Abstract
A coupled system of two isothermal in vitro DNA/RNA amplification reactions using different primers is modeled kinetically with realistic rate parameters and shown to exhibit oscillatory behavior in a flow reactor. One of the two isothermal amplification reactions acts as a predator of the other, the prey. The mechanism of the oscillatory behavior is analyzed in terms of a hierarchy of kinetic models. The work provides an insight into the choice of parameters for experiments. The latter are important in providing detailed insight into the complex processes of ecological interactions and their evolution.
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Biebricher, Ch. K., M. Eigen and W. C. Gardiner Jr (1983). Kinetics of RNA replication. Biochemistry 22, 2544.
Biebricher, Ch. K., M. Eigen and W. C. Gardiner Jr (1984). Kinetics of RNA replication: plus-minus asymmetry and double-stranded formation. Biochemistry 23, 3186.
Biebricher, Ch. K., M. Eigen and W. C. Gardiner Jr (1985). Kinetics of RNA replication: competition and selection among self-replication of RNA species. Biochemistry 24, 6550.
Böddeker, B. and J. S. McCaskill (1998). Do self-replicant spots provide a plattform for heriditary molecular diversity? J. Theor. Biol., in press.
Boerlijst, M. C. and P. Hogeweg (1991). Spiral wave structure in pre-biotic evolution: hypercycles stable against parasites. Physica D48, 17.
Bray, W. C. (1980). Hypercycles, parasites and packages. J. Theor. Biol. 85, 399.
Ehricht, R., Th. Ellinger and J. S. McCaskill (1997). Cooperative amplification of templates by cross-hybridization (CATCH). Eur. J. Biochem. 243, 358.
Eigen, M. (1989). The molecular quasispecies. Adv. Chem. Phys. 75, 149.
Eigen, M. (1971). The quasispecies model. Naturwissenschaften 58, 465.
Eigen, M. and P. Schuster (1977). The hypercycle: A principle of natural self-organisation. Naturwissenschaften 64, 541.
Eigen, M. and P. Schuster (1978a). Naturwissenschaften 64, 7.
Eigen, M. and P. Schuster (1978b). Naturwissenschaften 65, 341.
Ellington, A. D., M. P. Robertson and J. Bull (1997). Ribozymes in wonderland. Science 276, 546.
Emlen, J. M. (1984). Population Biology. MacMillan, New York, USA.
Foerster, P., B. Wlotzka and J. S. McCaskill (1994). Spatially resolved evolution studies in an open reactor. Ber. Bunsenges. Phys. Chem. 98, 1203.
Gebinoga, M. and F. Oehlenschläger (1996). Comparisons of 3SR reaction systems. Eur. J. Biochem. 235, 256.
Goldbeter, A. (1996). Biochemical Oscillations and Cellular Rhythms. The Molecular Bases of Periodic and Chaotic Behaviour. New York: Cambridge University Press.
Gray, P. and S. K. Scott (1985). Sustained oscillations and other exotic patterns of behavior in isothermal reactions. J. Chem. Phys. 89, 22.
Guatelli, J. C., K. M. Whitefield, D. Y. Kwoh, K. J. Barringer, D. D. Richman and T. R. Gingeras (1990). Isothermal, in vitro amplification of nuclei acids by a multienzyme reaction modeled after retroviral replication. Proc. Natl. Acad. Sci. USA 87, 1874.
Guckenheimer, J. and P. Holmes (1993). Nonlinear Oscillations, Dynamical Systems, and Bifurcation oc Vector Fields, volume 42 of Applied Mathematical Science, New York: Springer.
Hofbauer, J. and K. Sigmund (1988). The Theory of Evolution and Dynamical Systems, Cambridge: University of Illinois Press.
Lotka, A. J. (1910). Contribution to the theory of periodic reactions. J. Phys. Chem. 14, 271.
Lotka, A. J. (1920). Undamped oscillation derived from the law of mass action. J. Amer. Chem. Soc. 42, 201.
Luisi, P. L., P. Walde and T. Oberholzer (1994). Enzymatic RNA synthesis in self-reproducing vesicles: an approach to the construction of a minimal synthetic cell. Ber. Bunsenges. Phys. Chem. 98, 1160.
Murray, J. M. (1982). Parameter space for Turing instability in reaction-diffusion mechanisms: a comparison of models. J. Theor. Biol. 98, 1431.
Murray, J. M. (1993). 2nd edn. Mathematical Biology, Berlin: Springer.
Olsen, L. F. (1983). An enzyme reation with strange attractor. Phys. Lett. 94, 454.
Spiegelmann, S. (1971). An approach to the experimental analysis of precellular evolution. Q. Rev. Biophys. 4, 213.
Swinney, H. S. (1984). Chemical chaos, in Non-equilibrium Dynamics in Chemical Systems, C. Vidal and A. Pacault (Eds), p. 124. Berlin: Springer.
Volterra, V. (1926). Variazionie fluttuazioni del numero d’individui in specie animali conviventi. Mem. Acad. Lincei. 2, 31.
Volterra, V. (1931). Variations and fluctuations of a number of individuals in animal species living together, in Animal Ecology, R. N. Chapman (ed.), New York: McGraw Hill, p. 409.
Wlotzka, B. and J. S. McCaskill (1997). A molecular predator and its prey: coupled isothermal amplification of nucleic acids. Biology & Chemistry 4, 25.
Wright, M. C. and G. F. Joyce (1997). Continuous in vitro evolution of catalytic function. Science 276, 614.
Wu, X. G. and R. Kapral (1994). Effects of molecular fluctuations on chemical oscillations and chaos. J. Chem. Phys. 100, 5936.
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Ackermann, J., Wlotzka, B. & McCaskill, J.S. In vitro DNA-based predator-prey system with oscillatory kinetics. Bull. Math. Biol. 60, 329–354 (1998). https://doi.org/10.1006/bulm.1997.0001
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DOI: https://doi.org/10.1006/bulm.1997.0001