Introduction

Based on a set of ordinary differential equations describing the kinetics of cellulose-binding modules (CBM) binding to bacterial cellulose, the model is designed to predict the efficiency and affinity of the binding process. Given an initial concentration of CBM injected into the system, the model is enabled to calculate the time allowed for a certain percentage of protein binding sites on bacterial cellulose to be saturated.

Mathematical Background

Model I

• Variables:
  • CBS(0): initial concentration of cellulose binding sites (CBS)
  • CBS(t): concentration of unoccupied CBS at time t
  • CBM(0): initial concentration of CBM injected into the system
  • CBM(t): concentration of unbound CBM
  • CBS_CBM(t): concentration of binding complex (CBS bounded with CBM)
• Parameters:
  • k_on: association rate constant
  • k_off: dissociation rate constant
  • K_D = k_off/k_on: equilibrium dissociation constant
• Binding Kinetics:
  • 
  • Assume CBM(t) = CBM(0) due to large concentration of CBM injected into the system compared to initial concentration of cellulose binding sites.
  • With the boundary conditions:
    • CBS_CBM(0) = 0
    • CBS_CBM(∞) = CBS(0)
  • The ODE can be solved as:
    • 
    • where k_on CBM(0) >> k_>off

Lab Interaction

Parameters in the previous expression are determined by assay experiments where k_off and k_d are found, from which k_on is calculated: k_on=k_off/k_d.

LAB RESULTS HERE

With the parameters obtained from the experiments, the model is then enabled to predict an exact time period for the binding sites to be saturated, where the validity of the model is further confirmed by the experiments (refer to CBD expression experiments in the drive).

Results and Conclusions

References

1. Zhang, Mengmeng; Wang, Bin; Xu, Bingqian Mapping Single Molecular Binding Kinetics of Carbohydrate-Binding Module with Crystalline Cellulose by Atomic Force Microscopy Recognition Imaging J. Phys. Chem. B 2014, 118, 6714−6720s

Code