Insights into mechanism kinematics for protein motion simulation

Background: The high demanding computational requirements necessary to carry out protein motion simulations make it difficult to obtain information related to protein motion. On the one hand, molecular dynamics simulation requires huge computational resources to achieve satisfactory motion simulations. On the other hand, less accurate procedures such as interpolation methods, do not generate realistic morphs from the kinematic point of view. Analyzing a protein's movement is very similar to serial robots; thus, it is possible to treat the protein chain as a serial mechanism composed of rotational degrees of freedom. Recently, based on this hypothesis, new methodologies have arisen, based on mechanism and robot kinematics, to simulate protein motion. Probabilistic roadmap method, which discretizes the protein configurational space against a scoring function, or the kinetostatic compliance method that minimizes the torques that appear in bonds, aim to simulate protein motion with a reduced computational cost. Results: In this paper a new viewpoint for protein motion simulation, based on mechanism kinematics is presented. The paper describes a set of methodologies, combining different techniques such as structure normalization normalization processes, simulation algorithms and secondary structure detection procedures. The combination of all these procedures allows to obtain kinematic morphs of proteins achieving a very good computational cost-error rate, while maintaining the biological meaning of the obtained structures and the kinematic viability of the obtained motion. Conclusions: The procedure presented in this paper, implements different modules to perform the simulation of the conformational change suffered by a protein when exerting its function. The combination of a main simulation procedure assisted by a secondary structure process, and a side chain orientation strategy, allows to obtain a fast and reliable simulations of protein motion.The authors wish to acknowledge the financial support received from the Spanish Government through the Ministerio de Economia y Competitividad (Project DPI2011-22955), the Regional Government of the Basque Country through the Departamento de Educacion, Universidades e Investigacion (Project IT445-10) and UPV/EHU under program UFI 11/29 and by Grants from the Department of Education, Universities and Research of the Basque Government (PI2010-17), from the Department of Industry of the Basque Government (ETORTEK Program IE05-147 and IE07-202), from the Bizkaia Country (Exp. 7/13/08/2006/11 and 7/13/08/2005/14), and from the Spanish Ministry of Economy and Innovation (BFU2010-17857 and SICI-CONSOLIDER Program CSD2008-00005) (all to L.A.M.-C.)

Kinematic Flexibility Analysis: Hydrogen Bonding Patterns Impart a Spatial Hierarchy of Protein Motion

Elastic network models (ENM) and constraint-based, topological rigidity analysis are two distinct, coarse-grained approaches to study conformational flexibility of macromolecules. In the two decades since their introduction, both have contributed significantly to insights into protein molecular mechanisms and function. However, despite a shared purpose of these approaches, the topological nature of rigidity analysis, and thereby the absence of motion modes, has impeded a direct comparison. Here, we present an alternative, kinematic approach to rigidity analysis, which circumvents these drawbacks. We introduce a novel protein hydrogen bond network spectral decomposition, which provides an orthonormal basis for collective motions modulated by non-covalent interactions, analogous to the eigenspectrum of normal modes, and decomposes proteins into rigid clusters identical to those from topological rigidity. Our kinematic flexibility analysis bridges topological rigidity theory and ENM, and enables a detailed analysis of motion modes obtained from both approaches. Our analysis reveals that collectivity of protein motions, reported by the Shannon entropy, is significantly lower for rigidity theory versus normal mode approaches. Strikingly, kinematic flexibility analysis suggests that the hydrogen bonding network encodes a protein-fold specific, spatial hierarchy of motions, which goes nearly undetected in ENM. This hierarchy reveals distinct motion regimes that rationalize protein stiffness changes observed from experiment and molecular dynamics simulations. A formal expression for changes in free energy derived from the spectral decomposition indicates that motions across nearly 40% of modes obey enthalpy-entropy compensation. Taken together, our analysis suggests that hydrogen bond networks have evolved to modulate protein structure and dynamics

Sign Gradient Descent Algorithms for Kinetostatic Protein Folding

This paper proposes a sign gradient descent (SGD) algorithm for predicting the three-dimensional folded protein molecule structures under the kinetostatic compliance method (KCM). In the KCM framework, which can be used to simulate the range of motion of peptide-based nanorobots/nanomachines, protein molecules are modeled as a large number of rigid nano-linkages that form a kinematic mechanism under motion constraints imposed by chemical bonds while folding under the kinetostatic effect of nonlinear interatomic force fields. In a departure from the conventional successive kinetostatic fold compliance framework, the proposed SGD-based iterative algorithm in this paper results in convergence to the local minima of the free energy of protein molecules corresponding to their final folded conformations in a faster and more robust manner. KCMbased folding dynamics simulations of the backbone chains of protein molecules demonstrate the effectiveness of the proposed algorithm.Comment: 6 pages, Accepted in 2023 International Conference on Manipulation, Automation and Robotics at Small Scales (MARSS 2023

