Digital Object Identifier (DOI): 10.1007/s002850200152 J. Math. Biol. 45, 261–277 (2002) Mathematical Biology Gabriele Grassi · Mario Grassi · Anne Kuhn · Reinhard Kandolf Determination of hammerhead ribozyme kinetic constants at high molar ratio ribozyme-substrate Received: 1 February 2001 / Revised version: 1 September 2001 / Published online: 23 August 2002 – c  Springer-Verlag 2002 Abstract. Hammerhead ribozymes provide valuable tools in the field of gene therapy due to their cleavage specificity and the broad range of RNA targets. A major prerequisite for the selection of suitable ribozymes for in vivo application is represented by in vitro determination of ribozyme cleavage kinetic constants. From the experimental cleavage data, kinetic con- stants are usually calculated under the assumption of rapid conversion of the substrate into the ribozyme-substrate complex. However, this condition is often not satisfied for ribozymes carrying additional RNA stretches, due to cloning strategies or necessary for ribozyme ex- pression in the cell. To overcome this problem, we propose a mathematical model which is able to calculate ribozyme kinetic constants in the case of non-rapid conversion of substrate into ribozyme-substrate complex. In addition, our system gives the opportunity to evaluate the nature of the S conversion into ES through the determination of a model parameter. The validity of the proposed model is restricted to the hypothesis of a ribozyme excess over the substrate at the beginning of the cleavage reaction and to the absence of any mass exchange with the external environment. 1. Introduction Hammerhead ribozymes are catalytic RNA molecules capable of inducing the site- specific cleavage of a phosphodiester bond within an RNA molecule [3, 8]. Natural- ly occurring hammerhead ribozymes are cis-acting molecules, being the ribozyme and the substrate on the same molecule. However, it is possible to design trans- acting hammerhead ribozymes that can cut a separate RNA molecule [22]. The structural model proposed for trans-acting hammerhead ribozymes has three es- sential features: (i) three double helices numbered I, II, and III (helices number I and III are also called binding arms); (ii) a triplet cleavage site within the tar- get RNA which is composed, in most of the naturally occurring ribozymes, of the trinucleotide triplet GUC; (iii) two stretches of highly conserved sequences which represent the catalytic active core [9]. Hammerhead ribozymes specifically bind to their targets by helices I and III (the binding arms) according to the Watson – Crick base pairing. As helices I and III are not conserved [22], it is possible to G. Grassi (corresponding author),A. Kuhn, R. Kandolf: Department of Molecular Pathology, Institute for Pathology, University of T¨ ubingen, Liebermeisterstrasse 8, D-72076, T ¨ ubingen, Germany. e-mail: gegrassi@med.uni-tuebingen.de M. Grassi: Department of Chemical, Environmental and Raw Materials Engineering – DICAMP, University of Trieste, Piazzale Europa 1, I-34127 Trieste, Italy Key words or phrases: Hammerhead ribozymes – Kinetic constants – Modeling