Team:MITADTBIO Pune/Model
Mathematical modeling of the biological systems is a crucial step in understanding the kinetics of the system. To survive, bacteria are forced to monitor their environment constantly and to adapt to changing conditions immediately. Therefore,
bacteria have established special signal transduction systems to execute adaptive responses to changing environmental conditions. The simplest circuits consist of two protein components (two-component systems): a sensor kinase, often anchored in the cytoplasmic membrane, and a cytoplasmic response regulator that mediates an adaptive response, usually a
change in gene expression. KdpD/KdpE two-component system (TCS) is a delicate interaction between sensor histidine kinase KdpD and the regulatory response protein KdpE.[1]
Various groups have argued for K+ as the control signal for KdpD, and suggested that the primary stimulus might be either the level of intracellular K+,processes associated with K+ transport, or the external K+ concentration.[2] Having made a composite part of the K+ responsive promoter PkdpF from the KdpFABC operon system and ligating it upstream of GFP protein (BBa_E0040), we wanted to find out the dynamic range between of our promoter gives optimal expression which respect to different concentrations of K+ ions.
Although it is known that during enzymatic activities proteins form a number of temporary complexes, for our purpose and for the sake of simplicity, a rather simple reaction mechanism was used to describe this system.[3]br> The basic reaction equations are as follows:
For our purpose we’ve used ordinary differential equations adopted from (Gayer, 2014) model and demonstrate how change in potassium ions concentration affects the GFP. The dynamic range found from the model was later in turn validated experimented to check the accuracy of the model. The level of expression was checked using a fluorescence spectrophotometer. Modeling was done using MATLAB R2019a.
Level of KdpD, KdpE and KdpF were assumed to be constant.
According to our literature survey and studying iGEM HKUST team 2015 model, it was established that the fluctuation of the concentration of KdpF as well as KdpD and KdpE was only within 10 μM and 3 μM respectively. The ranges we are interested in are relatively on the lower spectrum. The concentrations of KdpD, KdpE and KdpF concentrations were therefore assumed to be constant in the model. It was also assumed that the initial concentration of mRNA for GFP, immature GFP and mature GFP was zero. Here are the ordinary differential equations used in modelling:
$$\frac{d(KdpD^*)}{dt} ={(k1(KdpD)α(ATP)-k_-1(KdpD^*)β(ADP)-k2(KdpE)(KdpD^*)+k_-2(kdpE^*)(kdpD)}$$
$$\frac{d(KdpE^*)}{dt} ={k2(KdpE)(KdpD^*)-k_-2(kdpE*)(KdpD)-k3(kdpE^*)(kdpD)}$$ $$ where k3= k_h\frac{(kdpF)}{(kdpF)+K_h}$$ $$ and where kh= k_0h\frac{C_k+}{C_0k+}$$
$$(KdpE-DNA) =\frac{(KdpE^*)^2(DNA_0)}{k_b}$$
$$(DNA_f) ={(DNA_0)-(KdpE-DNA)}$$
$$As (DNA_0)>>{(KdpE-DNA)}$$
We can assume
$$(KdpE-DNA) ={(KdpE^*)(DNA_0)}{k_b}$$
$$\frac{d(mRNA_gfp)}{dt}={(K_tr θ)(KdpE-DNA)-(k_deg,gfp,mRNA+μ)}{mRNA_GFP}$$
$$d{(GFPm)}{dt} ={w(GFPi)-ym(GFPm)}$$
The corresponding K+ concentration vs mature GFP is as follows :
According to the model, the promoter is bound to show good activity within range 0-0.2mM of K+ concentration. Above these concentrations, the down regulation of gene is observed. The modelling gives us a good range to start for our experimental data. The results derived from testing BBa_K3306002 in different concentrations of potassium standard and then blood will provide us with real time data that can then validate the accuracy of the model.
All the values and the list of parameters that we've used for this model can be found here..