Kinetic Parameter Calculation via Linearized Reaction Network
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Solution Overview
Problem
Existing methods for calculating kinetic parameters of a reaction network are computationally intensive and cannot efficiently handle observed signals that do not observe all states of the network, leading to delays and inaccuracies in kinetic parameter determination.
Innovation Solution
A method that eliminates hidden states from the differential equations of a reaction network, forming intermediate differential equations without hidden states, and uses a direct estimation method to minimize an intermediate objective function, enabling faster calculation of kinetic parameters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional iterative methods are used to calculate kinetic parameters from observed signals, then measurement precision can be maintained, but computational time increases significantly and productivity decreases
Solution Approach 1:
The patent applies preliminary action by performing a linearization transformation of the differential equations before parameter estimation. The observed signals are pre-processed to eliminate hidden states and transform the nonlinear system into a linear form, allowing direct calculation of kinetic parameters without iterative optimization. This preliminary transformation enables direct estimation methods that compute parameters in closed-form, dramatically reducing computational time while preserving accuracy.
Solution Approach 2:
The patent substitutes the mechanical iterative optimization process with a direct mathematical transformation approach. Instead of using iterative numerical methods that repeatedly solve nonlinear equations, the invention transforms the problem into a linear algebraic system that can be solved directly through matrix operations. This substitution replaces the iterative computational mechanism with a direct calculation mechanism, eliminating the time-consuming iteration cycles while maintaining parameter estimation precision.
2Measurement precision
If hidden states are included in the differential equations, then measurement precision is maintained, but device complexity and computational burden increase
Solution Approach 1:
The patent applies the taking out principle by extracting and eliminating hidden states from the differential equations. The method identifies which states are directly observable and which are hidden, then mathematically eliminates the hidden states from the system equations. This extraction process transforms the complex system with unobservable variables into a simplified system that only contains observable variables, reducing computational complexity while preserving the ability to accurately determine kinetic parameters from measured signals.
Solution Approach 2:
The patent uses an intermediary approach by introducing a transformation matrix that mediates between the full state vector (including hidden states) and the observable signals. This intermediary transformation allows the system to work with simplified equations containing only observable variables, while the mathematical structure preserves the information needed to accurately estimate parameters. The intermediary transformation acts as a bridge that eliminates complexity without losing essential dynamic information.
3Productivity
If direct estimation methods are used to eliminate hidden states, then productivity increases and computational time decreases, but measurement precision may be compromised
Solution Approach 1:
The patent applies parameter changes by transforming the mathematical form of the differential equations through linearization. The nonlinear parameters and variables are transformed into a linear structure where kinetic parameters appear as coefficients in a linear system. This parameter transformation enables direct estimation methods to achieve both high productivity and high precision, as the linearized system allows closed-form solutions that are computationally efficient and mathematically exact under the transformation framework.
Data Source
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AI summary
According to the present invention there is provided a method of calculating kinetic parameters of a reaction network, the method comprising the steps of: providing an intermediate objective function, wherein said intermediate objective function comprises a linearized intermediate discrepancy function which comprises intermediate parameters which have been determined by applying a reparameterization function to the parameters of the discrepancy function, wherein the intermediate discrepancy function is linear with respect to all of said intermediate parameters; determining values for each of the intermediate parameters in said linearized intermediate discrepancy function, which minimize the intermediate objective function, using a direct estimation method; determining values for the parameters of the discrepancy function by applying an inverse of the reparameterization function to said determined values of the intermediate parameters; determining values for the kinetic parameters from said determined values for said parameters of the discrepancy function. There is further provided a tangible data carrier comprising program code arranged for causing a processor to carry out said method.