Verification of Real Time Systems

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Transcript Verification of Real Time Systems

Modeling and Analysis
Techniques in Systems Biology.
CS 6221 Lecture 1
P.S. Thiagarajan
Basic Info
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P.S. Thiagarajan
COM2 #03 – 55 ; Tel Ext. 67998
[email protected]
www.comp.nus.edu.sg/~thiagu
Course web page:
– www.comp.nus.edu.sg/~cs6221
– We will be using the IVLE system extensively.
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Office Hours
• Send mail first and fix an appointment.
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Course Material
• Selected Parts of the text book :
– Systems Biology in Practice: E. Klipp, R. Herwig, A.
Kowald, C. Wierling, H. Lehrach (Wiley)
• Selected Survey papers, book chapters.
• Lecture slides.
• Research Articles.
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Assignments
• Lab Assignments
–3
– tool based (Cell Illustrator, COPASI, SimBio)
– Individual
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Term Papers
• Read a paper or –more likely- a bunch of
papers on a topic.
• Summarize in the form of a term paper.
• First assignment: Common
• Second assignment:
– More substantial
– Can be aligned to your interests
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Talk
• Give talk based on the second term paper.
– 25 + 5 minutes.
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Grading (Tentative)
• Lab assignments 45% (15 + 15 + 15)
• Term papers
40% (15 + 25)
• Talk:
15%
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What is the Course About?
• Computational systems biology
– Computational aspects of systems biology.
• Systems biology:
– Not just focus on individual components.
• genes, mRNAs, proteins, membranes, ligands ….
– But study a system of such components and their
interactions.
• Many different views of systems biology.
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Why Systems Biology?
• Biology has traditionally –and extremely
successfully!- focused on what individual
parts of a cell do .
• Bio-chemistry of large and small molecules
– The structure of DNA and RNA
– Proteins, ligands,…
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Why Systems Biology?
• But functionality of a system is determined
crucially by the interactions of the parts.
• Many fundamental biological processes are
dynamic.
– cell growith/division/differentiation
– Metabolism,….
• Many diseases are marked by malfunctioning
of these processes.
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Why Systems Biology?
• Advances in experimental technology are
producing vast amounts of data concerning
biological processes.
– Which genes get expressed “when” in controlled
conditions.
• One would like to understand this data in a
systemic way.
• Enter: computational systems biology!
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The CSB Approach
• View selected biological processes as
dynamical systems.
–
–
–
–
Model
Simulate
Analyze
Predict
• Many research communities study dynamical
systems …
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What do we need ?
• Biology for computer scientists.
– basic biological sub-systems/processes
– experimental techniques.
• Modeling, analysis and simulation techniques.
• Biologists as collaborators!
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Current Status
• Modeling techniques.
– Mathematical
• differential equations, Linear algebra, probability
theory, statistics, Boolean networks, Markov chains,
Bayesian networks,….
– CS-specific:
• Automata, Petri nets, Hybrid functional Petri nets,
hybrid automata, Bayesian
networks/inferencing/learning, Markov chains, Model
checking….
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Current Status
• Metabolism
– Kinetics “laws” (models).
– Enzyme kinetics, law of mass action, Michelis-Menten
kinetics
– Metabolic network models and flux analysis.
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Current Status
• Signal Transduction
• Receptor-ligand interactions
• Protein actors
• signaling dynamics
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Current Status
• Other biological processes
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•
•
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biological oscillations
protein folding kinetics
cell cycle
Gene expression, regulation
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Current Status
• Modeling tools
• Cell Illustrator, COPASI, SimBio, …..
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What shall we do?
• Selected basic topics.
– To illustrate the current state of the field.
– To critically examine what is missing.
– To discuss promising lines of research.
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What can CS offer?
• We “know” how to deal with complex
systems.
– Hierarchy
• silicon realization of circuits, digital design, microarchitectures, assemble language, programming
languages, GUIs, …
– separation of concerns.
– concepts (models), techniques, tools at each layer
and for connecting the layers.
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What can CS offer?
• Deal with other disciplines.
– Multi-media
– Control
– Manufacturing
– Communications
– Business!
• Using computing power via algorithms and
data structures!
• Computational thinking?!
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What can CS offer?
• Find the right level abstractions.
– approximations
• Handle distributed dynamics
• Deal with hybrid behaviors
• Build tools.
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What the Course is NOT about.
• We will not deal with:
– Traditional “Bio-Informatics” topics
• data mining, sequence analysis, …
– Computational aspects of structural biology
• Proteins structure, folding…
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Contents
• Bio-chemical networks
– The basics of chemical kinetics
• Three types of bio-chemical networks
– Gene networks
– Metabolic networks
– Signaling pathways
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Bio-pathways
• Many studies of biological sub-systems boil
down to studying:
– bio-pathways
• A network of bio-chemical reactions.
