Rate-Independent Constructs for Chemical Computation

This paper presents a collection of computational modules implemented with chemical reactions: an inverter, an incrementer, a decrementer, a copier, a comparator, a multiplier, an exponentiator, a raise-to-a-power operation, and a logarithm in base two. Unlike previous schemes for chemical computation, this method produces designs that are dependent only on coarse rate categories for the reactions (“fast” vs. “slow”). Given such categories, the computation is exact and independent of the specific reaction rates. The designs are validated through stochastic simulations of the chemical kinetics.

[1]  R. Jackson,et al.  General mass action kinetics , 1972 .

[2]  D. Gillespie.  A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions , 1976 .

[3]  D. Gillespie.  Exact Stochastic Simulation of Coupled Chemical Reactions , 1977 .

[4]  Otto E. Rössler,et al.  Irregular Oscillations in a Realistic Abstract Quadratic Mass Action System , 1980 .

[5]  Péter Érdi,et al.  Mathematical Models of Chemical Reactions: Theory and Applications of Deterministic and Stochastic Models , 1989 .

[6]  Steven H. Strogatz,et al.  Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering , 1994 .

[7]  S. Strogatz.  Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering , 1995 .

[8]  M. Magnasco.  CHEMICAL KINETICS IS TURING UNIVERSAL , 1997 .

[9]  Irving R. Epstein,et al.  An Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves, Patterns, and Chaos , 1998 .

[10]  Ron Weiss,et al.  Cellular computation and communications using engineered genetic regulatory networks , 2001, Cellular Computing.

[11]  Ron Weiss,et al.  Toward in vivo Digital Circuits , 2002 .

[12]  E. Shapiro,et al.  An autonomous molecular computer for logical control of gene expression , 2004, Nature.

[13]  Daniel T Gillespie,et al.  Stochastic simulation of chemical kinetics. , 2007, Annual review of physical chemistry.

[14]  J. Keasling.  Synthetic biology for synthetic chemistry. , 2008, ACS chemical biology.

[15]  Matthew Cook,et al.  Computation with finite stochastic chemical reaction networks , 2008, Natural Computing.

[16]  Lulu Qian,et al.  A Simple DNA Gate Motif for Synthesizing Large-Scale Circuits , 2008, DNA.

[17]  Maung Nyan Win,et al.  Frameworks for programming biological function through RNA parts and devices. , 2009, Chemistry & biology.

[18]  Robert M. Dirks,et al.  Selective cell death mediated by small conditional RNAs , 2010, Proceedings of the National Academy of Sciences.

[19]  G. Seelig,et al.  DNA as a universal substrate for chemical kinetics , 2010, Proceedings of the National Academy of Sciences.

[20]  Keshab K. Parhi,et al.  Writing and Compiling Code into Biochemistry , 2010, Pacific Symposium on Biocomputing.

[21]  Keshab K. Parhi,et al.  A synthesis flow for digital signal processing with biomolecular reactions , 2010, 2010 IEEE/ACM International Conference on Computer-Aided Design (ICCAD).

[22]  Hua Jiang,et al.  Binary Counting with Chemical Reactions , 2011, Pacific Symposium on Biocomputing.

[23]  Mark A. Stalzer,et al.  Efficient Formulations for Exact Stochastic Simulation of Chemical Systems , 2011, IEEE/ACM Transactions on Computational Biology and Bioinformatics.