Feb 20, 2017

Biochemical pathways:
Models of regulation
• History of the rise of Bioinformatics and Computational
Biology.
• Basic information theory.
• Cell as an information-processing system.
• DNA and Proteins as informational molecules.
• Computation in network of genes, protein structure,
protein-protein interactions.
• Biochemical pathways and cellular processes: Models
of regulation.
• Basics of metabolic control analysis.
• Network analysis of biochemical pathways.
• Introduction to some biological repositories of
information.
• Assignment/Project
 Flow of Information inside the cell

F
L
O Transcription rate -
W ~ 1,000 nucleotides/min
of
Translation rate -
I ~ 900 amino acids/min
N
F
O Production of the
R protein to the binding
M
A of dimer - about 3 min
T
I
O
N
Bi-directional Information Transfer Across Levels
Living systems are made up of cells – single or multi-cellular

Acetabularia
(3cm)
Bacteria Human RBC
(E.coli 3µm) (7µm) Muscle Cell (50µm) Amoeba (330µm)

Cellular functions are controlled by networks of biochemical reactions

Cellular behaviour is an
emergent property of networks
of inter-connected chemical
reactions of the molecular
species in the cell.

CHEMISTRY DRIVES ALL LIFE PROCESSES

Cell as an information processing system:

Information (genomic or extra-cellular

signals) processing inside the cell occurs
through multiple steps and involves multi-
unit systems
 Metabolic pathways – scales of description Amino acid
biosynthesis
pathways

Aromatic amino acid

biosynthesis pathway

Tryptophan
biosynthesis
pathway
Tryptophan biosynthesis pathway

TrpG, TrpE

TrpD

TrpF

TrpC

TrpA, TrpB
Complex network of biochemical reactions in cells
co-ordinate and control cellular functions

two interacting sets

GENETIC METABOLIC
REACTIONS REACTIONS

Gene induction, Conversion of substrate

repression, molecules by enzymes,
replication, enzyme inhibition or
transcription activation

Slow TIME SCALE Fast

(minutes, hours) (seconds)
 MODELLING BIOCHEMICAL PATHWAYS
Three complementary approaches

REVERSE ENGINEERING LARGE NETWORKS

Model existing pathways based on Construction & analysis of

information derived from – functionally related
• Genome sequences pathways from large scale
• Protein sequences gene expression and
protein interaction data
• Biochemical & Genetic information
using network theory

FORWARD ENGINEERING ‘Rational Network Design’

Artificial genetic and enzymatic
All designs that are not physically networks with specific
forbidden are realizable, properties constructed based
but not all realizable designs are on mathematical models
functionally effective
(in relation to context and constraints
of the system and environment).
 BIOCHEMICAL PATHWAYS ARE SEQUENTIAL REACTIONS
Information for short and long range regulation is transferred primarily through
feedback and feed-forward loops

Cellular behaviour is the emergent property of many complex biochemical reactions

networked through feedback/feed-forward processes with overlapping and wide-ranging
time scales

Biochemical details of each pathway may be different, but they possess certain general
features which can be described using the rules of chemical kinetics.

The resultant dynamics underlie different functional behaviour

Stability – Homeostasis
Multistability – Ability to operate on alternative conditions
Threshold Sensitivity – Switching behaviour
Oscillatory – Rhythmic and cyclic processes
Chaotic – Bursting activity & irregular behaviour
Transient processes – Stochastic phenomena and spatial waves

Thus generality in dynamics across a large variety of biochemical

processes allow theoretical studies to be functionally meaningful and useful.
Biochemical pathways and cellular processes

Models of regulation

Gene circuits

Databases and software for pathway analysis

 Feb 21, 2017

Biochemical pathways:
Models of regulation
 BIOCHEMICAL PATHWAYS ARE SEQUENTIAL REACTIONS

Information for short and long range regulation is transferred

primarily through feedback and feed-forward loops

Cellular behaviour is the emergent property of many complex

biochemical reactions networked through feedback/feed-forward
processes with overlapping and wide-ranging time scales

Biochemical details of each pathway may be different, but they possess certain
general features which can be described using the rules of chemical kinetics.

The resultant dynamics underlie different functional behaviour

Stability – Homeostasis
Multistability – Ability to operate on alternative conditions
Threshold Sensitivity – Switching behaviour
Oscillatory – Rhythmic and cyclic processes
Chaotic – Bursting activity & irregular behaviour
Transient processes – Stochastic phenomena and spatial waves

Thus generality in dynamics across a large variety of biochemical

processes allow theoretical studies to be functionally meaningful and useful.
Biochemical reactions are highly networked reactions
Primary mode of regulation to co-ordinate and control is through
Single, Multiple & Coupled Negative (inhibition/repression) and
Positive (activation/induction) Feedback Processes

desensitize the reaction pathway to perturbations

It ensures stability and conservation of energy and are,
therefore, naturally selected to be the most common
form of regulation in pathways

are potentially destabilizing

Employed for excitable dynamics & amplification in
switching & rapid response processes.

