Finding Km Values http://www.brenda-enzymes.org/ Finding Km Values • BRENDA – Kinetic activity database – Catalogs enzyme activity and other kinetics-focused papers – EC Number • #.#.#.#(##) – Identifies enzyme – Not species specific – Can also search for substrates & ligands Ex: Find Km for Succinyl-CoA Synthetase Tissue-Specific in Humans GDP-Forming: Anabolic Metabolis ADP-Forming: Catabolic Metabolis Finding Km ValuesFinding Km ValuesEx: Find Km for Succinyl-CoA SynthetaseSlide Number 4Slide Number 5 Review1-10000000001-10000000001-1-1000000001-100000000101-1-10000000001-10000000101-1 Draw the pathway 1-10000000001-10000000001-1-1000000001-100000000101-1-10000000001-10000000101-1 100000000-1010000000-1001000000-1000101000-100001-10000000000101-100000001-10 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 c.

1. Finding Km Values
http://www.brenda-enzymes.org/
Finding Km Values
• BRENDA
– Kinetic activity database
– Catalogs enzyme activity and other
kinetics-focused papers
– EC Number
• #.#.#.#(##)
– Identifies enzyme
– Not species specific
– Can also search for substrates &
ligands
Ex: Find Km for Succinyl-CoA
Synthetase
Tissue-Specific in Humans
GDP-Forming: Anabolic Metabolis
ADP-Forming: Catabolic Metabolis

2. Finding Km ValuesFinding Km ValuesEx: Find Km for
Succinyl-CoA SynthetaseSlide Number 4Slide Number 5
Review1-10000000001-10000000001-1-1000000001-
100000000101-1-10000000001-10000000101-1
Draw the pathway
1-10000000001-10000000001-1-1000000001-100000000101-1-
10000000001-10000000101-1
100000000-1010000000-1001000000-1000101000-100001-
10000000000101-100000001-10
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

3. 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

4. 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

5. 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
NumberReactionsEnzymevFWD MAXvREV
MAXKm1(mM)Km2(mM)Kp1(mM)Kp2(mM)1[aca]+[oaa] <-->
[coa]+[cit]Citrate Synthase64.80.6480.050.0120.50.122[cit] -->
[icit]Aconitase31.20.3121.80.73[icit] <--> [suc]+[gly]isocitrate
lyase1.1720.011720.1450.590.134[aca]+[gly] <--> [coa] +
[mal]malate synthase200.20.0570.0310.15[mal] --> [oaa]malate
dehydrogenase1841.840.8330.04436[icit] --> [akg]isocitrate
dehydrogenase10.20.1020.030.37[akg] --> [sca]alpha-
ketoglutarate dehydrogenase9.9650.099650.0618[sca] -->
[suc]succinyl-Coa synthase57.3440.573440.159[suc] -->
[fa]succinate dehydrogenase1.020.01020.150.1210[fa] -->

6. [mal]fumarase87.70.8770.252.3811[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.
Systems Biology Workshop

7. 10/8/2016
A couple of things…
• Voter registration ends tomorrow (10/9)
• Group Project
– Pick a partner by Wednesday (10/10)
– Will give me partner name on Wednesday
– Email me project topic by Friday (10/12)
– Project will be due 10/22 (a Monday)
Intro to Systems Biology*
• Systems biology: the study of biological function and
mechanisms,
underpinning inter- and intra-cellular dynamic networks, by
means of
signal- and system-oriented approaches
• Systems biology approach means
– Investigating components of cellular networks and their
interactions
– Applying experimental high-throughput techniques
– Integrating computational and theoretical methods with
experimental efforts
*Dr. Carlo Cosentino – CMU University

8. • Geneticist: p53 oscillation to regulate the cell
cycle
• Chemist/Pharmacology: binding energy of
protein-drug complexes
• Mathematician/Engineer: dynamic patterns of
pulsatile flow in a heart
What can be modeled?
Biomedical Engineer can technically model all of the above.
Model Behaviors
• Governed by inputs and outputs
• Could be qualitative vs. quantitative,
deterministic vs. stochastic, discrete vs.
continuous
• Steady state: asymptotic behavior (reversible
vs. irreversible)
The modeling process

