Synthetic Biology: Gene Expression and Feedback Circuits
We want to speed up the response of a gene that is expressed constitutively, while keeping the steady state protein concentration unchanged. How can we do it?
– Increasing both
To increase the response rate of a gene, considering that its expression rate (alpha) is constant, we must modify -deltaP. An increase in the degradation rate (delta) makes the protein less stable and, therefore, faster (higher speed). To maintain the “steady state” unchanged, knowing that P*=alpha/delta, we must also increase the production rate (alpha) to keep the ratio constant.
A gene is expressed constitutively. Consider now two cells, A and B. If the initial concentration of the protein is very large in cell A and 0 in cell B, the final concentration of the protein after a long time is
– The same in both cells
The expression of a protein P is controlled by an activator A without cooperativity (Hill coefficient n=1). How does the amount of P depend on the concentration of A, if A is much smaller than the activation threshold (Michaelis constant) K?
– It grows linearly with A
The expression of a protein P is controlled by an activator A with high cooperativity (Hill coefficient n>>1). How does the amount of P depend on the concentration of A, if A is much larger than the activation threshold K?
– It’s basically independent of A and large
A protein is expressed constitutively and degraded enzymatically. If we ignore the saturation of the protease, we can conclude that a larger concentration of the enzyme implies that
– The protein reaches its steady state faster
In comparison with constitutive expression, a direct negative feedback is
– Faster and more robust
Consider a protein subject to negative feedback with repression threshold K, maximum expression rate alpha, and decay rate delta. This circuit is
– Sensitive with respect to K and robust with respect to alpha and delta
How many stable equilibria does a direct negative feedback circuit have?
– Always one
How many stable equilibria does a direct positive feedback circuit with no cooperativity have?
– It depends on the value of the circuit parameters
Consider a direct positive feedback circuit in a bistable regime. Which of the two basins of attractor is larger?
– That of the highest stable equilibrium
Consider a direct positive feedback circuit in a bistable regime. Which of the equilibria is robust to variations in the maximum expression rate alfa?
– Both the OFF and the unstable equilibria.
`The expression of a protein P is controlled by an activator A without cooperativity (Hill coefficient n=1). How does the amount of P depend on the concentration of A, if A is much larger than the activation threshold (Michaelis constant) K?
– It’s basically independent of A and large.
Without cooperativity, a minimal presence of the activator causes the protein to begin to express. At small concentrations of A, the concentration grows rapidly. However, there comes a point where the concentration of the protein saturates and does not vary. When A is much larger than K, we are at this point, and the concentration of P is very large and independent of A.
The sensitivity coefficient will depend on whether it is an activator or a repressor, as it will have a positive or negative sign. This is because if it is an activator, d0/dt will be positive, but if it is a repressor, d0/dt will be negative, as it is decreasing.
Consider a direct positive feedback circuit in a bistable regime. What happens when the decay rate delta increases?
– The ON equilibrium disappears
– The unstable equilibrium disappears
The ON and the unstable equilibrium disappear because they annihilate each other.
Consider these three circuits: (1) a protein that activates its own expression; (2) two proteins that activate each other’s expression; and (3) two proteins that inhibit each other’s expression. Which circuit or circuits constitute a positive feedback?
– All three
Two genes regulate each other’s expression. In this case, the concentrations of the two proteins
– May oscillate or tend to equilibrium