A combination of negative and positive feedback processes

is useful for optimal performance requiring stability, sensitivity and
multiplicity of dynamics.
 Biochemical reactions are controlled and co-ordinated
mainly through feedback processes.
Most biosynthetic pathways have multiple levels of feedback control

Monovalent Divalent
Control Control

Nested Sequential
Control Control
isoenzymes

Concerted Cumulative
Control Control

Cascaded
Control
 Biosynthesis of Aromatic Amino Acids

β-Aspartyl kinase

Divalent, Nested and Sequential

control in bacteria

Concerted control of b - Asp. kinase in

Gene Repression
Rhodopseudomonas capsulatus

Dual nested feedback in E.coli

tryptophan biosynthetic
pathway

Enzyme inhibition
 REVERSE
ENGINEERING

Model existing pathways based on

information derived from –

• Genome sequences

• Protein sequences

• Biochemical & Genetic information

 Construction & analysis of
LARGE functionally related pathways
NETWORKS from large scale gene expression
and protein interaction data
using network theory

Genome-Scale in silico
Metabolic Model of
Helicobacter pylori 26695,
Schilling, et al, J. Bact. (2002)

Genome sequence
annotation, biochemical and
physiological data.
388 enzymatic and transport
reactions (accounting for 291
open reading frames)

For less characterized

organisms and their genomes
 Yeast Cell Cycle Network
Protein-protein interaction and DNA
microarray time series data
Inside circle - 300 proteins
184 dynamic proteins (coloured
acc. to their time of peak expression)
& 116 static proteins (in white).
Outside circle: 412 of the 600
dynamic proteins identified
in the microarray analysis, no
physical interactions of good
reliability could be found.

• Missed subunits of stable

complexes already in the
network;
• the majority, may participate
in transient interactions, which
are not detected by current Dynamics of protein complex assembly during the
interaction assays. Sce cell cycle.de Lichtenberg, et al. SCIENCE 2005

This analysis required much statistics and mathematical analysis

 FORWARD ENGINEERING

‘Rational Network Design’

Artificial genetic and enzymatic networks with specific
properties constructed based on mathematical models
The bacteriophage λ paradigm The Toggle:- switched by IPTG
Two opposing negative feedback and ATC which induce the plac
processes lead to switch-like behaviour and ptet. Nature (2000)

Two nested negative feedback

 EXPECTATIONS FROM THEORETICAL STUDIES

Identification of common features in different

pathways

Identification of differences in similar pathways in

different organisms
functional implications

Predict new behaviour

Design new pathways

Correct pathological states

Molecular Biology, Genetics, Biochemistry, Mathematics, Statistics,

Databases, Visualisation, Network Theory, Computational methods
Feb 22, 2017
 Forward Engineering of gene circuits
(Rational network design)
Construction of desired network with specific properties predicted
from mathematical models using knowledge from biochemistry,
molecular biology, and genetics.

Boolean/Logical Circuits in Biology :

Organisms take decisions based on input signals and give a binary (0/1)
response in some cases.

Repressor

RNAP Inducer Jacob & Monod Model of the

prokaryotic operon (1961)

Gene A
Promoter Operator

“It is obvious from analysis of these [bacterial genetic regulatory]

mechanisms that their known elements could be connected into a wide
variety of ‘circuits’ endowed with any desired degree of stability”
 Basic digital circuits:

A A A
And C Or C C
B B B Nand

AB C AB C AB C
00 0 00 0 00 1
01 0 01 1 01 1
10 0 10 1 10 1
11 1 11 1 11 0

A repressible system –The NOT gate:

If repressor is input and
the gene product is output,
then if repressor is 1, gene product is 0
and vice versa.....
the input is inverted.
 Forward Engineering

Genetic Circuit Engineering Paradigm

Design - Simulate - Implement & Test

Such “ Rational Network Design ” can -

a) Engineer new cellular behaviour, and

b) Improve understanding of naturally occurring networks.

 Synthetic transcriptional regulatory networks
1.Single negative feedback:
Induced by ATC - an analog of tetracycline.
Nature (2000).
Regulation vs Autoregulation

The bacteriophage λ paradigm

2.Two nested negative feedback: Two opposing negative feedback
processes lead to switch-like behaviour
The Toggle: switched
by IPTG and ATC which
induce the plac and
ptet. Nature (2000).
Bistability

3.Three negative feedback:

The Repressilator:
Oscillates due to mutual
repression of the three
repressors. Nature (2000)
Development of Gene Circuits The Circuit Engineering Vision
Develop a standard library of interoperable “parts” that corresponds
to various control functions (http://parts.mit.edu)
may help in controlled gene expression in gene therapy

Develop integrated computational infrastructure for

Computer Aided Design (CAD) of genetic circuits
Simulation and dynamic analysis
Build increasingly complex genetic circuits using well-characterized parts
 TWO COMMON DESIGNS OF REGULATION (MOTIFS)
IN BIOCHEMICAL PATHWAYS

v Negative auto-regulation in metabolic pathways

and gene regulation
desensitize the pathway to perturbations
It ensures stability and conservation of energy and are,
therefore, naturally selected to be the most common
form of regulation in pathways

v Time required to complete the whole sequence

of reactions to yield any observable quantity -
widespread presence of time delay
 Biosynthesis of Aromatic Amino Acids

