Team:BOKU-Vienna/Model

Modeling

Modeling.

With D.I.V.E.R.T. it is possible to create a large library of a mutant gene in vivo. An important part of creating a library is the amount of mutations introduced in this gene. Few mutations may not be enough to change a gene’s property, a huge amount of mutations, however, can lead to unfavorable effects regardless of small positive influences. Thus, the exact knowledge of the distribution of mutations is vital for creating functional libraries with D.I.V.E.R.T. Underneath, we are modeling how the distribution of clones containing a different amount of mutations changes over time and how this distribution is affected by a different growth rate µ and mutation rate f.

Introduction – total cell count:

The growth of microorganisms, or in other words the total cell count, in liquid culture can be described as:

The alteration of the total cell count X(t) over a specific time t depends on the specific growth rate µ and the total cell count at this specific time X(t). By solving this differential equation, the total cell count at any time can be calculated by: This formula shows the well-known exponential growth of microorganisms in liquid culture in excess of substrate. Whereas the total cell count at a specific time t is annotated as X(t), the cell count of clones with i mutations is written as Ai(t).

Solution of the differential equation for i = 0: