Image:ReactionNets-structure-mis-n04-01-nets.png

Chemical reaction network $$A=\langle \mathcal{M},\mathcal{R}\rangle$$ designed to solve the maximal independent set problem, given an undirected graph. The detail algorithm can be found in BioSysBio Abstract, Appendix B.

The set $$\mathcal{M}$$ of molecular species consists of eight species:
 * $$\mathcal{M}=\{s_1^0, s_1^1, s_2^0, s_2^1, s_3^0, s_3^1, s_4^0, s_4^1\}$$.

(Note: species $$s_1^0$$ is denoted as $$\mathsf{s10}$$ in the figure.)

The set $$\mathcal{R}$$ of reaction rules is composed of three sets:
 * $$ \mathcal{R} = (\mathcal{V} \cup \mathcal{N} \cup \mathcal{D})$$

where
 * $$\mathcal{V}=\bigcup_{i=1}^4\mathcal{V}^i$$, $$\mathcal{N}=\bigcup_{i=1}^4\mathcal{N}^i$$, and $$\mathcal{D}=\bigcup_{i=1}^4\mathcal{D}^i$$.

Specifically,



\begin{matrix} \mathcal{V}=\{&\underbrace{s_2^0 + s_3^0 \rightarrow 2 s_1^1},& \underbrace{s_1^0 + s_3^0 \rightarrow 2 s_2^1},& \underbrace{s_1^0+s_2^0+s_4^0 \rightarrow 3s_3^1},& \underbrace{s_3^0\rightarrow s_4^1}&\}\\ &\mathcal{V}_1&\mathcal{V}_2&\mathcal{V}_3&\mathcal{V}_4&\\ \end{matrix} $$,



\begin{matrix} \mathcal{N}=\{&\underbrace{s_2^1 \rightarrow s_1^0, s_3^1 \rightarrow s_1^0},& \underbrace{s_1^1 \rightarrow s_2^0, s_3^1 \rightarrow s_2^0}&, \underbrace{s_1^1 \rightarrow s_3^0, s_2^1 \rightarrow s_3^0, s_4^1 \rightarrow s_3^0},& \underbrace{s_3^1\rightarrow s_4^0}&\}\\ &\mathcal{N}_1&\mathcal{N}_2&\mathcal{N}_3&\mathcal{N}_4&\\ \end{matrix} $$,

and

\begin{matrix} \mathcal{D}=\{&\underbrace{s_1^0 + s_1^1 \rightarrow \emptyset}, & \underbrace{s_2^0 + s_2^1 \rightarrow \emptyset}, & \underbrace{s_3^0 + s_3^1 \rightarrow \emptyset}, & \underbrace{s_4^0 + s_4^1 \rightarrow \emptyset}&\}\\ &\mathcal{D}_1&\mathcal{D}_2&\mathcal{D}_3&\mathcal{D}_4&\\ \end{matrix} $$.