β-Aspartyl kinase

Divalent, Nested and Sequential

control in bacteria

Concerted control of b - Asp. kinase in

Gene Repression
Rhodopseudomonas capsulatus

Dual nested feedback in E.coli

tryptophan biosynthetic
pathway

Enzyme inhibition
 Gene Repression

Enzyme
inhibition

Promoter Gene
 INHERENT DELAY IN GENETIC REGULATION PROCESS

F
L Transcription rate -
O ~ 1,000 nucleotides/minute
W
Translation rate -
of ~ 900 amino acids/minute

I Production of the protein

N
to the binding of dimer -
F
O ~ 3 min
R
M
A
T
I
O
N
Promoter Gene
 MOTIVATION
v Negative feedback loops, common in biochemical
pathways, are known to provide stability, and withstand
considerable variations and random perturbations of
biochemical parameters.
(Savageau, 1974; Becskei and Serrano, 2000)

v A generic feature in all intracellular biochemical

processes is the time required to complete the whole
sequence of reactions to yield any observable quantity –
widespread presence of time delay in biological functions.

v Theoretically time delay is known to be the source of

instability, and has been attributed to lead to oscillations
or transient dynamics in several biological functions.
 Interaction of these two opposing factors

- instability and homeostasis -

are common features in intracellular processes

Effect of these divergent forces in the

dynamics of gene expression?

 Approaches

v Designed simple negatively regulated pathways

using common genetic parts so that both
theoretical and experimental studies can be done.

v Made deterministic and stochastic mathematical

models of the simple pathways.

v Constructed experimental gene circuits and

compared experimental results with theoretical
predictions.
 Designing negatively auto-regulated gene circuits –
with and without delay in repression

(-) (-)
S1 S2 S1 S’ S2

Basic Circuit Delay Circuit

The presence of one or more genes (“Delay element”) increase the length
of the transcript, thereby introducing a delay in establishment of negative
feedback by the repressor in Delay circuit compared to the Basic circuit.
 Designing negatively auto-regulated gene circuits with real parts

(a) Basic Circuit (TG) (b) Delay (C2TG)

TG: tetR gene and reporter gene C2TG: two copies of cI gene from λ phage
(gfp) after promoter (pLtet-01). before the repressor gene so that the
production of the repressor is delayed.
 Modelling the “Delay”

Delayed feedback is designed by increasing the length of

the mRNA before the repressor

Time taken to transcribe the repressor in the delay circuit

is more and introduces a delay in establishment of
feedback in this circuit as compared to the basic circuit.

Here the “delay” is assumed to be at the level of

production of the repressor.

In prokaryotes, transcription and translation are coupled and

translation of a given segment of mRNA does not lag
significantly behind the transcription of that segment. Thus, the
delay represents the time of appearance of the protein and
hence includes transcriptional and translational delay.
 Model of the Repression Process

Action of the repressor is only at the level of transcription.

The amount of mRNA (m) produced at any given instant is a function of
the number of free promoters (g) available.

k1
[Repressor] + [Promoter] [Repressor-Promoter complex]
k2

k1 and k2 are the rates of the forward and backward reactions

The rate of change in free promoter concentration:

gt is the total number of promoters, and g and p are the concentrations of

free promoters and the repressor protein
 The Four Variable Deterministic Model

gtotal
RNAP
ptet tetR gfp
g TetR
Transcription β1
k1 mRNA α1
Repression
Translation β
2
k2
TetR GFP Proteins
α2 α3 m = mRNA;
p = TetR (repressor);
gt = total no. of promoters; f = GFP (reporter);
α1, α2, α3 = degradation rates of m, p, f; g = free promoters;
β1, β2 = rates of transcription & translation;
k1, k2 = reaction rates for the promoter-repressor complex reaction;
τ1 and τ2 = time delays on the production of p and f from the
common mRNA;
 The Four Variable Deterministic Model

gtotal m = mRNA;
RNAP p = TetR (repressor);
ptet tetR gfp
g TetR f = GFP (reporter);
Transcription β1
k1 g = free promoters;
mRNA α1
Repression
Translation β
2
k2
TetR GFP Proteins
α2 α3

gt = total no. of promoters;

α1, α2, α3 = degradation rates of m, p, f;
β1, β2 = rates of transcription & translation;
k1, k2 = reaction rates for the promoter-
repressor complex reaction;
τ1 and τ2 = time delays on the production of
p and f from the common mRNA;
 Steady State Analysis
Eigen value Analysis

Steady State Analysis

What happens when

there is no change ?
dm/dt = 0
dp/dt = 0
df/dt = 0
dg/dt = 0

Eigen value Analysis:

What happens for small perturbation to the steady state?
Does it grow, come back, or oscillate around steady state ?
Feb 27, 2017
 MODELLING BIOCHEMICAL PATHWAYS
Three complementary approaches

