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. For a specific type of cell after 3hours, the concentration of cells per ml of solution is about400/mL. After 10 hours the concentration has gone up to 2000/mL.Determine the initial concentration of cells. Assumegrowth kinetics are X =X0e^ut whereX0 is initial concentrationof cells (i.e. number of cells at t=0), u is the rate constant andX is the concentration of cells after a certain timehas elapsed.



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Patrina Schowalter
Patrina SchowalterLv2
28 Sep 2019

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Related questions

3. Equilibrium

Insulin resistance occurs when cells no longer bind insulin in a normal manner, thus inhibiting the cells from transporting glucose inside the cell. Without intercellular glucose the cells cannot produce energy to support life.

Let’s suppose part of your project requires you to study the equilibrium reaction between the new variation of insulin you synthesized and cell receptors on the walls of cells. This is the equilibrium expression you propose.

cell receptor + free insulin cell receptor-insulin complex

or in abbreviated terms

R + I R-I

You devise a method of measuring the free insulin in solution. You run two experiments under the same conditions, except one experiment uses your modified insulin and the other experiment uses normal insulin. Table 1 below provides the initial conditions of your experiment and Table 2 provides the data you collected after equilibrium was established.

Initial Conditions for both experiments – all environmental conditions are kept constant (e.g. temperature at 34oC, pressure at 1 atm, pH at 7.4). A single stock nutrient and cell receptor solution was prepared with a concentration of 70 uM. 50 mL the solution was used in all experiments. The insulins were added as powders, so the volumes essentially remained unchanged.

Table 1: Initial Experimental Conditions

Experiment 1

Experiment Control

[free modified insulin] = 100.0 uM

[free normal insulin] = 100.0 uM

[cell receptor] = 70.0 uM

[cell receptor] = 70.0 uM

Table 2: Unbound Free Modified Insulin and Unbound Free Normal Insulin Levels at Equilibrium

Experiment 1

Experimental Control

[free modified insulin] = 35.0 uM

[free normal insulin] = 50.0 uM

Write the equilibrium expression for this reaction using [I] to represent the insulin concentration, [R] the cell receptor concentration, and [I-R] to represent the cell receptor-insulin complex concentration. (10 pts) Show all work.

Determine an equilibrium constant for both the modified insulin and the normal insulin reaction at 34oC based on the data above. (10 pts)

[free modified insulin]

[receptor]

[Insulin-receptor]

I

C

E

[free normal insulin]

[receptor]

[Insulin-receptor]

I

C

E

Which type of insulin binds more strongly to the cell receptor? Explain your answer. (10 pts)

Suppose the concentration of the receptor in the stock solution dropped to 50.0 uM. If you ran the experiment again with the same initial concentration of free modified insulin as above, what would you expect the free modified insulin’s equilibrium concentration to be? (10 pts)

[free modified insulin]

[receptor]

[Insulin-receptor]

I

C

E

Can someone please help me with this? I dont understand what to fill in the ice tables.

Please answer questions at the end.

In this lab, you will add different volumes of “cell-free supernatant” (CFS) to fresh cultures of V. harveyi and observe bioluminescence. The CFS is prepared by culturing V. harveyi in liquid medium overnight, then separating the cells from the supernatant by centrifugation.

MATERIALS • overnight culture of V. harveyi in AB medium • fresh AB medium • 1 microcentrifuge tube • 3 glass culture tubes

PROCEDURE

1. This experiment will be performed with your lab group. Label the microcentrifuge tube and 3 glass cultures tubes with your group number. Also, label the 3 glass culture tubes as follows: “Media only,” “Cells+fresh media,” and “Cells+CFS.”

2. Using aseptic technique, pipet different volumes of fresh AB medium into the glass tubes as follows: 1 mL in the “Media only” tube, 800 ul in the “Cells+fresh media” tube, and 500 ul in the “Cells+CFS” tube.

3. Pipet 500 ul of the overnight culture into a microcentrifuge tube and centrifuge at maximum speed (>13,000 x g) for 5 min to pellet the cells.

4. After centrifugation is complete, transfer 300 ul of the cell free supernatant (CFS) from the microfuge tube to the glass tube labeled “Cells+CFS”. Be careful to avoid the cell pellet.

5. Remove the remaining supernatant from the microfuge tube using a micropipette and discard as culture waste.

6. Add 500 ul of fresh AB medium to the cell pellet in the microfuge tube and pipet up and down to resuspend until no clumps are visible.

7. Add 200 ul of the cell suspension to the “Cells+fresh media” tube and 200 ul of the cell suspension to the “Cells+CFS” tube. Note the time.

8. Place the 2 glass tubes containing cells in the 30 degree incubator/shaker.

9. After 1 hour and 2 hours, observe your tubes next to the “Media only” tube in a dark room. You will need to let your eyes adjust for at least 30 seconds (count to 30 slowly in the dark) before you can evaluate whether the cultures are luminescent or not. Also, make sure you try swirling the tubes in the darkroom and observe the tubes for a minute after you have stopped swirling. After the observation at the 1 hour time point, put your tubes back in the incubator shaker until the 2 hour time point.

