 In this module, we will talk about the batch cultures kinetics, which is the continuation of the previous module. In previous module, I talked about the relationship of biomass with time, but in this module, we will talk about that how the substrate concentration effect on during the fermentation process. So, the if we talk about the effect of substrate and concentration which we named as S. So, the growth yield which we called as the Y that is the increase in the cell mass which we called as DX which result due to the consumption of the small amount of the substrate mean Y is the yield factor yield in term of biomass. If our biomass is a product or our biomass is the growth and we know that growth is only happen when there is a utilization of the biomass sorry biomass substrate. So, biomass only increase when there is a utilization of the substrate mean depletion of the nutrients. So, yield factor Y is directly relation have the relation with the change in biomass by the utilization of the substrate. So, Y is equal to DX over DS. So, monod give the equation under such conditions. So, that propose the growth yield to constant reproducible quantity under identical conditions. Then you said that X t change in biomass at time t minus the initial biomass is equal to yield factor and S naught is the initial substrate concentration which we add at the start of the fermentation when we start our batch culture. So, the S t is that substrate amount at the end we can called as the residual substrate concentration. So, sometimes we can called as S t or sometimes we call only this residual substrate as S. So, when it is a maximum utilization of the substrate and we can say that the maximum growth rate we can say that specific highest growth rate constant which we called as the mu max that only increase then there is a constant increase in the biomass until and unless the substrate will not be exhausted. Sometimes the media not contain only a single substrate that have a number of substrate into that carbon source nitrogen source and other micro and macro nutrients. So, sometimes about out of all these nutrients any one of them become the limiting due to which the mu or a growth can be effected. So, in that case mu max is only achieved when there is a new no limiting substrate. So, if we say that if there is no more residual substrate for the growth then we can say that the X mass X maximum is equal to yield factor multiply by S naught and that is only possible when the growth is happen. So, as then some extent if the concentration of the S is increase it become toxic. So, if we want to have a maximum amount of substrate at the initial state then we can say that excess of everything is bad. So, sometimes that substrate if we add in excess that become have a some toxic effect. If we take the example of any medium if we add NaCl as a salt for the growth factor, but that is a very money in quantity. But if we use NaCl in a very bulk amount that can have some osmotic changes. So, that can have the negative effect on that. So, in this case when we say that when there is a substrate become depleted and there is no more residual substrate then the equation can be X is equal to Y dot S naught that is only possible when there is no more substrate in the medium. So, the specific growth rate in generally found to be the function of three parameters. Number one the concentration of the growth limiting substrate mean depend upon the limiting substrate when that become the limiting substrate the growth will retarded. And then the maximum growth rate which is called as mu max. And third one substrate specific constant which we called as KS. So, the Monod equation is you see here this is known as the Monod equation which have the good explanation of this effect of substrate on specific growth rate of any unicellular microorganism in which you can see that KS and the mu max are known as Monod parameters. Mu max is the maximum growth rate constant and KS is the substrate utilization constant. In order to calculate the Monod parameters mu max and KS we have to take the reciprocal of this equation which we called as Monod equation. So, by taking the reciprocal of this equation so, you can say that here is the 1 over mu and KS plus S over mu max. So, if this equation by the LCM method we can transform this equation into the this and then we have the final shape of this equation 1 over mu is equal to KS over mu max S plus 1 over mu max. But if we rearrange this equation that will come you see here here this is fit into the linear regression equation which is equal to Y is equal to A plus BX. So, in this equation you can easily see that 1 over mu max is equal to A and KS over mu max is equal to B which is the slope of the plot. So, if we plot a graph between 1 over mu and 1 over S then we have a straight line. So, if we then if there is a straight line so, the straight line slope will equal to KS over mu max but as concerned the intercept that will equal to the 1 over mu max. Easily when we have a effect of substrate and then by measuring the growth rate constant on each concentration of the substrate then we are able to calculate the monodd parameters mu max and KS. So, KS in growth parameters and in studying the fermentation parameters is very critical when we talk about in the later modules that how the KS effect and by estimating the KS how we can maintain the substrate that how can help in formulating the media for any fermentation process.