REVERSE ENGINEERING LARGE NETWORKS

Model existing pathways based on Construction & analysis of

information derived from – functionally related
• Genome sequences pathways from large scale
• Protein sequences gene expression and
protein interaction data
• Biochemical & Genetic information
using network theory

FORWARD ENGINEERING ‘Rational Network Design’

Artificial genetic and enzymatic
All designs that are not physically networks with specific
forbidden are realizable, properties constructed based
but not all realizable designs are on mathematical models
functionally effective
(in relation to context and constraints
of the system and environment).
 Forward Engineering - Gene Circuits (Contd)
MOTIVATION
v Negative feedback loops, common in biochemical
pathways, are known to provide stability, and withstand
considerable variations and random perturbations of
biochemical parameters.
v A generic feature in all biochemical processes is the time
required to complete the whole sequence of reactions to
yield any observable quantity – widespread presence of
time delay. Theoretically time delay is known to be the
source of instability, and may lead to oscillations or
transient dynamics in several biological functions.

Interaction of these two opposing factors - instability and

homeostasis - are common features in intracellular
processes. Effect of these divergent forces in the
dynamics of gene expression?
 Approaches

v Designed simple negatively regulated pathways

using common genetic parts so that both
theoretical and experimental studies can be done.

v Made deterministic and stochastic mathematical

models of the simple pathways.

v Constructed experimental gene circuits and

compared experimental results with theoretical
predictions.
 Designing negatively auto-regulated gene circuits –
with and without delay in repression

(-) (-)
S1 S2 S1 S’ S2

Basic Circuit Delay Circuit

The presence of one or more genes (“Delay element”) increase the length
of the transcript, thereby introducing a delay in establishment of negative
feedback by the repressor in Delay circuit compared to the Basic circuit.
 Model of the Repression Process

Action of the repressor is only at the level of transcription.

The amount of mRNA (m) produced at any given instant is a
function of the number of free promoters (g) available.
k1
Repressor + Operator-Promoter Repressor-Promoter complex
k2
k1 and k2 are the rates of the forward and backward reactions

The rate of change in free promoter concentration:

gt = the total number of operator-promoter sites, and

g = concentration of free operator-promoter sites
p = concentration of the repressor protein
The Four Variable Deterministic Model m = mRNA;
p = TetR (repressor);
gtotal
f = GFP (reporter);
RNAP
ptet tetR gfp g = free promoters;
g TetR
Transcription β1
k1 mRNA α1
Repression
Translation β
2
k2
TetR GFP Proteins
α2 α3

gt = total no. of promoters;

α1, α2, α3 = degradation rates of m, p, f;
β1, β2 = rates of transcription & translation;
k1, k2 = reaction rates for the promoter-
repressor complex reaction;
τ1 and τ2 = time delays on the production of p
and f from the common mRNA;
 Steady State Analysis
Eigen value Analysis

Steady State Analysis

What happens when

there is no change ?
dm/dt = 0
dp/dt = 0
df/dt = 0
dg/dt = 0

Eigen value Analysis:

What happens for small perturbation to the steady state?
Does it grow, come back, or oscillate around steady state ?
 Equilibrium points

A = k 1α1α 2 B = k 2 α1α 2 C = −k 2 β1β 2 g t

 Linear Asymptotic Stability Analysis
The characteristic equation :
3 2
P(λ ) = (λ + α 3 )(a0λ + a1λ + a2λ + a3 ) = 0
a0 = 1

Four roots:
One is -α3 (< 0, negative)
Using Routh-Hurwitz criterion:
Δ1 = a2, Δ2 = a2 a1-a0a3, are > 0,
All roots have negative real parts,
System is stable around the positive equilibrium point
Parameter values used for deterministic and stochastic simulations
(Bundschuh et al, 2002; Elowitz and Leibler, 2000; Andersen, et al,
1998; Lutz and Bujard, 1997)

Parameter Deterministic Value

β2 4.3 x10-2 sec-1
β1 0.6 x10-9M sec-1
α1 5.7 x10-3sec-1
α2 1.15 x10-3 sec-1
α3 1.28 x10-4sec-1
k1 1.2 x 10+7M -1sec-1
k2 0.9 sec-1
gt 50

A basal delay of 3 minutes in Basic circuit (Rosenfeld et al, 2002)

and an additional delay of 1 minute for the Delay circuit.
 The short-term dynamics - TRANSIENTS
Transients are characterised by
1. Rise time – time taken to reach half-steady state value.

