Sharad Bhartiya Department of Chemical Engineering IIT Bombay · Historically, biology has been a...
Transcript of Sharad Bhartiya Department of Chemical Engineering IIT Bombay · Historically, biology has been a...
Sharad Bhartiya Department of Chemical Engineering
IIT Bombay
Mathemight- 07 Jan18-20,2013
Department of Chemical Engineering IIT Bombay January 20, 20013
Department of Chemical Engineering
From Biology to Mathematics
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A Reductionist Approach:
Observe, Understand and
Characterize Components
HT Analytical Methods genomics
transcriptomics
proteomics
simple.wikipedia.org
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Need a systems approach
Schmula.com
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Integrative Approach:
Systems Biology
1. Components
2. Reconstruction
3. Modeling/simulation
4. Feedback analysis
1250 computers v/s massive analog computing
Hundreds of feedback loops v/s many many large
Millions of components v/s many many more
Historically, biology has been a descriptional science
Modern Biology has led to quantification at molecular level (sub-system)
Similar to engineering systems that are quantified to a level that they are designed, optimized and optimally operated.
Principles of system science can be applied to
component biology: System-wide Approach
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Non-linear dynamics
Multiple feedback loops
Multiple interactions
Cascade structures
Feed forward loops
Interactions between modules
Timescale separation
Resulting in a Complex system
Experiment:
1. One maroon and One red Ball in a Box
2. Choose a ball randomly
3. Add and replace the same color ball into the box
4. What is the fraction of red balls after 50,000 steps
Picked maroon ball
Replaced the same
and added another
of same colour
P = 0.5
P = 0.5
P = 0.33
P = 0.66
P = 0.66
P = 0.33
Multiple outcomes possible depending on initial few steps
Fra
ctio
n o
f re
d b
alls
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Bottoms-up approach
Millions of components
Design manual available
Hundreds of feedback loops
Computer calculations
Robust
Top-down approach
No design principles available
No computation
Thousands of feedback loops
Molecular interactions
Robust
— Csete and Doyle, Science, 295, 2002
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DesignDesign
ControlControl
EvolveEvolve
Fault DiagnosisFault Diagnosis
OperationOperation
Economics
Model based
Smart systems/AI
Adaptive
Inherent
Robust performance/ stability
Molecular interaction
DNA repair/PCD
Evolution
Firefly Glows
Transgenic Plant made to Glow
Physiological state
Phosphorous release
using ATP
Metabolic network
Catalyzed by Luciferase Enzyme Protein network
Luciferase gene decoded RNA network
Luciferase Gene Genetic network
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Genotype to Phenotype: An Integrated
Approach
• Genome
• Transcriptome
• Proteome
• Metabalome
Phenotype
(physiological
consequence)
Upsala Glacier, BBC website
Environment
Randomness
Genome Gene expression is triggered
Transcriptome mRNAs are synthesized
Proteome Necessary enzymes are made
Metabalome Enzymes catalyze substrates
Phenotype Metabolites react to trigger
Presence of genome does not ensure a phenotype
It requires a specific state in the hierarchical chain.
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Modeling
Logical/Boolean networks
CFD
Delayed ODE
PDE
Stochastic models
Multiscale
Data mining
Estimation theory
Nonlinear systems theory
Feedback control theory
Sensitivity
Optimization
Stability
Analysis
Key: Identify design principles
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Example 1: Central Dogma Illustrated:
Tryptophan System of E. coli
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Operon Activation
and Transcription
RNAP R
Chorismate L-tryptophan
trp L trp R P/O P/O trp D trp E trp C trp B trp A
T
T T
Attenuator
RNAP RNAP RNAP RNAP RNAP
EEDD
T
T
T
T
F/B Mechanism I:
Genetic Repression
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Structural Enzymes
Anthranilate synthase
Phosphoribosyl
anthranilate
transferase
Indole glycerol
phosphate synthase
Tryptophan synthase
1 2
3 4
1 2
3
4 1 2
3
4
Translation
EEDD
BBAA
T
T
T T
F/B Mechanism II:
Attenuation
1 2
3 4
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Chorismate AS
Anthranilate PRA PRT
IGPS
CdRP
IGPS
InGP TS
L-tryptophan
Tryptophan Synthesis
EEDD
T EEDD
T
T
T
Active
T
T EEDD Inactive
F/B Mechanism III:
Enzyme Inhibition
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Example 1: Trp System: Model
Reduction
• Enables delineation of process and regulator
— Bhartiya, Rawool, Venkatesh, Eur. J. Biochem, 270, 2003
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Example 1: Tryptophan System in
Escherichia coli: Regulator and Process — Venkatesh, Bhartiya and Ruhela, FEBS Letters, 563, 2004
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Example 1: Multiple Loop v/s Single
Loop Design
CASE I: Multiple
CASE II:
Single
Are Multiple feedbacks loops a regulatory overkill?
(Freeman, Nature, 2003).
