Fermentation kinetics including product and substrate inhibitions plus biomass death: a mathematical analysis

Fermentation is generally modelled by kinetic equations giving the time evolutions for biomass, substrate, and product concentrations. Although these equations can be solved analytically in simple cases if substrate/product inhibition and biomass death are included, they are typically solved numerically. We propose an analytical treatment of the kinetic equations --including cell death and an arbitrary number of inhibitions-- in which constant yield needs not be assumed. Equations are solved in phase space, i.e. the biomass concentration is written explicitly as a function of the substrate concentration.Comment: 4 pages, 4 figure

Short-term effects of unilateral lesion of the primary motor cortex (M1) on ipsilesional hand dexterity in adult macaque monkeys

Although the arrangement of the corticospinal projection in primates is consistent with a more prominent role of the ipsilateral motor cortex on proximal muscles, rather than on distal muscles involved in manual dexterity, the role played by the primary motor cortex on the control of manual dexterity for the ipsilateral hand remains a matter a debate, either in the normal function or after a lesion. We, therefore, tested the impact of permanent unilateral motor cortex lesion on the manual dexterity of the ipsilateral hand in 11 macaque monkeys, within a time window of 60 days post-lesion. For comparison, unilateral reversible pharmacological inactivation of the motor cortex was produced in an additional monkey. Manual dexterity was assessed quantitatively based on three motor parameters derived from two reach and grasp manual tasks. In contrast to the expected dramatic, complete deficit of manual dexterity of the contralesional hand that persists for several weeks, the impact on the manual dexterity of the ipsilesional hand was generally moderate (but statistically significant) and, when present, lasted less than 20 days. Out of the 11 monkeys, only 3 showed a deficit of the ipsilesional hand for 2 of the 3 motor parameters, and 4 animals had a deficit for only one motor parameter. Four monkeys did not show any deficit. The reversible inactivation experiment yielded results consistent with the permanent lesion data. In conclusion, the primary motor cortex exerts a modest role on ipsilateral manual dexterity, most likely in the form of indirect hand postural control