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Introduction: Background Material
Published in Nassir H. Sabah, Neuromuscular Fundamentals, 2020
In general, a reaction cannot proceed unless reacting molecules possess a minimum energy known as the activation energy, Ea, of the reaction (Figure 1.14). The horizontal coordinate, representing the progress of the reaction along a reaction pathway, is referred to as the reaction coordinate. It is usually a geometric parameter, such as bond length or bond angle, that changes during the conversion of one or more reactants into one or more products. A simple classical example is the breaking of a covalent bond in the dissociation of a hydrogen molecule into two hydrogen atoms.
Some Underlying Physical Principles
Published in Clive R. Bagshaw, Biomolecular Kinetics, 2017
The activation energy, Ea, implies that there is some sort of barrier that must be surmounted if a reactant molecule, A, is to successfully convert to product, B. Indeed, the transition-state theory, outlined in Equations 3.21 through 3.24, indicates that this barrier includes a term for the activation entropy as well as the activation enthalpy. An elementary reaction is commonly depicted as in Figure 3.5a, where the height of the barrier above the ground-state free energy of reactant A is defined by ΔG‡, while the difference between the ground-state A and B energy positions is defined by ΔG. The peak of the barrier represents the transition state, which is conventionally denoted with the ‡ symbol. This is not equivalent to the “top of the mountain” but rather the “saddle of a mountain pass,” as shown in the contour plot (Figure 3.6). The path of lowest energy from ground state A to product B defines the reaction coordinate and is a measure of the progress of the reaction.
Adhesive Properties Studied by AFM
Published in Malgorzata Lekka, Cellular Analysis by Atomic Force Microscopy, 2017
The bond dissociation1 (or molecular complex unbinding) is usually approximated by a particle moving over an energy barrier of a one-dimensional energy landscape describing the binding pocket of two interacting molecules [3]. Figure 5.1 schematically presents one-dimensional energy landscape as a model for a single molecular bond or complex interaction as a function of a reaction coordinate x. The bound state (characterized by a deep energy minimum ΔG0 appearing at small distances, usually set as “zero”) is separated from the unbound one by a transition state (ΔGa) represented by an energy barrier located at the distance xb.
A molecular dynamics approach towards evaluating osmotic and thermal stress in the extracellular environment
Published in International Journal of Hyperthermia, 2018
David Fuentes, Nina M. Muñoz, Chunxiao Guo, Urzsula Polak, Adeeb A. Minhaj, William J. Allen, Michael C. Gustin, Erik N. K. Cressman
Figure 7(b) shows the pulling force as a function of time in pulling the RGD domain along the reaction coordinate, ξ, from the αVβ3 integrin binding site. Figure 7(a) provides a geometrical reference for the fibronectin–integrin configurations before and after pulling along the reaction coordinate. The configuration at the initial reaction coordinates begins with the structure of the original molecular model. The steered MD simulation pulls the fibronectin from the integrin binding site as illustrated. The point of maximum force occurs at approximately 100 ps and corresponds to the instant just before the bonds between integrin and fibronectin were broken. Figure 7(c) plots free energy as a function of the linear reaction coordinate. At large reaction coordinate values, fibronectin is disassociated from the integrin binding site and results in the largest free energy values. Free energy change is computed as the difference between the largest free energy value and the free energy when the fibronectin is close to the integrin binding site, ξ ≈ 5.5 nm. Under control conditions, 37 °C and 0 mM salt added, the free energy change required for fibronectin binding to integrin was computed as
Design, synthesis and characterization of enzyme-analogue-built polymer catalysts as artificial hydrolases
Published in Artificial Cells, Nanomedicine, and Biotechnology, 2019
Divya Mathew, Benny Thomas, Karakkattu Subrahmanian Devaky
In a simple enzyme-catalyzed reaction scheme (Figure 4), the reaction coordinate diagram shows that in order for the enzyme to catalyze the reaction, ΔGETS must be greater than ΔGES. Enzymes are efficient catalysts because they exhibit rapid catalytic turnovers. That is, enzymes typically have lower affinity for product than substrate, and many enzymes undergo conformational changes that favour the release of product. In a simple case, the kinetics can be described by the Michaelis–Menten equation.
The prediction of protein–ligand unbinding for modern drug discovery
Published in Expert Opinion on Drug Discovery, 2022
Qianqian Zhang, Nannan Zhao, Xiaoxiao Meng, Fansen Yu, Xiaojun Yao, Huanxiang Liu
The plain MD simulation is theoretically more accurate than other enhanced sampling methods for protein–ligand unbinding. D. E. Shaw et al. used the supercomputer ANTON for the first time to report an example of the unbiased MD simulation of spontaneous protein–ligand binding [21]. The umbrella sampling (US) method that was developed in early as the 1970s is a pioneer of enhanced sampling MD simulation that can promote the protein–ligand unbinding process. Later, the gradual proposal of additional enhanced sampling methods, such as SMD, MetaD, random acceleration MD (RAMD) and ligand Gaussian accelerated MD, greatly accelerated the study of protein–ligand dissociation kinetics. The computational methods for studying protein–ligand unbinding that have been developed in the past 20 years can be divided into two main categories, namely, biased sampling and unbiased sampling (Figure 1). WES [12] and MSM [13] are the two main unbiased sampling methods. Biased sampling methods have gradually been developed starting in approximately 2000. These methods can reduce the energy barrier of a system by adding an extra bias force or bias potential at the selected reaction coordinate (RC) or collective variable (CV) to accelerate sampling. Although unbiased sampling methods can provide highly accurate calculation results and do not introduce bias potential, they do not enable the facile observation of ligand dissociation on a reasonable time scale. The enhanced sampling method can accelerate protein–ligand dissociation but also reduces the accuracy of the prediction results. Here, we briefly introduce the basic principles of these methods and their derived variants.