Computer modeling of cellular processes
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Transcript of Computer modeling of cellular processes
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Computer modeling of cellular processes
Glycolysis: a few reactions
By
Raquell M. Holmes, Ph.D.
Boston University
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Dynamics:Answering different questions
• If glucose concentration is 300 mM outside of the cell, – How quickly is glucose converted to glucose 6-
phosphate?
– How does the concentration of glucose 6 phosphate change over time?
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Yeast GlycolysisLiquid, flasks, temp, ph
Agar, temp, ph
Experiment:Sample media or characterize cell content over time
Repeat under different conditions
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Results may look likeGlucose
0
50
100
150
200
250
300
350
0 2 4 6 8 10 12 14 16 18 20
time (minutes)
Glu
co
se
(m
M)
Ethanol
0
50
100
150
200
250
300
350
0 2 4 6 8 10 12 14 16 18 20
time (minutes)
eth
ano
l (m
M)
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Computer Modeling
•Method for analyzing what we know about a biological process
•Used to describe mechanisms behind changes
•Determines what can be seen or predicted
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Walking through a Computational Model
• Concept Map
• Factors and relationships between factors
• Describe relationships mathematically
• Solve equations: using computer tools
• View and interpret results
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Designing a dynamic experiment
• What components are involved?– Glucose, glucose 6 phosphate, fructose 6
phosphate…
• What chemical reactions involved?– Transport, chemical conversions…
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Glycolysis: Concept Map
Often drawings, schematics or chemical reactions
Glucose Glucose6-phosphate
Fructose6-phosphate
InternalGlucose
Ethanol
v1 v2 v3 v4
Cell
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Examples of relationships
Internal Glucose
[Glucose 6-phosphate] is determined by increase from Glucose conversion and decrease by conversion to Fructose 6-phosphate
Glucose6-phosphate
Fructose6-phosphate
v1 v2
Amount of glucose 6 phosphate= amount produced- amount converted
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Designing a dynamic experiment
• Describing relationship mathematically
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Relationship in terms of rates of change
The rate of change of Glucose-6-phosphate (S2) is the rate of Glucose conversion (v1) minus
the rate of conversion (v2) to Fructose-6-phosphate.
212 vvdt
dS
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Designing a dynamic experiment
• Describing relationship mathematically
• What rate laws are known to describe the enzymatic reaction?– Types of rate laws/kinetic models
• Constant, mass action, michaelis menten…
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Simplify
• Glucose transport (v1) • Facilitated diffusion
Glc
inouti
Glc
in
Glc
out
Glc
inout
KGlcGlc
KKGlc
KGlc
KGlcGlc
Vv
1
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•Mass action kinetics are used here to describe the enzymatic reactions.
•This is a simplification of the enzyme kinetics for this example.
Rate Equations
Substrates• Glucose: • Glucose-
6-phosphate:
Rate constants• Enzyme1:• Enzyme2:
222
111
Skv
Skv
1S
2S
1k
2k
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Initial conditions
• Concentrations of components– External glucose (i.e. 300mM)
• Enzymatic rates– Rate constant k (i.e. 50mM/min)– Michaelis-Menten constants, Hill Coefficients
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The model
Glucose6-phosphate
Fructose6-phosphate
v1 v2
Internal Glucose
212 vvdt
dS
222
111
Skv
Skv
S1=300mM
k1=55mM/mink2=9.8mM/min
Ordinary differential equation Rate equations Initial conditions
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Walking through a Computational Model
• Concept Map
• Factors and relationships between factors
• Describe relationships mathematically
• Solve equations: using computer tools
• View and interpret results
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Some Available ToolsGeneral1. Stella
– Install – Mac or PC
2. Excel– Install – Mac or PC
Customized3. GEPASI
– Install – Mac or PC
4. Virtual Cell– Browser: Java– Mac or PC
1. Concept mapping and system dynamics (changes over time).
2. Discrete events, algebraic equations
3. Biochemical kinetics and kinetic analyses.
4. Icon mapping, dynamics and space
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Stella
Concept Map
Rules as math
Initial Conditions
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GEPASI
Chemical Equations
Math
http://www.gepasi.org/gepasi.html
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Online Glycolysis models
http://jjj.biochem.sun.ac.za/database/
Concept map
Math-ruleInitial conditions
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Results
Glucose 6 phosphate
Fructose 6-phosphate
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Conclusions…
• Model based discoveries in glycolysis:: – Oscillations in concentrations of some but not all
metabolites.
– Control of process distributed throughout pathway
– Development of theoretical models
• Method integrates knowledge of pathway factors to examine pathway behaviors.
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Examples of other models
Calcium dynamics: Wave patterns in neuronal cellsVirtual Cell
Receptor signaling: IgE triggering mast cellsPersonal computer codes
Cell cycle regulation: length of wee 1 mutant cell divisions Matlab, Mathematica, personal computer codes
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Calcium dynamics in neuroblastoma cells
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Modeling
• Requires formalizing assumptions– Rate equations– Inclusion or exclusion from model
• Worst case scenario– See what you believe
• Best case scenario– See something unexplainable – Create new laboratory experiments