Bioengineering/matlab
Zorosenpai
Lecture_101018.pptxReview
| 1 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | -1 | -1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | -1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 1 | -1 | -1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | -1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | -1 |
Draw the pathway
| 1 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | -1 | -1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | -1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 1 | -1 | -1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | -1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | -1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
| 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | -1 |
| 0 | 0 | 0 | 0 | 1 | -1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | -1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | -1 | 0 |
rref
Rank:
Nullity:
Dimension:
Free variables:
Find J
E+S
ES
E+P
k1
k-1
k2
k-2
Previously we looked at rapid equilibrium (kp ~ k2) and therefor the [P] depended only on k2[ES] rate.
Michaelis-Menten is useful in calculating enzyme kinetics of a system where a substrate can reversibly bind to an enzyme
Under quasi-steady state assumption, we assume that the change of concentration of the enzyme and enzyme-substrate complex is equal to zero
The maximum velocity is the rate of the reaction at which the enzyme is saturate with substrate
Total enzyme is distributed between E and ES (ET = E + ES)
How to derive Rate Equations
Draw reaction scheme of all steps
Use mass action kinetics to write ODEs for concentration changes such that the right hand side contains all producing and consuming reactions
Determine total enzyme
Use quasi-steady state assumptions and E(total) to derive algebraic equations for concentration of enzyme
The reaction rate v is equal to the rate of product formation
E+S
ES
E+P
k1
k-1
k2
k-2
There enough substrate that ES concentration never really changes (E and ES reach equilibrium)
Enzyme is neither produced nor consumed
5
From Lecture 11: Kinetics of enzymatic reactions
Where is this from?
What assumptions are made if it is quasi-steady state?
Must show how this was attained in project
Example of disease: Tuberculosis
Caused by mycobacterum tuberculosis (MTB)
MTB is an aerobic, nonmotile bacilus
Can remain latent in its host
One of the top ten causes of death around the world
Multiple instances of total drug-resistant TB
Virulence Pathway
Phagocytosis by a macrophage is a multi-step procedure that ensures complete degradation
Once a pathogen is engulfed, it enters a phagosome which then fuses with a lysosome (phagolysosome complex)
The lysosome has all the needed components to digest the pathogen
MTB is able to remain and reproduce in the phagosome and inhibit the formation of the phagolysosome
As a secondary response, the lungs create granulomas to contain the pathogen
Pathway of Interest
The glyoxylate cycle (glyoxylate shunt) is an alternative anabolic pathway to the tricarboxylic acid cycle (TCA).
MTB is able to undergo the glyoxylate bypass in lung granulomas to create complex sugars and survive in the granulomas
For the project, I would compare something like the production of oxaloacetate with and without the glyoxylate shunt and discuss what effect that has on the production of citrate
Operates in low oxygen environments
10
| Number | Reactions | Enzyme | vFWD MAX | vREV MAX | Km1(mM) | Km2(mM) | Kp1(mM) | Kp2(mM) |
| 1 | [aca]+[oaa] <--> [coa]+[cit] | Citrate Synthase | 64.8 | 0.648 | 0.05 | 0.012 | 0.5 | 0.12 |
| 2 | [cit] --> [icit] | Aconitase | 31.2 | 0.312 | 1.8 | 0.7 | ||
| 3 | [icit] <--> [suc]+[gly] | isocitrate lyase | 1.172 | 0.01172 | 0.145 | 0.59 | 0.13 | |
| 4 | [aca]+[gly] <--> [coa] + [mal] | malate synthase | 20 | 0.2 | 0.057 | 0.03 | 1 | 0.1 |
| 5 | [mal] --> [oaa] | malate dehydrogenase | 184 | 1.84 | 0.833 | 0.0443 | ||
| 6 | [icit] --> [akg] | isocitrate dehydrogenase | 10.2 | 0.102 | 0.03 | 0.3 | ||
| 7 | [akg] --> [sca] | alpha-ketoglutarate dehydrogenase | 9.965 | 0.09965 | 0.06 | 1 | ||
| 8 | [sca] --> [suc] | succinyl-Coa synthase | 57.344 | 0.57344 | 0.1 | 5 | ||
| 9 | [suc] --> [fa] | succinate dehydrogenase | 1.02 | 0.0102 | 0.15 | 0.12 | ||
| 10 | [fa] --> [mal] | fumarase | 87.7 | 0.877 | 0.25 | 2.38 | ||
| 11 | [oaa] --> | 0.67 |
v in reverse was assumed to be 1/100 of v forward
How do we get vs and vp?
You will have an ODE for each product formed
Group Project
Introduction and Background
Methods for Model Construction
Results
Discussion of Model
Bonus: stoichiometric matrix and J for pathway
Project Suggestions
Glycolysis : Pyruvate Kinase Deficiency
Gluconeogenesis : Fructose-1,6-bisphosphate deficiency
Oxidative Phosphorylation : Cyanide or Malonate Poisoning
Pentose Phosphate Pathway : G6PD Deficiency
Urea Cycle : Ornithine Transcarbamoylase Deficiency
You are free to pick your own pathway and more than one group can have the same pathway.
You are also allowed to do shunts that bacteria can enter into (like glyoxylate shunt or GABA shunt) in stressful environments.
There is a decent amount of freedom to this project, so if you are interested in modeling something not listed, just e-mail me first.