9. • Determine the model scope
• Select model type
• Design and develop model
• Model analysis and application
Basic Modeling: Stoichiometric Representation
Substrate 1 Substrate 2
Substrate 3
v1 v2
v3
We can represent this network using linear algebra
This is a
stoichiometric
network
=
1
0
0
−1 0 −1
1 −1 0
0 0 1
��1

10. ���
��3
���
=
�����
�����
�����
�����
�����
�����
N v
����
����� = 0 At steady state
Linear Algebra Basics
Linearly Dependent vs. Independent
1
0
0
0
1
0

11. 1
1
0
1
0
0
0
1
0
0
0
1
x1 x2 x3 x1 x2 x3
x3 = x2 x1 +
Dependent Independent
1 0 0
0 1 0
0 0 1
Identity matrix (I)
• A matrix multiplied by
its inverse equals I
• IA = A = AI

12. • Must be a square matrix
Reduced Row Echelon Form
1. Leading entries in each row should be 1
• Considered Row-Echelon Form
2. Each leading 1 is the only non-zero in the column
1 −� 1 5
0 1 −1 �
0 0 1 6
1 0 0 19
0 1 0 10
0 0 1 6
Row reduce through a series of basic matrix operations between
rows (multiple rows, add rows, interchange rows, etc.)
Definitions
1. Basis: a linearly independent set
of vectors x1,…,xn
2. Dimension (dim(S)) : # of vectors
forming the basis set of S
3. Rank of matrix : # number of rows
that are nonzero in row reduced
echelon form
4. Nullity: dim(S) – Rank(S)

13. rref
Linear Algebra Review
Are these vectors linearly independent or linearly dependent?
Row reduce this matrix and find the rank and nullity of this
matrix, is it linearly independent or linearly dependent?
0 1 1 0 0
1 0 0 0 0
0 0 1 0 0
0 0 1 1 0
0 1 1 0 0
1 0 0 0 0
1 1 1 0 0
1 2 2 0 0
1 1 1 -1
1 2 4 3
1 3 9 3
1 4 16 5
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
Rank = 4

14. Nullity = 0
Dimension = 4
Linearly Dependent
Independent Dependent
Metabolic Networks
• Metabolism: biochemical process to acquire
energy and materials for cellular growth
• Metabolic flux: the rate of turnover of
molecules through a metabolism pathway
• Can describe metabolism by the biochemical
reactions in the organism
Example: find write in Nv form in
steady state
A B
v1 v2 v3 C
D E
v4
v5
v6

15. v7
• v1 produces A (1)
• v2 degrades A (-1)
• v4 degrades A (-1)
• v3, v5-v7 do nothing to A (0)
V1
V2
V3
V4
V5
V6
V7
A
B
C
D
E
1 -1 0 -1 0 0 0
Example: find write in Nv form in
steady state
1 -1 0 -1 0 0 0
0 1 -1 0 0 0 0
0 0 1 0 0 1 -1
0 0 0 1 -1 0 0
0 0 0 0 1 -1 0
V1

16. V2
V3
V4
V5
V6
V7
= 0
A B
v1 v2 v3 C
D E
v4
v5
v6
v7
What does this tell us?
1 -1 0 -1 0 0 0
0 1 -1 0 0 0 0
0 0 1 0 0 1 -1
0 0 0 1 -1 0 0
0 0 0 0 1 -1 0
V1
V2
V3
V4
V5

17. V6
V7
= 0
1 0 0 0 0 0 -1
0 1 0 0 0 1 -1
0 0 1 0 0 1 -1
0 0 0 1 0 -1 0
0 0 0 0 1 -1 0
Row Reduced
V1
V2
V3
V4
V5
V6
V7
= 0
What fluxes act on a substrate
i.e.
����
����
= ��� − ��� − ��� = 0
Row reduced echelon form can
also tell us more

