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Consider a simple model for gene expression with reactions
Let α = 1/2, κ = 20 log(2)/120, δ = log(2)/120 and γ = log(2)/600, and answer the following questions:
(i) Use the stochastic simulation algorithm (SSA) to obtain realizations of the stochastic process of gene expression and numerically compare with the deterministic ODE solution. Explore how the realizations become close to or a part from the ODE solution when the volume is changed. Determine the stationary probability distribution for the protein (you can do this numerically).
(ii) Now consider the additional binding reaction of protein P with downstream DNA binding sites D:
Note that the system is no longer linear due to the presence of a bimolecular reaction. Use the SSA algorithm to obtain sample realizations and numerically compute the probability distribution of the protein. Compare it to what you obtained in part (i). Explore how this probability distribution and the one of C change as the rate constants a and d become larger with respect to γ,α,κ,δ . Do you think we can use a QSS approximation similar to what we have done for ODE models?
(iii) Determine the Langevin equation for the system in part (ii) and obtain sample realizations. Explore numerically how good this approximation is when the volume decreases/increases.
a) The input of Hex- to - seven segment decoder is 1010. what will the display show b) A priority encoder has all inputs activated. Which input will be encoded. Why c) how many select input lines are needed for a 128- to - 1 multiplexer
A certain power supply provides a continuous 2 W to a load. It is operating at 60% efficiency. In a 24 h period, how many kilowatt-hours does the power supply use?
suppose that you have a balanced stereo signal in which the left and right channels have the same voltage amplitude 500 mVpp. This time, however, you want to be able to mix these two channels into a single inverted output
Calculate the average power delivered to the circuit. - Draw the admittance diagram. - Draw the phasor diagram of the currents Is, IR, and IL, and the voltage E.
A small gasoline engine can put out 24,000 N-m/min of mechanical power. The engine is used to drive an electrical generator that is 70 percent efficient. 1 N-m = 2.78 X 10-4W-h. Find the output of the generator in Watts.
Determine whether the following discrete-time systems are causal or noncausal, have memory or are memoryless, are linear or nonlinear, are time invariant or time varying. In the following parts, x[n] is an arbitrary input and y[n] is the response
A certain power amplifier with crossover distortion has the input/output voltage relationship vo (t) = vi (t)3 (2.39) a) Use example voltage values to show that this does not satisfy the relationship. b) Let vi (t) = sin (pi t) .
If cathode and anode connections in a mercury arc rectifier are inter changed, What will Happen?
Replace all the current sources by a single current source. Find the source voltage Vs.
The rectangular beam shown is made of a plastic for which the value of the modulus of elasticity in tension is one-half of its value in compression. For a bending moment M = 600 N.m, determine the maximum (a) tensile stress, (b) compressive stress..
Three point charges are positioned in the x-y plane as follows: 5 nC at y = 5 cm, -10 nC at y = -5 cm, and 15 nC at x = -5 cm. Find the required x-y coordinates of a 20-nC fourth charge that will produce a zero electric field at the origin.
Consider the CMOS clocked circuit in Figure. - Assume the effective capacitance at the vO1 terminal is 25 fF.- determine the time for which vO1 will decay by 0.5 V.
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