2. Overshoot - the fold increase above the steady state.

Transient
Steady state
Overshoot

Rise Time
Temporal dynamics of the repressor in the model in the presence of delay
(a) The long-term dynamics, (b) A close-up view of the same,
(c) The effect of delay on Rise Time, (d) The effect of delay on Overshoot
In (c) - (d), the curves are normalised by the steady state concentration.
 Effect of delay on Rise Time and Overshoot

No delay
d=10 seconds
d=20 seconds
d=40 seconds
No repression

üRise Time decreases and

Overshoot increases with
increasing delay.
üThe circuit behaves in an
unrepressed fashion for the
duration of the delay.
 Molecular reactions considered in the
The four variable stochastic model
deterministic model

dm
= β 1 g − α 1m
dt
dp
= β 2 m ( t −τ )
−α 2
p
dt
df
= β 2 m ( t −τ )
−α 3
f
dt
dg
= k 2 ( g t − g ) − k 1 gp
dt

ϕ represents the degradation products Gillespie’s Algorithm

of mRNA, TetR and GFP (Gillespie, 1977; Bratsun et al., 2005)
Parameter values used for deterministic and stochastic simulations
(Bundschuh et al, 2002; Elowitz and Leibler, 2000; Andersen, et al,
1998; Lutz and Bujard, 1997)

Parameter Deterministic Value Stochastic Value

β2 4.3 x10-2 sec-1 4.3x10-2 sec-1
β1 0.6 x10-9M sec-1 0.6 molecules sec-1
α1 5.7 x10-3sec-1 5.7x10-3 sec-1
α2 1.15 x10-3 sec-1 1.15 x10-3 sec-1
α3 1.28 x10-4sec-1 1.28 x10-4 sec-1
k1 1.2 x 10+7M -1sec-1 0.012 molecules -1sec-1
k2 0.9 sec-1 0.9 sec-1
gt 50 50

A basal delay of 3 minutes in Basic circuit (Rosenfeld et al, 2002)

and an additional delay of 1 minute for the Delay circuit.
 Effect of ‘delay’ on temporal dynamics
Deterministic model Stochastic model
No delay
d=10 seconds
d=20 seconds
d=40 seconds
No repression

Overshoot increases with increasing delay

The circuit behaves in an unrepressed fashion for the

duration of the delay.
The negatively auto-regulated pathway can show a transient overshoot
in gene expression and protein production due to the delay in the
kinetics of the repression process.
 THE PATHWAY IS STABLE FOR ALL PARAMETER VALUES –
SAME RESULT AS OF MATHEMATICAL ANALYSIS.

Parameter Values used for deterministic simulations

and the stability of the system on changing different parameters

(Bundschuh et al, 2002; Elowitz and Leibler, 2000; Andersen, et al, 1998;
Lutz and Bujard, 1997)
The negatively auto-regulated pathway, as
represented in these models, can show a
transient overshoot in gene expression and
protein production due to the delay in the
kinetics of the repression process.
Feb 28, 2017
 Designing negatively auto-regulated gene circuits –
with and without delay in repression

(-) (-)
S1 S2 S1 S’ S2

Basic Circuit Delay Circuit

The presence of one or more genes (“Delay element”) increase the length
of the transcript, thereby introducing a delay in establishment of negative
feedback by the repressor in Delay circuit compared to the Basic circuit.
 The Four Variable Deterministic Model

gtotal m = mRNA;
RNAP p = TetR (repressor);
ptet tetR gfp
g TetR f = GFP (reporter);
Transcription β1
k1 g = free promoters;
mRNA α1
Repression
Translation β
2
k2
TetR GFP Proteins
α2 α3

gt = total no. of promoters;

α1, α2, α3 = degradation rates of m, p, f;
β1, β2 = rates of transcription & translation;
k1, k2 = reaction rates for the promoter-
repressor complex reaction;
τ1 and τ2 = time delays on the production of
p and f from the common mRNA;
 Effect of ‘delay’ on temporal dynamics
Deterministic model Stochastic model
No delay
d=10 seconds
d=20 seconds
d=40 seconds
No repression

Overshoot increases with increasing delay

The circuit behaves in an unrepressed fashion for the

duration of the delay.
The negatively auto-regulated pathway can show a transient overshoot
in gene expression and protein production due to the delay in the
kinetics of the repression process.
Design of negatively auto-regulated transcriptional modules
(a) Basic Circuit (TG) (b) Delay (C2TG)
TG: tetR
gene and
reporter
gene
(gfp) after
promoter
(pLtet-01)

C2TG: two copies of cI gene from λ phage before the repressor

gene so that the production of the repressor is delayed. C2TG
has a delay length of 1.5 KB.
Control Delay circuit (TC2G): Position of repressor same as in TG, but
position of reporter is as in C2TG. This circuit is identical to the Delay circuit
(C2TG) in length, number of cistrons, and position of the Reporter gene,
except for the position of the repressor, TetR.
 Experimental kinetics of GFP

Basic (circle) & Delay (triangle) circuits upon induction

(25 ng/ml) in four independent experiments.

Normalised fluorescence versus time (minute);

Error bars - one standard dev.

