The effector can determine the drop of the living biomass (X) due to cell death, or the drop of the maximum specific growth rate (r). In both cases we admit that the response R can be described by means of model A1 (see Appendix and Table 1 for parametric definitions and units), where the subindex φ can take the values X and r according to the specific response considered: (1) A2. In accordance with the usual convention of a total biomass X, when X H dies at a given dose of the effector (X S being

the surviving biomass), the response R X in terms of biomass will be: (2) A3. Similarly, GSK872 clinical trial if the response R r in terms of the maximum specific rate is a decrease from r 0 to r in the absence of the effector, we will have: (3) The adequate formulations for an effector with stimulatory action (response with negative sign, see methodological section) are obtained in a similar way. Since the increase in cell number can only be attributed to the (-)R r response, the meaning of the (-)R X response is the increase of dry weight per cell. Thus, when biomass is estimated by means of absorbances or number of colony forming units, it is only pertinent to consider the response in terms of maximum specific rate. www.selleckchem.com/products/ly2874455.html A4. Bearing in mind the preceding specification, if a total

biomass X increases up to a value X S (where X S = X +ΔX) at a given dose of effector, the response will be: (4) A5. Similarly, if the response R r of the maximum specific rate is the increase to a value r from a value r 0 in the absence of the effector (with r = r 0 + Δr), we will have: (5) B. Hypothesis concerning biomass dynamics We accept that the biomass X grows according to a conventional logistic equation, whose differential expression is [18]: (6) where r 0 is the maximum specific growth rate in the absence of the effector, and X m is the maximum biomass. In the presence of the effector, the constant r 0 turns into the variable r (which is dependent on the dose); therefore, this differential form cannot allow an analytic solution. Therefore, next the expression (6) will be directly used later on in the numeric solution of the system. C. Optional

hypothesis concerning the dose The dose D is commonly considered a constant: it is the initial concentration of the effector, which is a good criterion when the biomass does not vary appreciably during the exposure time. However, this approach can be Mizoribine in vivo doubtful if the action of the effector reduces (without cancelling) the growth rate, because in this case the ratio of available effector to biomass diminishes with time. Indeed, it is difficult to accept that in a microbial culture the initial level of effector means the same against the initial biomass as against a biomass often larger by several orders of magnitude a few hours later. In fact, these considerations are implicit when a clearly specified value of the initial biomass is required for standardizing DR assays.