In: Biology

The lac operon possesses two kinds of genes, which includes structural genes and regulatory gene. Structural genes are transcribed into mRNA, and there are 3 types of structural genes,, namely lac Z, lac Y, and lac I. The regulatory genes are present in the lac operon: the operon and the promoter, which are not transcribed.

The structural gene

lac Z codes for protein beta-galactosidase.

lac Y codes for beta-galactosidase permease

lac A codes for beta-galactosidase transacetylase.

The repressor protein synthesized by gene "I" binds to the operator and inhibits the transcription. If the bacterium lacks lactose in its environment and then lactose is suddenly introduced,, a high concentration of lactose in the cell binds to the repressor. It makes it unavailable for binding and allows RNA polymerase to transcribe the structural genes.

A mutation in the "I" gene and operator gene (O) causes constitutive expression of the protein. The mutation in the "O" gene modifies the structure of the operator gene. As a result, the repressor no longer binds to the operator, and RNA polymerase initiates transcription continuously. Similarly, if lac “I” is mutated, the repressor protein would not function properly, and the lac operon would be overexpressed.

Based on the above-provided data, each region of the lac operon on the F' plasmid, I+ P+ Oc Z− Y+, determines as follows:

The promoter sequence is correct/functional.

The repressor protein is produced.

Permease is produced from the lac Y gene.

below is the mutated lactose (lac) operon in a partial
diploid.
I+ P+ Oc Z? Y+ / I- P+ O+ Z+ Y?
Predict the expression of the lac
genes in the presence of lactose and Explain your answer
by drawing a diagram how the presence of lactose
acts to either induceor repress
the expression of the lac genes

below is the mutated lactose (lac) operon in a partial
diploid.
I+ P+ Oc Z? Y+ / I- P+ O+ Z+ Y?
Predict the expression of the lac
genes in the presence of lactose and Explain your answer
by drawing a diagram how the presence of lactose
acts to either induceor repress
the expression of the lac genes

This question refers to the lac operon. Select the correct
phenotype for the genotype: I--P+O+Z+/I+P--O+Z-- [Terminology: β
Galactosidase activity = β Gal activity]
Select one: no β Gal activity, with no lactose (--) , β Gal
activity with lactose (+) no β Gal activity, with no lactose (--) ,
no β Gal activity with lactose (--) β Gal activity, with no lactose
(+) , β Gal activity with lactose (+) β Gal activity, with no
lactose (+) , no β...

This question refers to the lac operon. Select the correct
phenotype for the genotype: I--P--OcZ--/I+P--O+Z+
[Terminology: β Galactosidase activity = β Gal activity]
Select one:
a-no β Gal activity, with no lactose (--) , β Gal activity with
lactose (+)
b.no β Gal activity, with no lactose (--) , no β Gal activity
with lactose (--)
c-β Gal activity, with no lactose (+) , β Gal activity with
lactose (+)
d-β Gal activity, with no lactose (+) , no β...

Find the maximum and minimum of the function f(x, y, z) =
(x^2)(y^2)z in the region D = {(x, y, z)|x^2 + 2y^2 + 3z^2 ≤
1}.

Consider F and C below.
F(x, y, z) = yz i + xz j + (xy + 14z) k
C is the line segment from (3, 0, −1) to (6, 4, 2)
(a) Find a function f such that F =
∇f.
f(x, y, z) =
(b) Use part (a) to evaluate
C
∇f · dr along the given curve C.

How do you determine convexity/concavity of a function f(x,y)?
How about a function f(x,y,z)?

Calculate the directional derivative of
f(x,y,z)=x(y^2)+y((1-z)^(1/2)) at the point P(1,−2,0) in the
direction of the vector v = 5i+2j−k. (a) Calculate the directional
derivative of f at the point P in the direction of v. (b) Find the
unit vector that points in the same direction as the max rate of
change for f at the point P.

Given a scalar fifield φ(x, y, z)=3x2-yz and a vector
field F(x, y,
z)=3xyz2+2xy3j-x2yzk.
Find:
(i)F.∇φ.
(ii)F×∇φ.
(iii)∇(∇.F).

2. In each of the following problem sketch the graph of f(y)
versus y, determine the equilibrium solutions, and classify each
one as asymptotically stable, asymptotically unstable, or
semi-stable. Draw the phase line, and sketch several graphs of
solutions in the ty-plane. Here y0 = y(0).
(a) dy/dt = e ^y − 1, −∞ < y0 < ∞
(b) dy/dt = (e^-y) − 1, −∞ < y0 < ∞
(c) dy/dt = (y^2)* (1 − y)^ 2 , −∞ <...

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