Delay circuit shows a large overshoot in gene expression

Overshoot increases with increasing delay

No delay
d=10 seconds
d=20 seconds
d=40 seconds
No repression

4 independent
expts
Intra-population heterogeneity in gene expression
It is well established that individual cells in a population can
differ significantly in their response to environmental stimuli.
Is there a difference in heterogeneity in gene expression in
cells within a population between the Basic negatively auto-
regulated circuit and the Delay circuit ?
Theoretical studies with model circuits: Populations of 1000
model cells with the Basic and Delay circuits having plasmid
variation (copy number: 50±10, normally distributed).
Determine the distribution of GFP expression levels in the
cells at different time points.
Intra-population heterogeneity in gene expression
Theoretical

Experimental

Delay circuit shows a large heterogeneity in gene expression

Frequency
amongdistributions
the individual of GFP
cells in cell
within populations:
a population
(a) Basic (TG), and (b) Delay (C2TG) circuits at different time intervals.
 Heterogeneity of gene expression in a population of cells
Common measures of comparing variability (noise) in a system -
Coefficient of Variation CV = (standard deviation/mean)*100
Experiments

Basic (TG - dashed line + circle)

Delay (C2TG-solid line + square)

Inset:
Changes in Fano Factor (FF) for
both the circuits.
FF = (standard deviation)2/mean)

• During the time of the build-up of the overshoot (till 90 minutes):

CV of the Delay population > Basic population
• The initial decreasing trend in CV in both the circuits indicates reduction in the
intrinsic noise levels with time due to the establishment of the repression.
• Fano Factor shows continuing difference between the two circuits. Delay circuit
exhibits greater variability compared to the Basic circuit.
 Model Delay and Basic circuits -
No significant difference in their CV over time except at an
early time point.

Prediction is not consistent with the experimental results ?

 Kinetics of GFP fluorescence at different inducer concentrations

25 ng/ml of
Doxycycline

50 ng/ml

75 ng/ml

Basic (TG, triangles), Control Delay (TC2G, circles), and Delay (C2TG,
squares) circuits in four independent experiments at 1hr interval.
 Bimodality
TG C2TG
25ng/ml

50ng/ml

75ng/ml

Contour plots of GFP fluorescence distribution in cell populations.

At 1, 2 and 5 hrs after induction with different inducer concentrations -
(i) 25ng/ml, (ii) 50 ng/ml, and (iii) 75ng/ml, of Doxycyline.

The presence of bimodality in Delay circuit cell populations, induced at

25ng/ml, is a consequence of, but not an inherent property of, the delay
element in the circuit. Removal of this low-expressing fraction of cells
by gating shows that C2TG continues to have a greater spread than TG.
 This prediction is consistent with experimental results.
The experimental Delay circuit at 75ng/ml induction shows similar
difference in CV as is seen in the model circuits.

Coefficient of Variation for both Basic (dashed lines) and Delay (solid lines) circuits:
a) Experimental populations for inducer concentrations
(25 ng/ml - circles, 75ng/ml - triangles) till 60 min from three experiments;
b) Theoretical simulation (Basic: dashed line and Delay: solid line).

The hypothesis that delay in repression is the primary factor for

inducing increased inter-cellular heterogeneity in gene expression in
a population is shown theoretically and experimentally.
 CONCLUSIONS

The generic origin of delay in biochemical pathways and

negative regulation implies that there is a high likelihood that
the two properties shown in our study –
Transient Overshoot & generation of Heterogeneity
in gene expression in cell population
play important roles in gene regulation.
This motif of regulation can do two things before
the stabilising effect of repression sets in

The overshoot allows for gene It can act as a dominant source of

products be available in large large deterministic variability paving
amount for multi-step pathways way to increase the phenotypic
to function diversity in a population of cells before
the negative regulation sets in.

Our theoretical and experimental results provide important clues and

give possible rationale for delayed feedbacks to be such a generic
feature in gene organisation in cells.
 CONCLUSIONS

Robustness of the results

Experimental methodology used involved –
1) Population approach (Fluorimetry) – observations on ~ 109 cells
2) Cell level (FACS) – observation on ~ 104 cells
3) Theoretical model only highlighting the delay in repression
– calculations on ~ 103 cells
(no consideration of real factors, e.g., cell size changes, growth,
folding delays of GFP, nonlinearities involved in degradation, etc)

All three approaches show

“Overshoot” and “Heterogeneity” in gene expression
March 1, 2017
 MODELLING BIOCHEMICAL PATHWAYS
Three complementary approaches

REVERSE ENGINEERING LARGE NETWORKS

Model existing pathways based on Construction & analysis of

information derived from – functionally related pathways
• Genome sequences from large scale gene
• Protein sequences expression and protein
interaction data using network
• Biochemical & Genetic information
theory

FORWARD ENGINEERING

‘Rational Network Design’

Artificial genetic and enzymatic networks with
specific properties constructed based on
mathematical models, and tested experimentally
 REVERSE ENGINEERING

Model existing pathways based on biochemical & genetic

information
Construct simple mathematical models based on real
biological pathways

Study the dynamics of simple pathways having different

structural designs/arrangements of feedback regulation

Study the dynamic behaviour of these pathways under

realistic changes (mutations) and stochastic variation in
reaction rates or concentration of substrates.

HOW DO PATTERNS OF REGULATION AFFECT

FUNCTIONAL DYNAMICS ?
 Metabolic pathways – scales of description Amino acid
biosynthesis
pathways

Aromatic amino acid

biosynthesis pathway

Tryptophan
biosynthesis
pathway
 Biosynthesis of Tryptophan

Deficiencies lead to
Essential amino acid Depression, Insomnia, Autism,
Most cereal grains Pain Tolerance, Appetite Control,
are deficient Chemical Addiction, Jetlag, Auxin
production in higher plants, etc.