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G1 S M G2
Cyclin dependent kinese + cyclin •DNA repair
•Stress mediation
•Checkpoints
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Cig2Cdc2
Cdc13
Cdc2
Puc1
Cdc13
APC APC
P
P
P
P
P
Mik1
Mik1
Wee1
Wee1
Cdc13
Cdc2
P P
Rum1
P
Cdc13
Cdc2
Rum1
Puc1
Cdc2
Cig2
Cdc2
CAK
Cdc25
Cdc25
P
Rum1
PP1
P
A-DeP
Slp1
Slp1
APC
P
P
P
P
Ste9 P
SecSec
P
Separase
Separase
Ste9
APC
P
P
P
P
I
Cohsin Degradation for Sister
Chromatid Seperation
PP2I
PP1
PP1P
PP2
Ste9
Relative to previous works
• Synthesis of all proteins
• Role of multiple
phosphatases
• Detailed mitotic exit
regulation
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• Model could successfully simulate16 single, 14 double, 4 triple
deletion, 2 structural and 2 over expression mutants
• Math Question: Under what conditions will the limit cycle
become unstable? Identify sensitivity of period of oscillations to
parameters. Characterize DNA damage and repair.
Cycle time:
152 minutes
Synthetic Biology: Constructing Mathematical
Functions from biological components
Bistable circuits
Oscillators
Riboswitches
Logic Gates
Example 3:Bistable Circuits:
Natural
Bistable
ou
tpu
t
input
ON
OFF
Bistability in the lactose utilization network of E. coli
Nature 427, 737-740 (2004)
o Lactose utilization in E. coli.
o Lysis vs lysogeny in
bacteriophage λ.
o Sporulation in B. subtilis.
o Competence in B. subtilis.
A: TetR–VP16 (transactivator)
B: E-KRAB (transrepressor)
X: Erythromycin
PNAS July 5, 2005 vol. 102 no. 27 9517-9522
Circuit Design
Genetic Implementation
Example 3: Bistable Circuits:
Synthetic
Genes & Dev. 2007. 21: 2271-2276
A: Auto-feedback gene
B: Sensor gene
Natural Oscillatory Circuits
Example 4: Oscillatory Circuits: Natural
-
Nature Reviews Molecular Cell Biology 9, 981-991 (December 2008)
A: LacI
B: tetR
C: cI
Circuit Design
Genetic Implementation
Michael B. Elowitz and Stanislas Leibler; Nature. 2000
Repressilator
Tal Danino, Octavio Mondragón-Palomino, Lev Tsimring & Jeff Hasty; Nature.2010
Synchronized genetic clock
A: LuxI
B: aiiA
Frequency-modulated genetic arsenite biosensor
Nature 481,39–44 (05 January 2012)
Example 4: Oscillatory Circuits:
Synthetic
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Example 5: GAL system in yeast:
How to uptake galactose sugar
Yeast 1 (cerevisiae) and Yeast 2 (K. lactis) are evolutionary cousins
Both can metabolize galactose in absence of glucose
This is possible by the GAL system in the two yeasts
However the GAL system designs are different
Math Question: What is the evolutionary niche each have for their
respective designs
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• Developed detailed growth related dynamic models for
both organisms (validated with experiments) • Pannala et al., Wiley Interdisciplinary Reviews: Systems biology and medicine, (2010)
• Pannala et al., FEBS Journal, (2010) [Steady state K. lactis]
• Pannala et al., IET Systems Biology, (In press) [comprehensive S. cerevisiae]
• Pannala et al., Systems and synthetic biology, (2011) [comparative study]
S. cerevisiae K. lactis
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S. cerevisiae K. lactis
GAL80 mutant:
growth on glucose
Wildtype: growth
on galactose
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Evolutionary niche using optimization: MINLP
ConstraintConstraint--based Analysisbased Analysis
How often have I said to you that
when you have eliminated the
impossible, whatever remains,
however improbable, must be the
truth?
–Sherlock Holmes, A Study in
Scarlet
Flu
x C
Flux B
Flux A
Unbounded
Solution Space
Flu
x C
Flux B
Flux A
Unbounded
Solution Space
Flu
x C
Flux B
Bounded Convex Subset
Flu
x C
Flux B
Bounded Convex Subset
Constraints
(i) Stoichiometric (i)
(ii) Thermodynamic
(iii) Capacity
(iv) Rate
(v) Parameters
Based on the properties of the system.
Time constants for metabolic reactions are
very fast (sec - min) compared to cell growth
(hrs)
No net accumulation of metabolites in the cell
Thus, the steady-state approximation.
0 bvSX
dt
d
Venkatesh & Fell, Biotechnology and Bioengineering, 2004
Optimal
Biomass
Example 7: Elementary Modes
An elementary mode is a minimal subset of enzymes in
a network that can operate at steady state with all
irreversible reactions proceeding in the direction as
prescribed by thermodynamics
Elementary mode represents routes through substrate is
consumed to form products
Example 7: Methodology: Hypothetical
Network Elementary modes System chosen
Gayen and Venkatesh, BMC Bioinformatics. 2006; 7: 445
Example 7: Problem Formulation
Rates of external metabolites
In matrix form
Linear programming formulation
Experimentally
Determined
(known)
Gayen and Venkatesh, BMC Bioinformatics. 2006; 7: 445
Linear Algebra – metabolic flux analysis
Ordinary differential equations – lumped modeling
Partial differential equations – drug delivery, metastasis
Stochastic differential equations – heterogeneity, uncertain
Boolean algebra – large scale networks, drug discovery
Optimization – evolutionary biology, biotech
Statisitics – old companion of biologists
Artificial intelligence – bioinformatics
Lyapunov stability – perturbations before disease?
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Challenges: overcome jargon by reading biology
Interdisciplinary work requires interactive working
Be generous in sharing credit
Mathematics unifies seemingly different systems (a bacterial cell and a rocket) and this is her majestic might
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Prof. K.V. Venkatesh
P. Anbumathi
Venkat Pannala
Nikhil Chaudhary
Department of Chemical Engineering