Ellipsoidal Rejection Sampling for Molecular Cross-Section Estimation
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Solution Overview
Problem
Existing algorithms for estimating the cross-sectional area of molecules, such as MobCal, face challenges in determining sufficient orientations and achieving convergence, leading to slow and unreliable results in predicting ion mobility.
Innovation Solution
The ellipsoidal rejection sampling method improves upon previous algorithms by using a processor to predict the geometric structure of a molecule, assigning an ellipsoidal boundary, randomly selecting orientations, calculating the projected area, and iterating until consistent results are achieved within a predetermined range, providing a more efficient and accurate estimation of the cross-sectional area.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Monte Carlo techniques are used to calculate projection approximation cross-section, then numerical approximations can be obtained, but convergence is slow and it is difficult to determine sufficient orientations
Solution Approach 1:
The patent applies preliminary action by pre-assigning an ellipsoidal boundary to the molecule before performing Monte Carlo sampling. This boundary is calculated in advance based on molecular coordinates, and all subsequent random sampling operations are constrained within this pre-defined ellipsoid. This preliminary setup eliminates the need to repeatedly calculate bounding rectangles for each random orientation, significantly reducing computational overhead and accelerating convergence while maintaining calculation accuracy.
2Device complexity
If naive convergence tests are used in MobCal algorithm, then simplicity is maintained, but results can be misleading and reliability is reduced
Solution Approach 1:
The patent implements feedback by continuously monitoring the stability of cross-section values across successive iterations. The algorithm tracks the change in calculated cross-section area between consecutive random orientations and terminates only when this change falls below a predetermined threshold. This feedback mechanism provides reliable convergence detection without requiring complex convergence tests, maintaining algorithm simplicity while ensuring result reliability through objective stability criteria.
3Ease of manufacture
If rectangle bounding method is used to calculate molecular shadow area, then calculation is straightforward, but accuracy is limited compared to ellipsoidal boundary
Solution Approach 1:
The patent applies spheroidality by replacing the rectangular bounding box with an ellipsoidal boundary that better conforms to the actual molecular shape. The ellipsoid is defined by calculating the center of mass and moment of inertia tensor of the molecule, then deriving semi-axes from the eigenvalues. This curved boundary more accurately encloses the molecular volume and provides better geometric correspondence to spherical ions, improving cross-section calculation accuracy while maintaining computational efficiency through analytical ellipsoid equations.
Data Source
Figure 1
AI summary
A method of estimating the cross-sectional area of a molecule for use in the prediction of ion mobility gives gas phase interaction radii determination and cross-sectional algorithm computation to provide separation and characterisation of structurally related isomers. More specifically, the invention provides a method of correlating the differences in the molecular structures with differences in anti-cancer activity of pre-determined anti-cancer drugs by utilizing a new algorithm for estimating the cross-sectional area of the molecules of such drugs.