Chemical Reaction Networks for Computing Polynomials.

Area of Science:

• Biochemistry
• Computational Biology
• Systems Biology

Background:

• Chemical reaction networks (CRNs) are foundational models for molecular systems analysis.
• CRNs are increasingly explored for molecular computation applications.
• Existing CRN models have limitations in computing complex functions.

Purpose of the Study:

• To demonstrate that CRNs can compute any polynomial function mapping the unit interval to itself.
• To introduce a new encoding scheme for CRNs to achieve universal computation.
• To present molecular encoders and decoders for this new CRN computation model.

Main Methods:

• Encoding variables as ratios of two molecular types (type-0 and type-1).
• Utilizing the expansion of power-form polynomials into Bernstein polynomials.
• Designing molecular encoders and decoders for input/output conversion.
• Mapping CRN computations to DNA strand-displacement reactions.

Main Results:

• CRNs, with the proposed encoding, can compute any polynomial function within the unit interval.
• The encoding naturally leverages Bernstein polynomial expansions.
• Molecular encoders and decoders were successfully designed and presented.
• The method was demonstrated for generic CRNs and mapped to DNA strand-displacement reactions.

Conclusions:

• The novel encoding enables CRNs to perform universal polynomial function computation.
• This work expands the potential of CRNs in molecular computing.
• The presented method provides a pathway for implementing complex computations using biochemical systems.