- Parameter Influence On The Zeros Of NetworkDeterminants (2002)
- To a network N(q) with determinant D(s;q) depending on a parameter vector q Î Rr via identification of some of its vertices, a network N^ (q) is assigned. The paper deals with procedures to find N^ (q), such that its determinant D^ (s;q) admits a factorization in the determinants of appropriate subnetworks, and with the estimation of the deviation of the zeros of D^ from the zeros of D. To solve the estimation problem state space methods are applied.
- Determination of interaction between MCT1 and CAII via a mathematical and physiological approach (2008)
- The enzyme carbonic anhydrase isoform II (CAII), catalysing the hydration and dehydration of CO2, enhances transport activity of the monocarboxylate transporter isoform I (MCT1, SLC16A1) expressed in Xenopus oocytes by a mechanism that does not require CAII catalytic activity (Becker et al. (2005) J. Biol. Chem., 280). In the present study, we have investigated the mechanism of the CAII induced increase in transport activity by using electrophysiological techniques and a mathematical model of the MCT1 transport cycle. The model consists of six states arranged in cyclic fashion and features an ordered, mirror-symmetric, binding mechanism were binding and unbinding of the proton to the transport protein is considered to be the rate limiting step under physiological conditions. An explicit rate expression for the substrate °ux is derived using model reduction techniques. By treating the pools of intra- and extracellular MCT1 substrates as dynamic states, the time dependent kinetics are obtained by integration using the derived expression for the substrate °ux. The simulations were compared with experimental data obtained from MCT1-expressing oocytes injected with di®erent amounts of CAII. The model suggests that CAII increases the e®ective rate constants of the proton reactions, possibly by working as a proton antenna.