Tryptophan is an important food supplement

CASEbySTUDY
L- tryptophan is manufactured
fermentative processes, in which large DL-tryptophan made
quantities of bacteria are grown and chemically is expensive and
tryptophan extracted and purified the D-isomers are wasted

Much effort has been spent in developing efficient and high-yielding

strains of bacteria using genetic engineering methods.
Can theoretical studies help in predicting mutations that may
be candidates for constructing Tryptophan over-producing
strains ?
 Mathematical modelling of Tryptophan biosynthetic
pathway based on experimental data

Build a realistic but simplified model of the pathway

by considering existing experimental information

Simulate the model to predict dynamics and

concentrations of pathway variables

Modify parameters (mutations) or change

concentrations to study variations in the pathway
behaviour

Predict effects of mutations and other

perturbations relevant to experimental manipulations
for the desired product
 Biosynthesis of Aromatic Amino Acids
Erythrose 4-Phosphate
Negative
Phosphoenolpyruvate Feedback

Deoxy-h acid 7 phosphate

Dehydroquinic acid
Shikimic acid
Not in
Chorismic acid B. subtilis

Prephanic acid Anthranilic acid

Phenylpyruvic acid

Phenylalanine Tyrosine Tryptophan

Variation in regulation of the same pathway in different microorganisms

 Dual nested feedback in
E.coli Tryptophan biosynthetic pathway

GENETIC Two levels of control METABOLIC

Gene repression Enzyme inhibition
through Trp repressor by end product
 Modelling Tryptophan Biosynthetic Pathway

Facts & Assumptions

5 contiguous structural genes (trpEDCBA) code for the enzymes

Single polycistronic mRNA (7000 nucl.) under normal transcription

All enzymes act in a concerted manner and regulation is on the first enzyme

_ mRNA (A),
A
_ Enzyme (B),

R+C CR B Tryptophan (C)

Repressor (R) – inactive

C
Bound/Active Repressor (CR)
 Modelling Tryptophan Biosynthetic Pathway

Rate of change of
mRNA (A), Enzyme (B), and Tryptophan (C)
concentrations with time

Each function represents a biochemical process

F(C) - synthesis of mRNA depends on the

dA repressor-mediated process –
= F(C) - K1A
dt a function of C
dB
= KeA – K2B
dt G(B,C) - endproduct synthesis is a
dC function of enzyme inhibition which
= G(B,C) - KDC - F’(C)
dt depends on enzyme (B) and
endproduct (C) concentrations

KeA - enzyme synthesis ∞ to conc. of A F’(C) - utilisation of C in cellular

K1A, K2B, KDC - degradation kinetics processes (protein synthesis)
of A, B, C are first order processes
 F(C) represents the genetic repression process - 2 step process
• Tryptophan - Repressor binding (active repressor)
• active repressor-operator binding
Fraction of repressor bound to tryptophan
RT = Total
If binding is co-operative
repressor conc.
n = Hill co-efficient, KR = pseudo-Michaelis constant K0 = Dissociation
If the binding sites are identical const. for operator-
nC active Repressor
and non-interacting
n = binding sites, K d +C binding
Kd = dissociation constant

F(C) for the two cases would be D = Gene dosage; r = RT/K0

Cooperative & r # K nR DK m
binding F(C) = DK m $ ! n n
+
%1 + r " K R + (1 + r )C 1+ r

Non-cooperative & r # Kd DK m
F(C) = DK m $ ! +
binding % 1 + r " K d + (1 + r )C 1 + r
 G(B,C) represents the metabolic inhibition process

Tryptophan - Anthranilate Synthase binding follows Michaelis-Menten

kinetics with two binding sites

(KI = pseudo michaelis constant) K 2I

G (B, C) = 2
K I + C2

F’(C) represents the rate of utilisation of tryptophan

in cellular processes (e.g., protein synthesis)

Hyperbolic saturation function

Vmax = maximum rate of utilisation
KG= pseudo michaelis constant
' Vmax C
F ( C) =
Approximation: F’(C) = Vmax
KG + C

(Bliss et al 1983, Tyson,1983, Painter & Tyson 1984)

 Tryptophan Biosynthetic
MODEL Pathway Model

The time variation of concentrations of A, B, and C are -

dA = F(C) - K A
1
dt
dB = K A – K B
e 2
dt
dC = G(B,C) - K C - F’(C)
D
dt

A trp mRNA
B Enzyme (Asase)
C Tryptophan
Experimental parameter values for Tryptophan biosynthetic pathway in E.coli

Parameter Units Magnitude

D Operons/cell 1.3
Km mRNA/operon/sec 0.07
Ke Emzyme/mRNA/sec 0.28
K1, K2 1/sec 0.016, 0.0002
KR Molar 1/1.73 x10-4
KI Molar 10-4 (normal operon)
KI Molar 10-3 (feedback resistant)
KG Molar 10-6
KD 1/sec 0.0002
KP Moles end-prod/ 10-8
enzyme molec/cell
litres/cell
 The structure of feedback regulation is not universal
Different organisms show variability in regulatory designs