10. Note your observations. At the end of the lab, place your tubes in the tube waste.

Questions

1. What were the expected results? Explain the rationale of the experiment. If you didn’t obtain the expected results, hypothesize why not and describe how the experiment could be improved.

2. What are differences between luminescence and fluorescence?

3. Why do V. harveyi cultures glow more brightly when swirled vigorously? Be specific.

4. Imagine you have a mutant V. harveyi strain that can’t synthesize autoinducer and another mutant V. harveyi strain that makes a defective luciferase. If you streaked both strains near (but not touching) each other on the same plate, would you expect to see light produced? If so, by which strain, where, and why?

5. You have two identical tubes of wild-type V. harveyi (with the same cell concentration in each tube) in fresh media. To one tube, you add CFS from a light-producing V. fischeri culture, and to the other tube you add an equal volume of fresh media. If both tubes of V. harveyi have the same light production, what can you conclude? Explain.

6. Many biomedical research labs study quorum sensing in V. fischeri or V. harveyi. How is studying light production in marine bacteria relevant to human health? List at least 3 different examples.

7. Why do you think it is important for bacteria to be able to control the expression of some genes based on the number of individuals present?

describe the definitions of substrate, enzyme active site and its general characteristics, and apoand

holo-enzymes.

· describe the fact that enzyme catalysis is specific in terms of the type of reaction and the exact

substrate structure.

· Explain the difference in the “lock-and-key’ model and the induced fit model of enzyme

substrate interaction.

· describe that reaction rate constant thus reaction rate is dependent on the activation energy.

· describe the relationship between the energy of the transition state and the activation energy.

· describe the relative binding affinity of a substrate and its transition state to the enzyme.

· Explain how enzymes speed up reaction rate, i.e., how do enzymes lower the activation

energy. Note: Factors other than preferential stabilization of transition state also contribute to increased

reaction rate. They include 1) enzymes placing one substrate (reactant) next to the other substrate (reactant)

so that the reaction is no longer dependent on the collision rate of the two substrates; 2) enzymes sequester the

substrate(s), minimizing solvent competition thus speeding up the reaction; 3) in enzyme complexes with each

enzyme catalyzing one step in a multi-step reaction sequence, the product of one reaction is fed to the active site

of another enzyme for the next step without the product diffusing away from the enzyme complex thereby

increasing reaction rate.

· describe the Michaelis-Menten equation relating the initial velocity to total substrate

concentration.

· describe the assumptions that went into the derivation of the Michaelis-Menten equation. ([E]

is constant, steady state assumption, etc)

· describe the relationship between Vmax and kcat and the fact that kcat is a constant for a given

enzyme and substrate at a given temperature and solution condition; whereas Vmax can differ

for a given enzyme and substrate at a given temperature and solution condition, depending

on the enzyme concentration.

· describe the definition of Kd (equilibrium dissociation constant for ES into E and S).

· describe the relationship between Kd and the affinity of substrate for the enzyme, i.e., the

higher the Kd, the weaker the binding between E and S.

· describe the relationship between Kd and Km, i.e., in general, the higher the Kd, the higher theKm.

· Use the Michaelis-Menten equation and the relationship between Vmax and kcat to do

calculations.

· describe the other names for the catalytic rate constant, kcat (i.e., the turn over number; also

called krelease) and why it is so called (kcat reports on per unit time per enzyme molecule the

number of product molecules formed/released, thus the name turnover number or krelease).

· Determine Vmax and Km using both the Michaelis-Menten plot (initial velocity versus [S]) and

the Lineweaver-Burk Plot (the double reciprocal plot), given the data of initial velocity and

[S].

· Draw the Michaelis-Menten plot AND the double reciprocal plot (Lineweaver Burk), given

the Vmax and Km values.

· describe the fact that the term kcat/Km is the best parameter for measuring the catalytic

capability (efficiency) of an enzyme.

· describe the existence of irreversible enzyme inhibition and the general mechanisms of

irreversible inhibition.

· describe the different types of reversible inhibitions, namely the competitive, uncompetitive,

and mixed inhibitions (noncompetitive inhibition is a special case in which the inhibitor

binds E and ES with equal affinity therefore α is equal to α’ – Km is not affected).

· Describe each type of inhibition in terms of inhibitor binding site (active site or other than

the active site), how the inhibitor affects vmax and Km and the quantitative relationship of

each parameter with and without the inhibitor present and their relationship with [I] and KI

or KI

’

.

· Show the characteristics of each type of inhibition on a Michaelis-Menten plot (initial

velocity versus total substrate concentration), i.e. draw the curves with and without the

competitive inhibitor.

· Show the characteristics of each type of inhibition on a double reciprocal plot (LineweaverBurk

Plot) by drawing the lines with and without the competitive inhibitor.