18. 1 0 0 0 0 0 -1
0 1 0 0 0 1 -1
0 0 1 0 0 1 -1
0 0 0 1 0 -1 0
0 0 0 0 1 -1 0
V1
V2
V3
V4
V5
V6
V7
= 0
• There are 5 rows with leading numbers: Rank = 5
• Total columns = 7, therefore nullity = 7-5 = 2
• You have 2 basis (linearly independent) vectors (nullity) that
make up your kernel
(null space)
• Essentially: every possible set of steady state flux can be
expressed as a linear
combination of these vectors (J)
• J = ∑ ����
��������������
��=1 ����
2 columns without a non-leading number: nullity = 2
Work through on board

19. J = ��1��1 + ��2��2
Using row reduced echelon form, we can find J
Kinetic Modeling
• System dynamics are described with ODEs
• ����
����
= f(x1,…,xn ; p1,…,pn; t);
– x = substrate/products
– p = parameters
– t = time
• System state: a snapshot of the system at a given
time with sufficient info to predict the state at
future times
– Set of all possible states = system space
Reaction Kinetics and
Thermodynamics
• Purpose of metabolism is the extraction of
energy from nutrients
show how S1 breaks down into S2

20. • Law of mass action: Reaction rate of
probability of collision
– V = v(forward) – v(reverse)
Michaelis-Menten kinetics
Previously Now
S P
v
E+S ES E+P
Assumptions
1. E + ES = Constant (E total)
2. [S (t=o)] >> [E] (Briggs and Haldone quasi-steady state)
3. quasi-equilibrium: the reversible conversion of E,S to ES is
-1 >> k2)
Reaction Rate v is equal to product
formation and negative rate of
substrate consumption.
Single substrate, single
product reaction
E+S ES E+P
k1

21. k-1
k2
����
����
= −��1 �� �� + ��−1[����]
������
����
= ��1 �� �� − ��−1 ���� − ��2[����]
����
����
= −��1 �� �� + ��−1 ���� + ��2[����]
������
����
= ��1 �� �� − (��−1− ��2)[����]
����
����
= −��1 �� �� + (��−1+ ��2)[����]
����
����
= ��2 ����
Mass action equations
that depict concentration
in terms of degradation
and production

22. Upper Glycolysis
Substrates:
1. Glucose
2. Glucose 6-P
3. Fructose 6-P
4. Fructose 1,6-bis P
5. ATP
6. ADP
v1
v2
v3
v4
v5
v6
v7
Glucose Glucose 6-P Fructose 6-P Fructose 1,6-bis P
ATP ADP ATP ADP
v3 v4 v2
v1
v5
v6
v7
1 -1 0 0 0 0 0
0 1 -1 0 0 0 0

23. 0 0 1 -1 0 0 0
0 0 0 1 -1 -1 0
0 -1 0 -1 0 0 1
0 1 0 1 0 0 -1
v7
What is the stoichiometric matrix?
Su
bs
tr
at
es
: 1. Glucose
2. Glucose 6-P
3. Fructose 6-P
4. Fructose 1,6-bis P
5. ATP
6. ADP
Stoichiometric matrix
1 -1 0 0 0 0 0
0 1 -1 0 0 0 0
0 0 1 -1 0 0 0
0 0 0 1 -1 -1 0
0 -1 0 -1 0 0 1
0 1 0 1 0 0 -1
v5

24. v2
v3
v4
v5
v6
v7
v1
%ODE for network
y(glu)=v1-v2;
y(g6p)=v2-v3;
y(f6p)=v3-v4;
y(f16p)=v4-v5-v6;
y(atp)=-v2-v4+v7;
y(adp)=v2+v4-v7;
%Rate Equations
v1=k1; %constant
v2=k2*y(glu)*y(atp);
v3=k3*y(g6p);
v4=k4*y(f6p)*y(atp);
v5=k5*y(f16p);
v6=k6*y(f16p);
v7=k7*y(adp);
%k-values
k1=1; %glycogen phosphorylase EC:2,4,1,1
k2=0.78; %glucokinase EC:2,7,1,2
k3=0.28; %phosphoglucose isomerase
k4=0.21; %6-phosphofructokinase
k5=0.0154; %fructose-16-bisphosphate
k6= 0.17; %fructose bisphosphate aldolase
k7=3.76;

