Solvent Accessible Surface Derivative Calculation
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Solution Overview
Problem
Current molecular dynamics simulations face limitations in accuracy and computational efficiency due to the use of approximate methods for calculating the derivatives of the solvent accessible surface area, which leads to high computational costs and reduced accuracy, especially when using periodic boundary conditions.
Innovation Solution
An exact method is developed to determine the solvent accessible surface area and its derivatives by considering each atom as a sphere and calculating the intersecting areas with neighboring spheres, using a formula to compute the derivatives, which reduces memory requirements and improves processing efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If approximate methods are used for calculating the derivatives of the solvent accessible surface area, then computational speed is improved, but measurement precision deteriorates
Solution Approach 1:
The patent divides the calculation of solvent accessible surface area derivatives into discrete contributions from each atom and its neighboring atoms. By segmenting the molecular system into individual atomic spheres and calculating their pairwise interactions separately, the method achieves both computational efficiency and exact results, resolving the contradiction between speed and precision.
2Measurement precision
If exact methods are used for calculating the derivatives of the solvent accessible surface area, then measurement precision is improved, but device complexity increases
Solution Approach 1:
The patent extracts and utilizes only the essential geometric information needed for derivative calculation - specifically the positions, radii, and intersection points of atomic spheres. By taking out only the necessary data elements and ignoring redundant information, the method achieves exact results with reduced computational complexity.
Solution Approach 2:
The patent changes the approach from numerical differentiation (which requires multiple function evaluations) to analytical differentiation based on geometric parameters. By expressing the solvent accessible surface area as a function of atomic positions and radii, and deriving exact analytical expressions for its derivatives, the method achieves both precision and efficiency.
3Productivity
If approximate methods are used for calculating the solvent accessible surface area, then computational efficiency is improved, but reliability deteriorates
Solution Approach 1:
The patent performs preliminary identification of intersecting atomic spheres and pre-calculates the geometric parameters needed for derivative computation. By preparing the necessary geometric information in advance and organizing it efficiently, the method ensures both high computational efficiency and reliable, exact results for the solvent accessible surface area derivatives.
Data Source
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Figure 3~4
AI summary
For determining knowledge about the dynamics of molecules (M), the derivatives of the surface of each molecule (M) that is accessible by a solvent is determined with respect to atomic coordinates, wherein the molecule (M) comprises a plurality of atoms, a sphere (Bi) is assigned to each atom, the sphere Bi) comprises a radius (ρi) and a center position (ri) and wherein the derivatives of the solvent accessible surface area of the molecule (M) are determined depending on the sum of the derivatives of the solvent accessible surface areas (S) of its atoms. In order to speed up the determination of the derivatives of the solvent accessible surface area, it is suggested to determine all the contours (Cm) for each sphere (B) that has an intersection with at least one intersecting sphere (Bi), wherein the intersection of said sphere (B) with each intersecting sphere (Bi) is defined by an intersecting circle (Ii), and the contour (Cm) comprises the area on the surface of said sphere ( B ) that is formed by at least one arc (a1, a2, a3) of the intersection line (Ii) of the surface of said sphere (B) either with the surface of the intersecting sphere (Bi) or - if said sphere (B) has a plurality of intersecting spheres (Bi)- with the surfaces of the intersecting spheres (Bi) that have an overlapping area on the surface of said sphere (B). The solvent accessible surface (S) of said sphere (B) is then determined as the surface of said sphere (B) substracted by the area of all contours (Cm) on the surface of said sphere ( B ) . (Figure 3)s