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The hierarchy of bio-chemical
networks
Bio-Chemical reactions
Metabolic pathways
A network of Bio-Chemical reactions
Signaling pathways
Gene regulatory
networks
Interacting networks of Bio-Chemical reactions
Cell functions
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Biopathways
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Gene Regulatory networks
• Boolean models
• Differential equations
• Bayesian networks.
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Metabolic pathways
• Petri nets
• Linear algebra
• Flux analysis
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Signaling Pathways
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•
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Differential equations.
Hybrid functional Petri nets
Hybrid automata
Stochastic models.
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Our Research
• ODEs based modeling.
– Parameter estimation techniques
• Stochastic approximations of ODEs dynamics.
– Parameter estimation, sensitivity analysis
• GPU implementations
• Probabilistic (statistical ) model checking
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Our Research
• Collaboration with biologists:
– Signaling pathways:
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AKT/MAPK pathway
Complement pathway
TLR3-TLR7 signaling pathways
DNA damage/repair pathways
• www.comp.nus.edu.sg/~rpsysbio
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Expected Outcomes
• Have a sound grasp of:
– current modeling and simulation techniques
(Signaling pathways)
– Reaction kinetics
– stochastic models and simulations
– Analysis techniques:
• Parameter estimation, sensitivity analysis
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Expected Outcomes
• Be aware of the limitations of current
techniques and state of knowledge
• Be ready to undertake modeling and
simulation work.
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Let us get started.
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Basic Biology: Sources
• Chapter 2 (Biology in a Nutshell) of the book
“Systems Biology in Practice” by E. Klipp et.al.
• Chapter 1 (Molecular Biology for Computer
Scientists) of the book “Artificial Intelligence
and Molecular Biology” by Lawrence Hunter.
• The internet!
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A major goal of biology
• Understand the molecular biology of
eukaryotic cells.
• Cell: the basic building block.
– Two major families: Prokaryotes and Eukaryotes.
– Eukaryotes
• More complex; genetic material is contained in the
nucleus;
• Most multi-cellular organisms are made up of
eukroyotes.; WE are made up of these types of cells.
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Cells
• In multi-cellular organisms;
– Cells are differentiated.
– Different types of cells have different functions
(and composition).
– Groups of cells for specific functionalities
• tissues.
• we have 14 different types of tissues.
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Source ?
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Major Classes of Bio-Molecules
•
•
•
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Carbohydrates
Lipids
Proteins
Nucleic acids
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Proteins
• Many functions!
• Build up the cytoskeletal structure of the cell (the
scaffolding)
• Responsible for cell movements (motility)
• Serve as catalytic enzymes for bio-chemical
reactions.
• Induce signal transductions.
• Control transcriptions and translation of genes
• Control degradation of proteins.
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Proteins
• Proteins consist of polypeptides.
– Polypeptide - a LONG chain of amino acids bonded
together by peptide bonds between adjacent
amino acid residues.
• The order of amino acids constituting a
peptide is fundamental.
– Primary structure
– coded by genetic information
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Proteins
• 20 (23?) different amino acids
• A protein can have 50 – 4000 amino acids
sequence. (50 – 1000 is the typical range)
• 201000 possible proteins!
• Actually, only a tiny fraction is found in nature.
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Nucleic Acids
• DNA (Deoxyribonucleic acid) molecules store
genetic information.
– Present in all living organisms
• RNA (Ribonucleic acid) takes part in a large
number of processes.
– Transferring hereditary information in the DNA to
synthesize proteins.
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The Central Dogma
• First enunciated by Francis Crick in 1958[1]
– re-stated in a Nature paper published in 1970:[2]
• Three major classes of information-carrying
biopolymers:
– DNA, RNA, proteins
– Information encoded as sequences of molecules.
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The Central Dogma
• In principle there can be 9 types of transfers:
DNA
RNA
Proteins
DNA
RNA
Proteins
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The Central Dogma
• The “simple” form of central dogma states:
DNA
RNA
Proteins
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The Central Dogma
• Information cannot be transferred back from
protein to either protein or nucleic acid.
• 'once information gets into protein, it can't
flow back to nucleic acid.'
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Current Known Information Flows
Special flows occur in retro viruses !
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Information Flows
(Replication)
DNA
DNA
DNA
mRNA
(Transcription)
Proteins
(Translation)
mRNA
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Mechanism of Cellular Functions
– Replication (of DNA)
– Transcription of RNA and Processing –by splicingto yield mRNA which migrates to the cytoplasm.
– Translation (by ribosomes) of the code carried by
mRNA into proteins.
