Riju the gene is fully expressed in the natural

Riju Nag (Applicant of the Ph.D post offered in this field offered by prof. Anna Ochab-Marcinek)As I have already stated in my application, that I am very interested in application of statistical physics onvarious fields of science. As just biodata and recommendation letters don’t give very good idea about howone can understand this topic , so I am writing this for you to assess whether I am in the right track inunderstanding the subject of research.Michael A. Savageau first passed the idea that the gene regulation can be analogous with demand theorythat is very familiar subject in economics. Some genes are regulated by Transcription Factors, while someothers are not . Regulating a gene requires a “cost” to maintain the regulatorysystem. When a gene is constitutively expressed , cost of maintaining a regulatory system is saved. But theproblem is , protein is produced even when it is not needed. To regulate or not to regulate a gene isdetermined by the balance of these two opposing driving forces during the course of evolution of theorganism.When gene Y is regulated, and the cost to maintain theregulatory system is r, then the fitness function is given by,f = pb + pc +r(Where gene Y is expressed constitutively and its needed with probability p)(b is benefit)(c is cost)If Y is not encoded in the genome, then no fitness can be found in the gene , i.e. f=0If a gene has to be regulated by a signal, either an activator or a repressor can achieve the same purpose inthe sense to activate the expression of the gene using different mechanisms. If a gene receive N regulations,then there are 2N possible mechanisms that can generate a given input-output mapping.There are two possible ways for Nature to select a mode for the regulation:1. Nature has randomly selected an equivalent design, then selection is based on historical precedent.2. There are rules that govern the choice of mode/mechanismof each system.Savageau found in 1970s that the mode of gene regulation (positive or negative) is correlated with theprobability that the gene is fully expressed in the natural environment.Now, Microbes in fluctuating environments must constantly adapt their behaviour according to thefluctuations to survive. This may be achieved through sensing followed by response or through thegeneration of diversity. The generation of diversity is obtained by stochastic phenotype switching.Now, a stochastic process is a mathematical object , defined as a collection of random variables. Theevolution of stochastic statistical physics really baffled me. From Einstein’s explanation of Brownian motionto Bernoulli process , Random Walk , Werner process , Poisson process , its goes on.In simple words, stochastic process is adding a bit of randomness to a given system.Now, what this project aims? As far as I understood , this project will take into account the randomfluctuations of TF (referring to stochastic approach) and the costs of regulations and by using tools ofstatistical physics and theoretical modelling and computational testing by simulation, this project will accountfor the changes that will be seen from the classical Savageau’s demand rules which can further be justifiedexperimentally by biologists.