Computing Algebraic Functions with Biochemical Reaction Networks

Abstract

In biological organisms, networks of chemical reactions control the processing of information in a cell. A general approach to study the behavior of these networks is to analyze common modules. Instead of this analytical approach to study signaling networks, we construct functional motifs from the bottom up. We formulate conceptual networks of biochemical reactions that implement elementary algebraic operations over the domain and range of positive real numbers. We discuss how the steady state behavior relates to algebraic functions, and study the stability of the networks' fixed points. The primitive networks are then combined in feed-forward networks, allowing us to compute a diverse range of algebraic functions, such as polynomials. With this systematic approach, we explore the range of mathematical functions that can be constructed with these networks.

Biomolecular implementation of nonlinear system theoretic operators

“…Some of the ideas of [20] are found in [19], and hence are reflected in our constructs as well. However, no suggestions are found in [20] on how such operations can be implemented using real world biomolecular species such as DNA, RNA, and enzymes. In contrast, our approach clearly tackles this problem by using the concepts developed in [10] and [19].…”

“…It turns out that an elegant mathematical framework on how concentrations of abstract biochemical species should be used to implement several complex computational functions such as the square root, the n-th root, and division of two numbers was already well presented in [20]. Some of the ideas of [20] are found in [19], and hence are reflected in our constructs as well. However, no suggestions are found in [20] on how such operations can be implemented using real world biomolecular species such as DNA, RNA, and enzymes.…”

Strong Turing Completeness of Continuous Chemical Reaction Networks and Compilation of Mixed Analog-Digital Programs

“…following [8,12]), which guarantees that the result is obtained in the concentration of one distinguished molecular species, with a precision indicated by another distinguished molecular species (see Def. 4).…”

Kinetic Model for a Threshold Filter in an Enzymatic System for Bioanalytical and Biocomputing Applications

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14] Such multi-input reaction cascades are used in biosensing, biomolecular computing, and decision making devices and setups utilizing (bio)chemical processes with well-defined responses. [15][16][17][18][19][20] These systems require experimental design and theoretical understanding [21][22][23] of chemical and biochemical reactions that allow signal response modification and control.…”