Algebraic Phasing of Polyploid Haplotypes
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Solution Overview
Problem
Current methods for determining haplotypes in polyploid organisms, which have multiple copies of the same chromosome, are inefficient in identifying parent chromosomes with desirable traits, as they rely on statistical estimation and are not effective in resolving complex genetic data from polyploid samples.
Innovation Solution
A computer-based algebraic phasing system that processes a matrix of single-nucleotide polymorphisms (SNPs) using an algebraic phasing algorithm, applying rules to determine haplotypes by iteratively reducing ploidy levels and resolving variables, ultimately identifying the genetic makeup of parent organisms.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If statistical estimation methods are used to determine haplotypes in polyploid organisms, then the process can be performed with existing computational tools, but the accuracy and effectiveness in resolving complex genetic data are insufficient
Solution Approach 1:
The patent transforms the haplotype determination problem from a statistical estimation approach to an algebraic solution by changing the mathematical parameters and methods used. Specifically, it formulates the problem using systems of linear equations over finite fields, where genetic data is represented as algebraic variables and constraints are expressed as equations. This parameter change enables exact solutions rather than probabilistic estimates, directly improving measurement precision for haplotype determination in polyploid organisms.
2Reliability
If algebraic phasing algorithms are applied to resolve complex genetic data, then haplotype determination accuracy improves, but the computational complexity and processing requirements increase
Solution Approach 1:
The patent segments the complex algebraic phasing problem into manageable components by dividing the system of equations into smaller subsystems that can be solved independently or in a structured sequence. The method partitions genetic markers into groups and processes them through staged algebraic operations, reducing the computational burden while maintaining solution accuracy. This segmentation allows complex genetic data to be resolved effectively without requiring overwhelming computational resources.
Solution Approach 2:
The patent introduces intermediate algebraic representations and auxiliary variables as mediators between the raw genetic data and the final haplotype solutions. These intermediate structures include algebraic codes, syndrome calculations, and iterative refinement variables that bridge the gap between complex input data and resolved haplotypes. The intermediary algebraic framework transforms intractable problems into solvable forms, improving reliability without directly processing the full complexity of the original data.
3Loss of information
If iterative algebraic rules are applied to reduce ploidy levels and resolve variables, then the ability to identify parent chromosomes with desirable traits improves, but the processing time and computational steps increase
Solution Approach 1:
The patent performs preliminary algebraic transformations and pre-processing of genetic data before the main iterative phasing process. This includes initial encoding of genetic markers, pre-calculation of algebraic constraints, and preparation of data structures that facilitate faster iterative processing. By performing these preliminary actions, the method reduces the computational time required for subsequent iterative steps while preserving complete genetic information for accurate parent chromosome identification.
Data Source
AI summary
Embodiments of the present invention include method, systems and computer program products for algebraic phasing of polyploids. Aspects of the invention include receiving a matrix including a set of two or more single-nucleotide poloymorphisms (SNPs) for two or more sample organisms. Each row of the matrix is set to a ploidy based on a number of ploidies present in the two or more sample organisms. Each allele in the set of two or more SNPs is represented as a binary number. A set of algebraic rules is received, wherein the set of algebraic rules include an algebraic phasing algorithm. And the set of algebraic rules are applied to the matrix to determine a haplotype of a parent of the two or more sample organisms.