The French flag model shown diagrammatically in Figure 20.3 states that the spatial location of developmental decisions, such as the expression of a gene, are made by reading out different levels of a morphogen gradient. As a result, if we were to change the input morphogen concentration, there should be a corresponding change in the downstream transcriptional decisions. (i) In class we discussed the case of Bicoid in the development of the fruit fly. Let c(x) denote the steady state concentration of Bicoid as a function of position along the anterior-posterior axis of the embryo. In a simple model that takes into account degradation and diffusion, with a boundary condition c(x = 0) = c0, what is the equation for c(x)? (ii) Under these conditions, a certain gene is expressed at position xg. What is the Bicoid concentration at xg? How would the position of the expression of the gene change if we were to change the overall Bicoid concentration by a factor of ?, i.e. change the boundary condition to c(x = 0) = ?c0?
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We are given that the Bicoid concentration is affected by degradation and diffusion. The degradation rate is proportional to the concentration, and the diffusion rate is proportional to the second derivative of the concentration with respect to position. Let's Show more…
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The French flag model shown diagrammatically in Figure 20.3 states that the spatial location of developmental decisions, such as the expression of a gene, are made by reading out different levels of a morphogen gradient. As a result, if we were to change the shape of the input morphogen, there should be a corresponding change in the downstream transcriptional decisions. (a) Model the Bicoid gradient in Drosophila melanogaster as an exponential with decay constant $\lambda$ and concentration at $x=0$ of $[\mathrm{Bcd}]_{0} .$ Under these conditions, a certain gene is expressed at position $x_{0}$. What concentration of Bicoid is there at the point $x_{0} ?$ How would the position of the expression of the gene change if we were to change the overall Bicoid concentration by a factor a? (b) Let's assume that a feature in Drosophila development such as the cephalic furrow, the boundary between the body of the fly and the structure that will give rise to its head, is determined solely by the Bicoid gradient. Given that for the wild-type case the furrow occurs at about $35 \%$ egg length. how would you expect the furrow to move if the dosage of the bicold gene were changed by adding or subtracting copies of gene on the genome? This question was asked by Driever and NĂşsslein-Volhard (1988) by creating mutant flies with different dosages of Bicoid, as shown in Figure 20.37 Compare their data for the displacement of the cephalic furrow with the model calculated in (a) by plotting them together. Does the model hold? Discuss the possible explanations. (Relevant data for this problem can be found on the book's website.
Exercise 3.9.6: Gene activation: Consider a gene that is activated by the presence of a biochemical substance. Let g(t) denote the concentration of the gene product at time t, and assume that the concentration of the substance, denoted by S0, is fixed. A model describing the dynamics of g is as follows: dg/dt = Kag - kso * sqrt(g) / (k3 + g) where the k's are positive constants. (a) Interpret each of the three terms on the right-hand side of the equation (be sure to mention the meaning of the k's). (b) Show that the equation can be put in the dimensionless form dx/dt = S_r * r + x, where r > 0 and S_r > 0 are dimensionless groups. What are r and S_r in terms of the original model parameters? (c) A graph of S_r versus x is shown in Figure 3.24 for the case S_r = 0 and r = 0.4. On the same set of axes, sketch graphs of S_r versus x for various values of S_r > 0. We will keep r fixed at 0.4 throughout the remainder of this question.
Sri K.
1. Studies of the regulation of a gene using a reporter system are often conducted as follows: the coding sequence for the fire fly luciferase gene has been fused with the DNA upstream of the transcriptional start site. To learn more about how your gene of interest's expression is regulated, it is very convenient to measure the amount of light released by the fire fly gene product when it is introduced into tissue culture cells. You conduct an experiment testing the following conditions and get the results indicated in a table below: Condition Tested | Amount of light produced (arbitrary units) Control | + Increased temperature | +++ Decreased glucose in the culture media | - Decreased temperature | - Increased osmolarity | ++ Decreased pH | ++ Increased pH | ++ the gene is regulated by temperature the gene is regulated by a number of stress responsive pathways, except for low temperatures the gene is constitutively expressed at a low level and has its expression lowered by sugar or low temperature. High temperature causes the largest increase in gene expression but changes in osmotic concentration (osmolarity) and pH are also strong inducers of this gene. the gene is constitutively expressed at high levels the gene is regulated by sugar levels
Farhan A.
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