Team:EPF Lausanne/Modeling
Kinetic model
In our project different transistor elements are putted together in order to create logic gates and the idea is to chain these gates in order to create complex logic circuits within cells. Because of this chainability of different elements, we have a cascade of reactions which will eventually reach a stationary state. In order to study in depth the behavior of our system we decided to use a kinetic model, where time dependency of the concentration of different species is taken into account explicitly.
Assumptions
A model which is too complex and too detailed can surely describe experimental results with precision, but it is often difficult to interpret and to understand in details. It is therefore useful to come out with the simplest model that can reproduce the system behavior, which can then be understood in details and used to predict new results.
In order to find a simple model which can reproduce experimental results we have to do many simplifications and assumptions over reality. In this section we will try to keep track of the assumptions we made in order to clarify our model. Every assumption is analyzed details: assumptions are generally not uniques, but we will try to justify our choices.
The most important assumption underlying the kinetic model is the fact that the concentration of a given specie does not depends on spatial coordinates, i.e. it is the same in every region of the cell. This assumption is quite strong but it's a common approach in the literature and usually gives good results. Note however that within a cell the validity of concentration idea itself can be doubtful, since the number of molecules can be small and since these molecules can be localized to membranes or particular organels; in these cases it is necessary to consider the stochastic behavior of individual trajectories rather than global averages [1].
A challenging problem we faced to build our model concerns kinetic constants. Since dCas9 is a newly discovered gene regulation technology [2], gRNA/dCas9 and gRNA+dCas9/DNA binding kinetic is still under research. It is easy to imagine that binding/unbinding constants depend (at least sligthly) on the gRNA sequence because of the different chemical properties of nucleotides. However, we will consider that these binding/unbinding constants are gRNA-independent. For the gRNA/dCas9 interaction, this assumption is justified by the fact that the gRNA scaffold is always the same. For the gRNA+dCas9/DNA interaction [...]
dCas9 degradation is a fundamental process in our system: high levels of dCas9 within the cell are toxic [3], thus a continuous change in dCas9 population is needed to propagate the signal from one gate to another (remember, the output of a gate is a gRNA which will bound to a free dCas9 in order to propagate the signal to the next gate). We can imagine three different ways of gRNA/dCas9 complex degradation: the degradation of the whole complex, degradation of the dCas9 leaving the gRNA and the degradation of the targeting sequence of the gRNA leaving a non-functional and occupied dCas9. Since the unbinding probability of gRNAs from dCas9 proteins is extremely low [4], we consider only the degradation of the whole complex; we assume in addition that this degradation rate is the same of the dCas9 not bound to a gRNA.
Summary
- Concentrations depends only on time
- dCas9 binding/unbinging is gRNA-independent
- gRNA/dCas9 is degraded as a complex, whit the same rate as dCas9 alone
Constants
Equations
Simulation
Bibliography
[1] R. Phillips et al., Physical Biology of the Cell, Second Edition, Garland Science, 2013.
[2] L. S. Qi et al., Repurposing CRISPR as an RNA-Guided Platform for Sequence-Specific Control of Gene Expression, Cell 152, 1173–1183, 2013.
[3]
[4]