25. Taken from online database Taken from stoichiometric network
������
����
= ��1 �� �� − ��−1 ���� − ��2[����]
����
����
= ��2 ����
Glucose Glucose 6-P Fructose 6-P Fructose 1,6-bis P
v3 v4 v2
v1
v6
ATP ADP
v7
ATP ADP
v7
What is needed to solve Michaelis-Menten product
formation assuming E+P is irreversible?
Systems Biology WorkshopA couple of things…Intro to
Systems Biology*What can be modeled?Model BehaviorsThe
modeling processBasic Modeling: Stoichiometric
RepresentationLinear Algebra BasicsLinear Algebra
ReviewMetabolic Networks Example: find write in Nv form in
steady stateExample: find write in Nv form in steady stateWhat
does this tell us?Slide Number 14Kinetic ModelingReaction
Kinetics and ThermodynamicsMichaelis-Menten kineticsSlide
Number 18Upper GlycolysisSlide Number 20

26. Group Project
Paper Format Requirements
• 1000 – 1500 words (not including figure captions)
• 1.5 spaced
• Normal margins
• Times New Roman
• 12 point font
• 1.5 spacing
• Justified paragraphs
Figures
• All figures need a title, legend, axis labels and captions within
the paper.
• The caption should be detailed enough for the figure and
caption to stand alone
• Tables should be included with all of your k-values and ODEs.
• Required Figures:
o Original pathway including all , fluxes, and enzymes
o Altered pathway, shunted pathway, etc.
o Table of all enzymes, reactions, k-values, v-values, and
sources
o Matlab plots of original pathway and altered/shunted pathway
References
• MLA or APA format
• No max for # references. Minimum of 2 for cellular process
and disease
• Do need to reference papers discussing disease process
Submission
• Submit a zipped file of both written report and Matlab code

27. with the title:
o Systems_Project_Lastname1_Lastname2
Some Comments:
• Pathways should have at least 8 substrates
• You are allowed to take a large existing pathway and break it
down
o For example, how we took glycolysis, but only looked at
upper glycolysis
• Pathways should have reversible fluxes (not all will be
reversible, but you should pick a
pathway where some are)
Helpful Links:
1. https://www.brenda-enzymes.org/
• Extensive database of enzymes
2. https://www.genome.jp/kegg/pathway.html
• Extensive database of pathways and reactions
https://www.brenda-enzymes.org/
https://www.genome.jp/kegg/pathway.html
Written Report Contents
1. Outline System & Disease: “Introduction and Background” –
20 points
• Introduction into the cellular process and the disease you
picked.

28. o Explain the importance of system and how the disease could
inhibit/alter/etc. .it.
2. Explain how model was built: “Methods for Model
Construction” – 35 points
• how equations were derived
• what reactions were included/excluded
• model assumptions
• k-values
• acceptable reasons to exclude an interaction
o interaction not confirmed in cells
o interaction not relevant to disease/system
• unacceptable reasons to exclude an interaction
o kinetic data not available
o my code won’t work
o someone didn’t do this part of the report
3. Analyze the plots from you model: “Results derived from the
Model” – 20 points
• Insert the plots from your model
• Give general statements about the concentrations you attained
4. Explain how model was modified for disease process and
compare model output to what
you would’ve expected and how this modified pathway would
affect the biological system:
“Model Modification for [disease/disorder]” – 25 points

29. • Is your model accurate?
o Explain how you expected the models would look
o Explain why the model may be inaccurate
• Does your model reflect what actually occurs in nature?
Group ProjectPaper Format RequirementsWritten Report
Contents