Stability analysis of the GAL regulatory network in Saccharomyces cerevisiae and Kluyveromyces lactis

<p>Abstract</p> <p>Background</p> <p>In the yeast <it>Saccharomyces cerevisiae</it>, interactions between galactose, Gal3p, Gal80p, and Gal4p determine the transcriptional status of the genes required for the galactose utilization. Increase in the cellular galactose concentration causes the galactose molecules to bind onto Gal3p which, via Gal80p, activates Gal4p, which induces the GAL3 and GAL80 gene transcription. Recently, a linear time-invariant multi-input multi-output (MIMO) model of this GAL regulatory network has been proposed; the inputs being galactose and Gal4p, and the outputs being the active Gal4p and galactose utilization. Unfortunately, this model assumes the cell culture to be homogeneous, although it is not so in practice. We overcome this drawback by including more biochemical reactions, and derive a quadratic ordinary differential equation (ODE) based model.</p> <p>Results</p> <p>We show that the model, referred to above, does not exhibit bistability. We establish sufficiency conditions for the domain of attraction of an equilibrium point of our ODE model for the special case of full-state feedback controller. We observe that the GAL regulatory system of <it>Kluyveromyces lactis </it>exhibits an aberration of monotone nonlinearity and apply the Rantzer multipliers to establish a class of stabilizing controllers for this system.</p> <p>Conclusion</p> <p>Feedback in a GAL regulatory system can be used to enhance the cellular memory. We show that the system can be modeled as a quadratic nonlinear system for which the effect of feedback on the domain of attraction of the equilibrium point can be characterized using <it>linear matrix inequality </it>(LMI) conditions that are easily implementable in software. The benefit of this result is that a mathematically sound approach to the synthesis of full-state and partial-state feedback controllers to regulate the cellular memory is now possible, irrespective of the number of state-variables or parameters of interest.</p

Ovarian Activity and Oestrous Signs among Group-Housed, Lactating Sows: Influence of Behaviour, Environment and Production

Animal welfare concerns require the development of housing systems that allow the animals to express their natural behaviour. One example of this is the group-housing system for lactating sows. The present study aimed at exploring ovarian activity in such a system. Thirty-eight sows farrowing individually outdoors during spring and summer, and indoors during autumn and winter, and group-housed in groups of four during weeks 3–7 of the lactation period, were monitored regarding reproductive functions, behaviour and production during their first to fourth lactation period. Average ovulation frequency during lactation was 47%. Only 50% of these ovulating cases were accompanied by a standing oestrus. Lactational ovulation frequency was higher in later parities (p < 0.001). Ovulation frequency was higher (p < 0.05) during winter (74%) and spring (69%), than during summer (10%) and autumn (23%). Occurrence of lactational ovulation was associated with some aspects of suckling behaviour and also with litter weight gain (p < 0.05). Forty-nine per cent of the lactational ovulations occurred during the seventh week of lactation. Timing of ovulation seemed positively (p = 0.08) associated with weight loss during lactation. Compared with the sows that were anoestrus during lactation, oestradiol-17β values were higher (p < 0.05) only in the week before occurrence of lactational ovulation. Weaning-to-oestrous interval was prolonged (p < 0.05) among the sows that ovulated during lactation. The present study identifies several factors influencing ovarian activity among group-housed sows, thereby providing tools for the control of lactational ovulation in group-housing systems

A convex optimization approach to cancer treatment to address tumor heterogeneity and imperfect drug penetration in physiological compartments

The clinical success of targeted cancer therapies is limited by the emergence of drug resistance often due to pre-existing tumor genetic heterogeneity and acquired, therapy-induced resistance. Targeted therapies have varied success in addressing metastatic disease, due to their ability to penetrate certain physiological compartments. This paper considers an evolutionary cancer model that incorporates tumor cell growth, mutation and compartmental migration and leverages recent results on the optimal control of monotone and convex systems to synthesize switching treatment strategies where a single drug or a predetermined combination of drugs is used at a given time. The need for switching is motivated by clinical considerations such as the limited effectiveness of any single targeted therapy against multiple resistance mechanisms arising in a single patient and the inability to design drug combinations at effective doses due to toxicity constraints. An optimal and clinically feasible switching therapy is obtained as the solution of a convex optimization problem that exploits the diagonally-dominant structure of the model. We demonstrate that this method yields an effective strategy in mitigating disease evolution in the presence of imperfect drug penetration in two compartments on an experimentally identified model of anaplastic lymphoma kinase (ALK)-rearranged lung carcinoma

Non-smooth progress function algorithm for frequency-shaping control design

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