Binding protein-dependent transporters: an answer of mathematics to biology

The problem discussed in this paper is to find a minimal model which is consistent with all experimental results known so far in binding protein-dependent transport systems. It is clear that the binding protein in its loaded form must communicate with the membrane components of the cell to transfer the substrate from the outside into the inside of the cell. It is shown that this simple reaction network is not able to explain most of the experiments in this field. There is a suggestion that the unloaded form of the binding protein also communicates with the membrane components. We show in this paper that this is a possible answer since the resulting network meets all qualitative experimental findings. Two mathematical models describing both situations are set up. We discuss in a mathematical analysis the characteristics of the solutions of these systems and compare the results with the actual experiments. Only the rate of transport is experimentally accessible. Hence, we calculate the rate of transport in our artificial system and discuss its qualitative behaviour.