Team:UANL Mty-Mexico/Modeling/transport and accumulation

Transport and accumulation

Before us, team iGEM Groningen 2009 made a model for an arsenic accumulator at the population level; that is, they set some ODEs that represent the change on the total intracellular arsenic (considering not a single cell, but the whole culture, or more exactly, the total cell volume) with respect to time. Nevertheless, as the precise value for some parameters were unavailable, specially for the ArsB effect, part of their model remains aparameterized and they perform a quasi-steady state analysis.

After considering the effect of their metallothioneins (As-binding proteins), GlpF, ArsB and ArsR, they ended with the following time derivative:

\begin{equation} \[\frac{\mathrm{d[As(III)in] } }{\mathrm{d} x} = -(ArsR::As) - (MBP::ArsR::As) - (nf\cdot fMT::As)- (k_{1}\cdot ArsB::As) + (Vs/Vc)\cdot k_{2}\cdot GlpF::As\] \end{equation}

We built upon their model and made the following modifications:

We assume that ArsB is non functional, so that the only protein affecting As transport is GlpF.

We assume that the intracellular As concentration at the population level (that is, considering total cell volume) is homogeneously distributed and should be the same as in a single cell.

They also characterized the BioBrick corresponding to the GlpF transporter

Core model

ODEs

Parameters

Simulations

Steady state analysis

Model considering lethal level of intracellular free As

Population level model