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Legend:
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Post-translational Modifications
• Proteins undergo many modifications to
implement cellular functions
– Phosphorylation (Activation of proteins)
– Dephosphorylation (Deactivation of proteins)
– Methylation and acetylation (Gene silencing. Plays
a role in cell differentiation)
– Cleavage (Cutting of genes and proteins. For
degradation and apoptosis)
– Ubiquitination (Marking of proteins for further
degradation)
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Interaction roles of proteins
• Proteins have specific roles in the form of
chemical interactions.
– Kinase (Catalyzes phosphorylation, thereby
activating other proteins)
– Phosphatase (Catalyzes dephosphorylation)
– Transcriptional Co-factors
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Role of Bio-pathways
• Apoptosis
– programmed cell death
• Differentiation
– Cells getting specialized for specific functions
• Cell-cycle
– Growth and replication of cells
• Many others!
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Example: Wnt Signaling Pathway
• Most studies on each of the two types of pathways (Signaling
and GRN) done in isolation
• Wnt canonical pathway, starts with the binding of the Wnt
ligand to Frz receptor
• Chain of chemical reactions occur, which results in the
transcription factor β-Catenin being translocated to the
nucleus
• Cofactor with TCF/LEF to up-regulate the transcription of
several genes
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Wnt Signaling Pathway (Canonical)
Wnt
Dsh
Degradation
Cytoplasmic
When
It
will inhibit
Wnt ligand
the
Complex
B-catenin
formation
bindscan
will
to
form
be
Frz,
of
then
the
phosphorylated
Dsh
translocate
when
degradation
is GSK-3B
recruited
to by
binds
tothe
the
and phosphorylates
plasma
complex
nucleus
membrane
where
and gets
it binds
‘marked’
and
APC
to
anddegradation
for
gets
co-factors
Axin
activated
Tcf and Lef
p
Dsh
GSK-3B
p
B-Catenin
Lef
B-Catenin
p
APC
p
Axin
Tcf
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Reaction Kinetics
Sources
• Chapter 5 (Metabolism) of the book “Systems
Biology in Practice” by E. Klipp et.al.
• Other related material to be uploaded.
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Bio-Chemical Reactions
• Bio-Chemical reaction:
– A basic unit of biological processes.
– Convert molecules of one type into another
• Can be modeled at different levels of
abstraction (time scales).
– Microscopic: single molecules and their
interactions
– Macroscopic: Concentrations and rates (changes
of concentration per time unit).
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Reactions
• Bio-chemical reaction:
– Involves bio-molecules.
• Proteins, carbohydrates, lipids,…
– Creation and transformation of bio-molecules.
– Control the flow of energy , materials and
information through the cell.
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Kinetic Models of Reactions
• Reaction:
– A chemical process resulting in inter-conversion of
the reactants.
• motion of electrons cause chemical bonds to break and
form.
• Reaction types
– Isomerization
• structural rearrangement (transform one isomer to
another)
• no change in net atomic composition
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Reaction Types
• Direct combination or synthesis:
– two or more chemical elements or compounds
unite to form a more complex product.
• 2H2 + O2 → 2H2O
• Chemical decomposition
– a compound is decomposed into smaller
compounds:
• 2H2O → 2H2 + O2
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Reaction Types
• Single displacement or substitution
– an element being displaced out of a compound by
a more reactive element:
• 2Na + 2HCl → 2NaCl + H2
• Double displacement
– two compounds in aqueous solution exchange
elements or ions to form different compounds.
• NaCl + AgNO3 → NaNO3 + AgCl
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Reaction Kinetics
• Kinetics:
– Determine reaction rates
• Fix reaction law and
• determine reaction rate constant
• Solve the equation capturing the dynamics.
• The reaction rate for a product or reactant in
a particular reaction:
– the amount (in moles or mass units) per unit time
per unit volume that is formed or removed.
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Reaction Rates
• Influenced by:
– Temperature
– Concentration
– Pressure
– Light
– Order (zero, first, second)
– catalyst
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Rate Laws
• Rate law:
– An equation that relates the concentrations of the
reactants to the rate.
• Differential equations are often used to
describe these laws.
• Assumption: The reactants participating in
the reactions are abundant.
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Rate Laws
• Mass action law:
– The reaction rate is proportional to the probability
of collision of the reactants
– Proportional to the concentration of the reactants
to the power of their molecularities.
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Mass action law
S1 + S2
V
P
V = k. [S1] [S2]
[S1] is the concentration (Moles/ litre) of S1
[S2] is the concentration (Moles/ litre) of S
k is the rate constant
V, the rate of the reaction
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Mass action law
S1 + S2
V1
V2
2P
V = (V1) - (V2) = k1. [S1] [S2] – k2 [P]2
[S1] ([S2]) is the concentration (Moles/litre) of S1 (S2)
k1 and k2 are the rate constants
V1, the rate of the forward reaction
V2, the rate of the backward reaction
V, the net rate
Molecularity is 1 for each substrate (reactant) of the forward
reaction and 2 for the backward reaction
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Mass-action Kinetics
k1
E+S
ES
k3
E+P
k2
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To be continued……..