· Given the Michaelis-Menten or double reciprocal plot with and without the inhibitor,

determine the type of inhibitor.

· describe the fact that transition state analogs are potent inhibitors.

· Explain why transition state analogs are potent inhibitors.

· describe that not all enzymes obey Michaelis-Menten kinetics.

· describe situations when an enzyme will not obey Michaelis-Menten kinetics (when the enzyme

catalyzes reactions with multiple substrates or when the enzyme is allosteric, i.e. binding of

the substrate at one active site affects the other active site(s) for the same substrate).

· Name the four types of catalytic mechanisms. (electrostatic catalysis, general/specific acid

base catalysis, metal ion catalysis, covalent catalysis)

· Contrast acid/base catalysis to general acid/base catalysis, i.e., comment on their similarity

and difference.

· Name the eight common general acid/base pairs in proteins and write the formula of the

acid and base form for each pair (hint: consider the eight amino acids that have ionizable

side chains…)

· describe the meaning of covalent catalysis.

· describe the reaction catalyzed by chymotrypsin and the three catalytic residues in

chymotrypsin.

· Draw the interactions among the three catalytic residues (catalytic triad).

· State the catalytic role of each of the catalytic residues and how they accomplish that.

· describe the steps in the formation of the acyl-enzyme intermediate, and the substrate and

products in this first part of the chymotrypsin mechanism.

· Draw the transition state structure for the formation of the acyl-enzyme intermediate and

indicate by drawing how it is preferentially stabilized.

· describe the steps in the regeneration of chymotrypsin (deacylation), the substrates and

product of this second part of the chymotrypsin mechanism.

· Draw the transition state for deacylation and explain how it is preferentially bound to or

stabilized by the enzyme.

· Explain what general acid and base catalysis refers to and what groups act as the general acid

and base in the chymotrypsin mechanism.

· Explain what covalent catalysis refers to in the chymotrypsin mechanism.

· Explain the basis for the substrate specificity of chymotrypsin (consider the composition of

the active site – chymotrypsin specifically cleaves peptide bonds adjacent to aromatic

residues)

· Explain the term “serine protease”. Answer: these are proteases (enzymes that

hydrolyze peptide bonds) that have serine as a catalytic residue (that acts as a

nucleophile, which can attack the carbonyl carbon of the peptide bond).

· Key features of Hexokinase, enolase and lysozyme mechanisms that were discussed in class

(specific methods of catalysis utilized by these enzymes; general description of overall

catalytic transformation)

· describe the four regulatory strategies of enzyme catalysis

· describe the definition of feedback inhibition (mechanism of cellular regulation that regards an

enzyme that catalyzes the production of a given substance that then inhibits the cell when

concentration of that substance has reached an appropriate level – this balances/regulates

amount of product provided with amount needed)

· describe the most common type of covalent modification and the types of enzymes

responsible for the addition and removal of the chemical group in this covalent

modification.

· Explain the general mechanism of phosphorylation in regulating enzyme activity.

· describe the general naming scheme for active and inactive proteases.

· describe that protease inhibitors exist to inhibit protease.

· describe that enzymes are regulated through covalent and non-covalent processes.

· Noncovalent regulation

o Describe noncovalent modification in general terms. Elaborate on the relation

among enzyme activity, allostery, effector molecules (small molecules) and control

proteins.

o Concerning allosteric regulation, some enzymes have multiple active sites for the

same substrate and the binding of the substrate increases the activity of the enzyme

by stabilizing the R (more active) state over the T (relatively inactive) state. (Lecture

13: “Noncovalent Modification: Allosteric Regulators”)

ß Draw a curve for the initial reaction velocity versus substrate concentration.

ß describe and explain the specific shape of the v0 vs. [S] plot.

ß Draw on the same graph above a v0 vs. [S] curve for the enzyme in the

absence of allostery. and how th i.e., in the absence of conformational change

upon substrate binding. Comment on the shape of this curve.

ß Comment on the benefit of allosteric activation.

ß When an inhibitor is present for such an allosteric enzyme, the v0 versus [S]

plot will shift. Draw a v0 vs. [S] curve with and without the inhibitor.

ß When an activator is present for such an allosteric enzyme, the v0 versus [S]

plot will shift. Draw a v0 vs. [S] curve with and without the inhibitor.

ß When an activator is present for such an allosteric enzyme, the v0 versus.

ß describe the relationship between feedback inhibition and allosteric regulation

and the reason behind the term “feedback inhibition”.

· Covalent regulation

o describe the most common covalent modification, the enzymes that catalyze the

modification and the removal of that modification, respectively and the amino acid

residues that tend to be the site of this modification.

o Write the structure of the added group bonded to those residues and the reaction for

this covalent modification.

o Rationalize the effectiveness of phosphorylation on altering the activity of an

enzyme.

o describe the mechanism of chymotrypsinogen activation to chymotrypsin (cleavage of

zymogen by trypsin).

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