To sketch the graph of the nonlinear function g(p) = βp n K n +p n , for n >> 1 and to find the simple shape the function approaches as n → ∞ , if the basal expression is given as p ˙ = α + βp n K n +p n - δp . The phase portrait for the system for δK - α > β , δK - α = β 2 , and δK - α < 0 is to be plotted. To plot the bifurcation diagram for the system, assuming δK > β , and to indicate how the location and stability of the fixed points p* vary with respect to α . To discuss how p behaves if is very slowly increased from α = 0 to α > δK , and then very slowlydecreased back to α = 0 . To show that such a pulsed stimulation leads to hysteresis. Concept Introduction: The basal expression is p ˙ = α + βp n K n +p n - δp Here α is the basal transcription rate, β is the maximal transcription rate, K is the activation coefficient, and δ is the decay rate of the protein.

Question

Want to see the full answer?

Answer 1

Question

Chapter 3.7, Problem 7E

Interpretation Introduction

Interpretation:

To sketch the graph of the nonlinear function $g(p) = βpnKn+pn$ , for $n >> 1$ and to find the simple shape the function approaches as $n→∞$ , if the basal expression is given as $p˙ = α +βpnKn+pn - δp$ . The phase portrait for the system for $δK - α > β$ , $δK - α = β2$ , and $δK - α < 0$ is to be plotted. To plot the bifurcation diagram for the system, assuming $δK > β$ , and to indicate how the location and stability of the fixed points $p*$ vary with respect to $α$ . To discuss how $p$ behaves if is very slowly

increased from $α = 0$ to $α > δK$ , and then very slowlydecreased back to $α = 0$ . To show that such a pulsed stimulation leads to hysteresis.

Concept Introduction:

The basal expression is

$p˙ = α +βpnKn+pn - δp$

Here $α$ is the basal transcription rate, $β$ is the maximal transcription rate, $K$ is the activation coefficient, and $δ$ is the decay rate of the protein.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

9.7 Given the equations 0.5x₁-x2=-9.5 1.02x₁ - 2x2 = -18.8 (a) Solve graphically. (b) Compute the determinant. (c) On the basis of (a) and (b), what would you expect regarding the system's condition? (d) Solve by the elimination of unknowns. (e) Solve again, but with a modified slightly to 0.52. Interpret your results.

12.42 The steady-state distribution of temperature on a heated plate can be modeled by the Laplace equation, 0= FT T + 200°C 25°C 25°C T22 0°C T₁ T21 200°C FIGURE P12.42 75°C 75°C 00°C If the plate is represented by a series of nodes (Fig. P12.42), cen- tered finite-divided differences can be substituted for the second derivatives, which results in a system of linear algebraic equations. Use the Gauss-Seidel method to solve for the temperatures of the nodes in Fig. P12.42.

9.22 Develop, debug, and test a program in either a high-level language or a macro language of your choice to solve a system of equations with Gauss-Jordan elimination without partial pivoting. Base the program on the pseudocode from Fig. 9.10. Test the program using the same system as in Prob. 9.18. Compute the total number of flops in your algorithm to verify Eq. 9.37. FIGURE 9.10 Pseudocode to implement the Gauss-Jordan algorithm with- out partial pivoting. SUB GaussJordan(aug, m, n, x) DOFOR k = 1, m d = aug(k, k) DOFOR j = 1, n aug(k, j) = aug(k, j)/d END DO DOFOR 1 = 1, m IF 1 % K THEN d = aug(i, k) DOFOR j = k, n aug(1, j) END DO aug(1, j) - d*aug(k, j) END IF END DO END DO DOFOR k = 1, m x(k) = aug(k, n) END DO END GaussJordan