterase (EstN7) cloned from Bacillus cohnii strain N1, which has an apparent melting temperature of 26°C. EstN7 is a dimer with a classical α/β hydrolase fold. It has an acidic surface that is thought to play a role in cold-adaption by retaining solvation under changed water solvent entropy at lower temperatures. However, dynamics do not appear to play a major role in cold adaption. Comparison of B-factors with the closest related mesophilic and thermophilic esterases suggests there is little difference in dynamics with the catalytically important N-terminal cap comprising the main dynamic element. Molecular dynamics, rigidity analysis, normal mode analysis and geometric simulations of motion confirm the flexibility of the cap region but suggest that the rest of the protein is largely rigid. Rigidity analysis indicates the distribution of hydrophobic tethers is appropriate to colder conditions, where the hydrophobic effect is weaker than in mesophilic conditions due to reduced water entropy. The conformation of the cap region is significantly different to EstN7’s closest relatives, forming a bridge-like structure with reduced helical content providing more than one access tunnel through to the active site. Thus, it is likely that increased substrate accessibility and tolerance to changes in water entropy are the main drivers of EstN7’s cold adaptation rather than changes in dynamics.

A Novel Ortho-Triplex Tensegrity Derived by the Linkage-Truss Transformation With Prestress-Stability Analysis Using Screw Theory

This paper presents a novel tensegrity structure derived from the tensegrity triplex (also called the simplex or regular triangular prism) by using the linkage-truss transformation. In this paper, the tensegrity triplex is first transformed into a 6R linkage with vertical members as revolute joints and is coined the triplex linkage. With this, a novel 6R linkage was derived, whose joint axes are perpendicular to the joint axes of the triplex linkage and is coined the ortho-triplex linkage. Rigidity analysis based on screw theory demonstrates that both obtained linkages with infinitesimal mobility are prestress stable. Finally, transforming the ortho-triplex linkage to a truss, by using cables for tensional members and struts for compressional members, leads to a novel tensegrity that is coined ortho-triplex tensegrity. A non-dimensional quadratic form is further provided to analyze the sensitivity of prestress-stability in terms of the structural parameters. The process of derivation of this novel tensegrity presents a new way of designing tensegrity structures with prestress-stability analysis based on screw theory.