Lecture 3

Question 1

Example of Cooperatively - Hemoglobin and Myoglobin

Answer 1

• Oxygen transport from lung into body via erythrocytes
  -> Transporter molecules: hemoglobin (Hb4) => can carry 4 oxygen molecules
  -> Hemoglobin composed of 4 polypeptides with one heme group each
  -> Each heme group contains an iron atom, each iron can bind one O2
• Binding of O2 changes hemoglobin shape & binding affinity
  -> No O2 bound: least anity, 3 O2 bound: highest affinity
• Saturation curve of hemoglobin => allosteric eect
• Dependent on partial pressure of oxygen
• Reminder:
• Ideal gas law PV=nkT
• Gas mixture with parts xi:
• Partial pressure: Pi=xiP
• gas-liquid relationship:
• i: solubility ci = iPi
• Hb becomes saturated under high partial O2 pressure
• Dependent on pH, temperature & 2,3-diphosphoglyceric acid (DPG)

Question 2

Oxygen loading and unloading

Answer 2

• Blood in pulmonary artery has PO2=5kPa
• Aveoli in Lung have PO2=16kPa
• With Hb being 100% saturated at 10kPa
• Gas exchange only possible in tissue & Lung
• Respiring tissue: low PO2=5-7kPa
• Oxygen dissociates from Hb and diuses into cell

Question 3

Myoglobin

Answer 3

• Myoglobin found in muscle tissue
• One polypeptide and one heme group => can bind one oxygen
• Allows storage of oxygen in muscle tissue
• In anaerobic situation: oxygen dissociates & used for cell respiration
• Dierence to Hemoglobin: higher anity to oxygen at low partial pressure => Oxigen goes from Hb to myoglobin
• Low partial pressures: O2 used up in aerobic respiration
• Oxygen replaced during rest => excess post-exercise oxygen consumption

-> Has one Heme group, can bind one oxygen molecule, forms Oxymyoglobin

Question 4

Results - Consequences Hemoglobin binding

Answer 4

• Fit to empirical curve:
  K1 = 45.9mmHg
  K2 = 23.9mmHg
  K3 = 23.1mmHg
  K4 = 1.5mmHg
• Note K4 «_space;K3,K2,K1
• if 3 O2 molecules bound: high anity to bind fourth one.
• hard to dissociate fourth O2 molecule
• Fetal hemoglobin (HbF) dierent from normal hemoglobin (Hb).
• The fetal dissociation curve is shifted to the left => enhances uptake of oxygen.
• At 5kPa HbF 80% saturated, adult Hb only 50%
• PO2 in fetal tissue low due to high metabolism & cell growth => no problem to unload O2
• HbF replaced by adult Hb at birth
• Crocodile hemoglobin can bind bicarbonate
• enriches during diving, reduces O2 anity via allosteric aect => more oxygen released into blood
• Seals have high amount of muscle myoglobin

Question 5

Ultrasensitivity in the mitogen activated protein kinase cascade

Answer 5

• Mitogen activated protein cascade highly conserved (Mitosis inducing)
  -> Series if three protein kinases implicated in diverse processes
  -> Relays signals from membrane to nucleus
  -> MAPKKK: MAPK kinase kinase -> activates via phosphorylation
  -> MAPKK: MAPK kinase -> activates via phosphorylation
  -> MAPK
• Jak/Stat cAMP/PKA: transmit via single protein kinase
• Why are three kinases used for MAPK?
  -> Ultrasensitivity: enzyme responds more than gradual (MM-like)

Question 6

MAPK Cascade

Answer 6

• Ultrasensitivity via multiple steps of a kinase cascade
• Ultrasensitivity increasing with descending the cascade
• Highly robust against changes in parameter values
• Heinrich Model (2002):
  -> Kinases: no influence on signaling time and duration, but amplitudes
  -> High amplitude: fast kinases, slow phosphatases
  -> Either high amplitudes or long signaling duration

Question 7

Experimental Validation

Answer 7

• Measurement of MOS/MEK1/P42 of Xenopus oocyte cascade
• Stimulation with malE-Mos
• Turns a graded response into switch-like behavior
• Robust against noise

Question 8

Negative Autoregulatory Loop

Answer 8

• Common regulatory motif in engineering and biology
  -> Morning shower
• Circuits reach same steady state level
• TetR represses expression
• Relief through aTc: anhydrotetracycline
• Genes reside on plasmids introduced into E. Coli strain

Want to achieve:
- fast rise time of signal
- robustness against noise
- Benefit:
-> fast rise without excessive protein turnover

• Protein decay is not affected!

Question 9

Toggle Switch

Answer 9

• Constructed on a plasmid in E.coli
• Inducer 1: IPTG (Isopropyl beta-D-1-thiogalactopyranoside)
  -> P1: triggers lactose (lac) repressor
  -> suppresses Ptrc-2
• Inducer 2: Ptrc-2-R1
  -> pTAK plasmid
  -> P1: PLS1con suppressed by temperature sensitive cats
  -> pIKW plasmid
  -> PLtetO-1 suppressed by TetR

Question 10

Toggle Switch Dynamics

Answer 10

• Transient IPTG / Temperature pulses switch high/low state
• Switching takes about 6 hours from low -> high

Question 11

Dynamic systems

Answer 11

Every system reducible to higher-dimensional, first-order time derivative
-> will consider only first order derivative in time
* Linear System: xi appear in first power only
* Nonlinear System: xi appear as products, powers or functions

Phase Space
2n-dimensional space consisting of the possible values of is known as its phase space (x1, x·1, x2, x·2, …, xn, x·n)
all possible states of a system are represented

Question 12

Conclusions Law of Mass and Michaelis Menten

Answer 12

• Law of Mass Action allows modeling chemical reactions as ODE
• Allows to calculate equilibria and dynamic changes in concentration
• Michaelis Menten: enzyme kinetics, approached via quasi-steady state
• Cooperativity through multiple binding sites => allows for faster & switch like chemical behavior