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Transcript of Computer modeling of cellular processeseaton.math.rpi.edu/CSUMS/Papers/Pathways/raquell.pdf ·...
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Computer modeling of cellularprocesses
Glycolysis: a few reactionsBy
Raquell M. Holmes, Ph.D.Boston University
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Computational Biology
• Computational Biology ≠ Bioinformatics– More than sequences, database searches, and
statistics.
• A part of Computational Science– Using mathematical modeling, simulation and
visualization– Complementing theory and experiment
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Today’s journey
• Bioinformatics– From protein sequence– Metabolic pathway databases
• Metabolic behaviors• Computer modeling glycolysis
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Pathway for discussion
Karp: Cell and Molecular Biology Textbook
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Bioinformatics
Common starting point
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Many types of Protein Databases
• Sequence (103):– publication, organism, sequence type, function
• Protein properties (80):– Motifs, active sites, individual families, localization
• Structure (15)– Resolution, experiment type, type of chain, space
group.
Nucl. Ac. Res. 32, D3 2004
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Generic Protein Seq. Record
• Sequence: hexokinase• E.C. #: 2.7.1.1• Publication: Stachelek et al 1986• Organism: Yeast• Function: main glucose phosphorylating enzyme• Links: other databases or tools• Pre-determined Properties:
– families, folds…• Swissprot example for enzyme.
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What we learn from proteinsequence?
• Similarity searches :– Homology with other proteins– Conserved domains– Active sites
• How do we find the related pathway?• Are there metabolism databases?
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Databases on Molecular Networks
Metabolic Pathways from NAR (5):• EcoCyc:http://ecocyc.PangeaSystems.com/e
cocyc/– Began with E. coli Genes and Metabolism– BioCyc includes additional genomes
• KEGG: http://www.genome.ad.jp/kegg/– Encyclopedia of genes and genomes
• Others: WIT2, PathDB, UMBDD
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What is a metabolic pathway?Contains a series of reactions.
Reactions: Substrate, product(metabolites), enzyme, co-factors.
•Metabolism pathway databases–Search by name or sequence
•Pathway, Compounds, Reactions, Genes
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Example search resultsKEGG: search by compound or enzyme by key word.
Glucose: 82 hits 1.cpd:C00029 UDPglucose; UDP-D-glucose; UDP-glucose; Uridine diophosphateglucose
2. cpd:C00031 D-Glucose; Grape sugar; Dextrose3. cpd:C00092 D-Glucose 6-phosphate; Glucose 6-phosphate; Robison ester…….79. cpd:C11911 dTDP-D-desosamine; dTDP-3-dimethylamino-3,4,6-trideoxy-D-
glucose80. cpd:C11915 dTDP-3-methyl-4-oxo-2,6-dideoxy-L-glucose81. cpd:C11922 dTDP-4-oxo-2,6-dideoxy-D-glucose82. cpd:C11925 dTDP-3-amino-3,6-dideoxy-D-glucose
Grape sugar: FORMULAC6H1206
NAME D-Glucose grape sugar Dextrose
List of reactions involving compoundList of enzymes acting on compound
Map0010
Pathway
C00031
Compounds
R0029
Reaction
2.7.1.1
Enzyme
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• Home page– Navigation bar
• List of categories• Compounds
– List of results
•All-Carbohydrates•a sugar•a sugar phosphate•a sugar-1-phosphate•Aldonic-Acids•Carbohydrate-Derivatives
•Carbohydrates•Disaccharides
•Oligosaccharides•Polysaccharides
•Fructans•Glycogens•Large-branched-glucans•Long-linear-glucans•Pectin•Short-glucans•Starch
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KEGG: E.coli EcoCyc: E.Coli
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Summary I
• Protein ->enzyme->pathway database
• Pathway Database Content:– Species specific (BioCyc), general (KEGG)– Known and proposed enzymes, co-factors,
metabolites.– Searches return similar results (compounds,
reactions…) with different appearance.
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From Data to Dynamics
• Static Data
• What is the behavior of the pathway?– Expression data– Dynamics
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Expression data
• KEGG:– retrievable expression data sets
• EcoCyc:– input expression data to view in relation to
metabolic data.• Expression data is one way of viewing the
behavior of a system.
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Raw data
Submitted by:Hirotada MORI
Organism: E.coli
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isomerasehexokinaseEnzyme
++++++++++----
AnaerobicAerobic
MicroArray Data: fold changes in expression
Changes in gene expression:Single time pointVarious conditions
Hypothetical data
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Dynamics:Answering different questions
• If glucose concentration is 300 mM outsideof the cell,– How quickly is glucose converted to glucose 6-
phosphate?
– How does the concentration of glucose 6phosphate change over time?
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Yeast GlycolysisLiquid, flasks, temp, ph
Agar, temp, ph
Experiment:Sample media or characterizecell 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
cose
(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
an
ol
(mM
)
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Computer Modeling
•Method for analyzing what we know about abiological process
•Used to describe mechanisms behind changes
•Determines what can be seen or predicted
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Walking through aComputational 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 MapOften 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 increasefrom Glucose conversion and decrease by conversionto 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 ofrates of change
The rate of change of Glucose-6-phosphate (S2) isthe rate of Glucose conversion (v1) minus
the rate of conversion (v2) to Fructose-6-phosphate.
21
2vv
dt
dS!=
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Designing a dynamic experiment
• Describing relationship mathematically
• What rate laws are known to describe theenzymatic reaction?– Types of rate laws/kinetic models
• Constant, mass action, michaelis menten…
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Simplify
• Glucose transport (v1) • Facilitated diffusion
Glc
inout
i
Glc
in
Glc
out
Glc
inout
K
GlcGlcK
K
Glc
K
Glc
K
GlcGlc
Vv
+++
!
=+
1
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•Mass action kinetics are used hereto describe the enzymaticreactions.
•This is a simplification of theenzyme 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
21
2vv
dt
dS!=
222
111
Skv
Skv
=
= S1=300mMk1=55mM/mink2=9.8mM/min
Ordinary differential equation Rate equations Initial conditions
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Walking through aComputational 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 systemdynamics (changes over time).
2. Discrete events, algebraic equations
3. Biochemical kinetics and kineticanalyses.
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 factorsto 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 neuroblastomacells
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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