Angry birds

Problem:

Solution:

Define the reference frame with the origin at the bird's initial position, right is positive, up is positive.

Let the initial velocity of the bird to be $ \vec{v} $ and the launching angle be $ \theta $.


$ \begin{eqnarray*} v_x(t) &=& |\vec{v}|\cos\theta \\ v_y(t) &=& |\vec{v}|\sin\theta - gt \\ x(t) &=& (|\vec{v}|\cos\theta) t \\ y(t) &=& (|\vec{v}|\sin\theta) t - \frac{gt^2}{2} + 10 \\ \end{eqnarray*} $

Now put in the end conditions and simplify

$ \begin{eqnarray*} 12 = y(2.5) &=& (|\vec{v}|\sin\theta) (2.5) - \frac{g(2.5)^2}{2} + 10 \\ 13.3 &=& (|\vec{v}|\sin\theta) \\ 55 = x(2.5) &=& (|\vec{v}|\cos\theta) (2.5) \\ 22 &=& (|\vec{v}|\cos\theta) \\ \end{eqnarray*} $

Now we get $ \tan(\theta) = 13.3/22 $, or $ \theta = 31.15^o $.

Diophantine Equation

Problem:

$ x^2 + (y - \sqrt[3]{x^2}) = 1 $

Solution:

We have $ x^2 + y - 1 = \sqrt[3]{x^2} $, therefore $ (x^2 + y - 1)^3 = x^2 $, therefore $ x^2 $ must also be a cube.

The smallest non-trivial number that is both a square and a cube is 64, in that case, we have $ x = 8 $ and $ y = -59 $. In general, we can have $ x = n^3 $ and $ y = n^2 - n^6 + 1 $ for all integer $ n $.

Code

Problem:

Solution:

One number in 780 is correct but not correct position, but 738 is not correct, so 0 is correct and wrong position.

For 682, one number is correct but wrong position. We know 8 is impossible, but if the correct one is 6, then for 614, it couldn't be wrong position. Therefore we know 2 is correct and correct position.

By now, we know the answer is xx2, where one of them is 0, since 206 has two correct but wrong position, therefore the answer must be 0x2

Last but not least, we know 614 has one correct but wrong position, therefore the answer must be 042!

As always, the answer is 42!

Introduction to Biochemistry - End of session 3.7, 3.8 assessment

The change indicates an activation, therefore, the answer is

Addition of the allosteric ATCase activator, ATP
Performing the same experiment with the purified catalytic subunit of ATCase.

Heterotropic -> Different molecule
Allosteric -> Different site
Inhibition -> T state

Thefore the answer is:

A small molecule binds the enzyme at a site other than the active site, stabilizing the T state of the enzyme.

D - there is no reason for the substrate for D to accumulate when the free energy change is so large.

A high ratio of [ATP] over [AMP] in muscle cell means the energy state is high, so slow glycolysis.

Abundant citrate in muscle cell means we don't need pyruvate for the citric acid cycle, so slow glycolysis.

A high concentration of glucose in liver cells means we have a lot of substrate, so rapid glycolysis.

Glucagon signaling in the liver means the blood glucose is low, so slow glycolysis.

Liver pyruvate kinase and PFK-2.

This reaction is almost energy neutral (so that the equilibrium does not go one-way to either side)

The answer is shown in above.

An excess of acetyl CoA will inhibit the pyruvate dehydrogenase complex, and acetyl CoA will activate pyruvate caboxylase. The net result is an increase in gluconeogenesis.

3 and 6 are the concentration of the substrate, so they are
Fructose 6-Phosphate and Fructose 1,6-Bisphosphate respectively.

Fructose 2,6-Bisphosphate is an allosteric activator for PFK-1 and an allosteric inhibitor for FBPase-1, so the answer for 1, 2, 4, 5 are

+F2,6BP
-F2,6BP
-F2,6BP

+F2,6BP

 

High blood glucose stimulates the release of insulin.
The liver is more responsive than the muscle to glucagon.
Glycogenolysis is simulated by glucagon.

Glucose binds allosterically to glycogen phosphorylase

Individual with type I diabetes have reduced insulin production which lead to hyperglycemia

Hyperglycemia is too much sugar in the bloodstream.

Insulin

Type II Diabetes
Gestational Diabetes

Type I Diabetes
Type II Diabetes
Gestational Diabetes

Individual has type I diabetes, the 0 actually represents birth so this is young onset.

Individual has type II diabetes.

Patient 1 has diabete
Patient 2 is prediabetic

Ketone body production is the direct cause of metabolic acidosis.

A

False, the viral infection is environmental.

False, mutation in TYK2 is genetic.

Cytoplasmic receptors

Pro-apoptotic factors - beta cells handles infection by killing itself. That's why we have diabetes.
 

Mutation in PTPN2 results in reduced activity and increased risk for type I diabetes.

Pancreatic beta-cells undergo epitope spreading upon viral infection.

Insulin promotes glucose uptake and glycogen synthesis in muscle.
Insulin promotes glucose uptake and fat synthesis in adipose tissue.

When insulin level drops, plasma membrane glucose transporters are internalized and recycled.

It stimulates glycogen synthesis in response to insulin
It phospho-inhibits glycogen synthase kinase

It phospho-inhibits HSL, and
It promotes the synthesis of glycerol 3-P

Increased osmotic pressure of blood due to hyperglycemia

Inactive adipose tissue LPL due to lack of insulin correct
Increased liver VLDL release due to lack of insulin correct

It leads to vascular stiffening and retinopathy.

Fat layer under skin

Hypoglycemia is defined as too little sugar in the bloodstream.

IRS-1 activates phosphatidylinositol 3-kinase (PI3K) 

IRS-1 phosphorylation on serine residue
Conversion of PIP3 to PIP2 by a phosphatase

 

100:1 ratio of insulin to C-peptide and low glucose.

In type II diabetes, blood glucose is increased and blood fatty acids are increased.

Patient 1.

Increased intracellular calcium triggers the release of insulin vesicles

Potassium channels are closed by increased intracellular ATP

Sulfonylurea drugs close potassium channels leading to insulin release both in the presence and absence of glucose.

In Type II diabetes, insulin resistance develops in childhood, hyperglycemia develops in late adulthood, and decrease insulin production occurs in late adulthood.

Insulin secretion is normal in the first stage of the disease but tissues don’t respond to it as well.

Ectopic fat deposition interferes with GLUT-4 translocation
MCP-1 secreted from enlarged adipocytes recruits macrophages
TNFalpha stimulates fatty acid release from adipocytes that leads to ectopic fat deposition

Obesity is a major risk factor for Type II diabetes
Lipotoxicity and inflammation promote insulin resistance