Abstract
The measurement of thermodynamic properties of chemical or biological reactions were often confined to experimental means, which produced overall measurements of properties being investigated, but were usually susceptible to pitfalls of being too general. Among the thermodynamic properties that are of interest, reaction rates hold the greatest significance, as they play a critical role in reaction processes where speed is of essence, especially when fast association may enhance binding affinity of reaction molecules. Association reactions with high affinities often involve the formation of a intermediate state, which can be demonstrated by a hyperbolic reaction curve, but whose low abundance in reaction mixture often preclude the possibility of experimental measurement. Therefore, we resorted to computational methods using predefined reaction models that model the intermediate state as the reaction progresses. Here, we present a novel method called AKPE (ANN-Dependent Kinetic Parameter Extraction), our goal is to investigate the association/dissociation rate constants and the concentration dynamics of lowly-populated states (intermediate states) in the reaction landscape. To reach our goal, we simulated the chemical or biological reactions as system of differential equations, employed artificial neural networks (ANN) to model experimentally measured data, and utilized Particle Swarm Optimization (PSO) algorithm to obtain the globally optimum parameters in both the simulation and data fitting. In the Results section, we have successfully modeled a protein association reaction using AKPE, obtained the kinetic rate constants of the reaction, and constructed a full concentration versus reaction time curve of the intermediate state during the reaction. Furthermore, judging from the various validation methods that the method proposed in this paper has strong robustness and accuracy.
Highlights
The association of small chemicals or large biological molecules in a rapid, specific way is an essential step in various chemical or biological processes ranging from enzyme catalysis to regulation of immune responses [1,2]; extracting key thermodynamic information from those reactions will greatly benefit the understanding of those chemical or biological processes
The coefficients of the differential equations correspond to the kinetic parameters of the reactions. secondly, a neural network will be used to approximate the aforementioned differential equations according to experimental data, the coefficients in differential equations were incorporated into neural networks
By incorporating differential equations in continuous time regime, we arrive at a set of deterministic rate-based equations describing the model, taking the existence of an intermediate state into account, the reaction dynamics of different fraction of MPro-C can be described with mass action kinetics below: 2Mf a(t)ka d[MI] dt
Summary
The association of small chemicals or large biological molecules in a rapid, specific way is an essential step in various chemical or biological processes ranging from enzyme catalysis to regulation of immune responses [1,2]; extracting key thermodynamic information from those reactions will greatly benefit the understanding of those chemical or biological processes. Two of the most prominent thermodynamic properties that define a reaction are association rates and reaction intermediate state concentrations [3]. The rate of association spans a range from 102 to 109 M−1s−1; it is limited either by diffusion or subsequent chemical processes such as conformational rearrangement [1]. Association rates can be categorized as time-dependent and time-independent [2,4]. Time-independent reactions rates look at molecule diffusion and interactions on a mass scale that exhibit overall reaction kinetics. Time-independent reaction rates can be modeled through approximation [7]
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