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• Assuming mass law kinetics we can write down a system of ordinary differential
equations for the 6 species.
• But we don’t know how to solve systems of ordinary (non-linear) differential
equations even for dimension 4!
• We must resort to numerical integration.
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Given:
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Initial values chosen “randomly”
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Michaelis-Menton Kinetics
• Describes the rate of enzyme-mediated
reactions in an amalgamated fashion:
– Based on mass action law.
– Subject to some assumptions
• Enzymes
– Protein (bio-)catalysts
• Catalyst:
– A substance that accelerates the rate of a reaction
without being used up.
– The speed up can be enormous!
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Enzymes
• Substrate binds temporarily to the enzyme.
– Lowers the activation energy needed for the reaction.
• The rate at which an enzyme works is influenced by:
– concentration of the substrate
– Temperature
• beyond a certain point, the protein can get denatured
– Its 3 dimensional structure gets disrupted
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Enzymes
• The rate at which an enzyme works is influenced by:
– The presence of inhibitors
• molecules that bind to the same site as the substrate
(competitive)
– prevents the substrate from binding
• molecules that bind to some other site of the enzyme but reduces
its catalytic power (non-competitive)
– pH (the concentration of hydrogen ions in a solution)
• affects the 3 dimensional shape
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Michaelis-Menton Kinetics
k1
E+S
ES
k3
E+P
k2
i)
A reversible formation of the Enzyme-Substrate complex ES
ii) Irreversible release of the product P from the enzyme.
This is for a single substrate; no backward reaction; at least negligible
if we focus on the initial phase of the reaction.
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Michaelis-Menten Kinetics
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Michaelis-Menton Kinetics
k1
E+S
ES
k3
E+P
k2
Use mass action law to model each reaction.
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(1)
This is the rate at which P is being
produced.
Assumption1:
[ES] concentration changes much more slowly than those of [S] and [P] (quasisteady-state)
We can then write:
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This simplifies to:
(2)
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Michaelis-Menton Kinetics
(1)
(2)
Define
(Michaelis constant)
(3)
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Assumption1:
[ES] concentration changes much more slowly than those of [S] and [P] (quasisteady-state)
Assumption2: The total enzyme concentration does not change with time.
[E0] = [E] + [ES]
[E0] - initial concentration
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Michaelis-Menton Kinetics
[ E ]  [ E0 ]  [ ES ]
[ S ]([ E0 ]  [ ES ])  K M [ ES ]
[ S ][ E0 ]  K M [ ES ]  [ ES ][ S ]
[ S ][ E0 ]
 [ ES ]
[S ]  K M
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Michaelis-Menton Kinetics
[ S ][ E0 ]
 [ ES ]
[S ]  K M
v  k3[ ES ]
(1)
[ S ][ E0 ]
v  k3
[S ]  K M
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Michaelis-Menton Kinetics
Vmax is achieved when all of the enzyme (E0) is
substrate-bound.
v  k3[ ES ]
(assumption: [S] >> [E0])
at maximum rate,
[ ES ]  [ E0 ]
Thus,
vmax  k3[ ES ]  k3[ E0 ]
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Michaelis-Menton Kinetics
[ S ][ E0 ]
v  k3
[S ]  K M
vmax  k3[ E0 ]
vmax [ S ]
v
[S ]  K M
This is the Michaelis-Menten equation!
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Michaelis-Menton Kinetics
[ S ][ E0 ]
v  k3
[S ]  K M
vmax  k3[ E0 ]
vmax [ S ]
v
[S ]  K M
This is the Michaelis-Menten equation!
So what?
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Michaelis-Menton Kinetics
vmax [ S ]
v
[S ]  K M
Consider the case:
vmax
v
2
vmax
vmax [ S ]

2
[S ]  K M
[S ]  KM  2[S ]
K M  [S ]
The KM of an enzyme is therefore the substrate concentration at
which the reaction occurs at half of the maximum rate.
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Michaelis-Menton Kinetics
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Michaelis-Menton Kinetics
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Michaelis-Menton Kinetics
• KM is an indicator of the affinity that an
enzyme has for a given substrate, and hence
the stability of the enzyme-substrate complex.
• At low [S], it is the availability of substrate
that is the limiting factor.
• As more substrate is added there is a rapid
increase in the initial rate of the reaction.
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Modeling Bio-Chemical networks
• Enzyme catalyzed reaction
(a)
E
S
S+E
k1
k2
S.E
k3
S.E
t1 : k1[S][E]
E+P
P
t3 : k3[S.E]
t2 : k2[S.E]
(b)
E
S
P
t4 : Vmax[S] / (KM + [S])
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