Hi-Fidelity Simulation of the Self-Assembly and Dynamics of Colloids and Polymeric Solutions with Long Range Interactions

Modeling the equilibrium properties and dynamic response of the colloidal and polymeric solutions provides valuable insight into numerous biological and industrial processes and facilitates development of novel technologies. To this end, the centerpiece of this research is to incorporate the long range electrostatic or hydrodynamic interactions via computationally efficient algorithms and to investigate the effect of these interactions on the self-assembly of colloidal particles and dynamic properties of polymeric solutions. Specifically, self-assembly of a new class of materials, namely bipolar Janus nano-particles, is investigated via molecular dynamic simulation in order to establish the relationship between individual particle characteristics, such as surface charge density, particle size, etc., and the final structure formation. Furthermore, the importance of incorporating the long range electrostatic interaction in achieving the corresponding final morphology is discussed. The dynamic properties of polymeric solutions are investigated via two parallel pathways. In the first approach, force-extension behavior of the flexible polyelectrolytes is probed via fine-grained Brownian dynamics simulation of the bead-rod model. The presented model accurately incorporates the excluded volume interaction in order to capture the effect of salt concentration on the force-extension response of polyelectrolyte chain as observed in the single chain experiments. It is shown that accurate incorporation of the excluded volume effect on a long chain of more than 500 Kuhn segments is necessary to reach the universal scaling both for equilibrium properties and force-extension response. Next, a new force law is extracted using a novel discrete Pade approximant from the constant-force ensemble result of the bead-rod model. The new force law is implemented in the coarse-grained meso-scale bead-spring model with hydrodynamic interactions in order to investigate the dynamics of flexible macromolecules in the athermal solvent. In the second approach the computational cost of the long range hydrodynamic interaction in dilute solution of polymeric chains with constrains is reduced via development of a new computational technique based on the conjugate gradient and Krylov subspace methods. Moreover, an algorithm for estimating the contribution of various forces to the transient polymeric stress tensor is introduced and employed in order to investigate transient dynamics of the solution of the flexible polymeric chains

Computational Modeling and Design of Protein and Polymeric Nano-Assemblies

Advances in nanotechnology have the potential to utilize biological and polymeric systems to address fundamental scientific and societal issues, including molecular electronics and sensors, energy-relevant light harvesting, â??greenâ?? catalysis, and environmental cleanup. In many cases, synthesis and fabrication are well within grasp, but designing such systems requires simultaneous consideration of large numbers of degrees of freedom including structure, sequence, and functional properties. In the case of protein design, even simply considering amino acid identity scales exponentially with the protein length. This work utilizes computational techniques to develop a fundamental, molecularly detailed chemical and physical understanding to investigate and design such nano-assemblies. Throughout, we leverage a probabilistic computational design approach to guide the identification of protein sequences that fold to predetermined structures with targeted function. The statistical methodology is encapsulated in a computational design platform, recently reconstructed with improvements in speed and versatility, to estimate site-specific probabilities of residues through the optimization of an effective sequence free energy. This provides an information-rich perspective on the space of possible sequences which is able to harness the incorporation of new constraints that fit design objectives. The approach is applied to the design and modeling of protein systems incorporating non-biological cofactors, namely (i) an aggregation prone peptide assembly to bind uranyl and (ii) a protein construct to encapsulate a zinc porphyrin derivative with unique photo-physical properties. Additionally, molecular dynamics simulations are used to investigate purely synthetic assemblies of (iii) highly charged semiconducting polymers that wrap and disperse carbon nanotubes. Free energy calculations are used to explore the factors that lead to observed polymer-SWNT super-structures, elucidating well-defined helical structures; for chiral derivatives, the simulations corroborate a preference for helical handedness observed in TEM and AFM data. The techniques detailed herein, demonstrate how advances in computational chemistry allot greater control and specificity in the engineering of novel nano-materials and offer the potential to greatly advance applications of these systems

A New Phenomenon: Sub-Tg, Solid-State, Plasticity-Induced Bonding in Polymers

Polymer self-adhesion due to the interdiffusion of macromolecules has been an active area of research for several decades [70, 43, 62, 42, 72, 73, 41]. Here, we report a new phenomenon of sub-Tg, solid-state, plasticity-induced bonding; where amorphous polymeric films were bonded together in a period of time on the order of a second in the solid-state at ambient temperatures nearly 60 K below their glass transition temperature (Tg) by subjecting them to active plastic deformation. Despite the glassy regime, the bulk plastic deformation triggered the requisite molecular mobility of the polymer chains, causing interpenetration across the interfaces held in contact. Quantitative levels of adhesion and the morphologies of the fractured interfaces validated the sub-Tg, plasticity-induced, molecular mobilization causing bonding. No-bonding outcomes (i) during the compression of films in a near hydrostatic setting (which inhibited plastic flow) and (ii) between an 'elastic' and a 'plastic' film further established the explicit role of plastic deformation in this newly reported sub-Tg solid-state bonding