_ A mRNA
A
_ B Enzymes

R+C CR B C tryptophan
R inactive repressor

C
CR active repressor

Pathways with different structural designs show

• distinct functional dynamics, and

• degrees of robustness to environmental noise
 Three major regulatory schemes
Dual control through end-
product inhibition of enzyme
activity and repressor- Control by repressor- Control by endproduct
mediated repression of mediated repression of inhibition of enzyme
transcription of the operon. transcription alone activity

E.coli and Salmonella Rhizobium Chromobacterium violecium,

typhimurium leguminosarum Loose-repressing mutants
(2 genes) of E.coli.
HOW DO PATTERNS OF REGULATION
AFFECT FUNCTIONAL DYNAMICS ?
March 2, 2017
 REVERSE ENGINEERING
Dual nested feedback in E.coli Tryptophan biosynthetic pathway

GENETIC Two levels of control METABOLIC

Gene repression Enzyme inhibition by
through Trp repressor end product
 Tryptophan Biosynthetic
MODEL Pathway Model

The time variation of concentrations of A, B, and C are -

A trp mRNA
B Enzyme (Asase)
C Tryptophan
 Three major regulatory schemes
Dual control through end-
product inhibition of enzyme
activity and repressor- Control by repressor- Control by endproduct
mediated repression of mediated repression of inhibition of enzyme
transcription of the operon. transcription alone activity

E.coli and Salmonella Rhizobium Chromobacterium violecium,

typhimurium leguminosarum Loose-repressing mutants
(2 genes) of E.coli.
 Modelling Regulated Pathways

HOW DO PATTERNS OF REGULATION

AFFECT FUNCTIONAL DYNAMICS ?

Do pathways with different structural designs show

• distinct functional dynamics, and
• degrees of robustness to environmental noise ?
 D Operons/cell 1.3
Km mRNA/operon/sec 0.07
Ke Emzyme/mRNA/sec 0.28
K1, K2 1/sec 0.016, 0.0002
KR Molar 1/1.73 x10-4
KI Molar 10-4
10 parameters (normal operon)
KI Molar 10-3
(feedback resistant)
KG Molar 10-6
KD 1/sec 0.0002
KP Moles end-prod/enzyme molec/cell 10-8
litres/cell
For non-dimensionalization, the variables are changed as

A0 = [KR /(Kb Kc t02)] B0 = [KR /( Kc t0)] C0 = K R

t0 = [KR /(DKaKbKc)]1/3

a 1 = K 1 t0 a 2 = K 2 t0 a 3 = K D t0

g = Vmax t0 / KR
 The dimensionless form of the equations are

a1, a2, a3 degradation rates of A,B and C

r gene repression strength
b enzyme inhibition strength
g and K' Tryptophan utilization in the cell.

This is the basic model for

Tryptophan biosynthetic pathway in E.coli
 Experimental parameter values for
Tryptophan biosynthetic pathway in E.coli

Parameter Units Magnitude

D Operons/cell 1.3
Km mRNA/operon/sec 0.07
Ke Emzyme/mRNA/sec 0.28 Wild type -
K1, K2 1/sec 0.016, 0.0002
a1 = 1
KR Molar 1/1.73 x10-4
a2 = 0.01
KI Molar 10-4 (normal operon)
KI Molar 10-3 a3 = 0.01
(feedback resistant) g=4
KG Molar 10-6
r = 10
KD 1/sec 0.0002
KP Moles end-prod/ 10-8
enzyme molec/cell
litres/cell
 Three major regulatory schemes
Dual control through end-
product inhibition of enzyme
activity and repressor- Control by repressor- Control by endproduct
mediated repression of mediated repression of inhibition of enzyme
transcription of the operon. transcription alone activity

E.coli and Salmonella Rhizobium Chromobacterium violecium,

typhimurium leguminosarum Loose-repressing mutants
(2 genes) of E.coli.
 Two Negative feedback System
Repressor mediated repression and allosteric inhibition

• x ,y, z scaled concentrations of A,B, C

• γ the strength of repression of C on A
• n the co-operativity of repressor mediated repression
• g related to the utilization of end product in cellular processes
• α1, α2, α3 degradation rates of x, y and z
• β strength of enzyme inhibition of C on the enzyme E
• k related to the utilization of end product in cellular processes
 Analysis of the two negative feed back system
1. Behaviour of the normal pathway
Parameter values used are:
a1 =1; a2 = 0.01; a3 = 0.01; g = 4; γ = 10; β = 0.33; k= 0.0173

The pathway is stable under normal values of parameters

2. Changing the strength of repression:

No change in dynamics on 100-fold increase in γ,

but as repression strength increases
less tryptophan is synthesized.
3. Effect of sudden perturbation

In stable region: γ = 10.

No effect of perturbation.

The pathway is robust to random perturbation

in end product.
 For wild type parameters!
!n = 2, a1 = 1.0,!
!a2 = a3 = 0.01,!
!g= 4, γ = 10
!
The steady state values are!
!A=0.5,!
!B=866.5!
!C=0.03.!

Bliss, et. al. 1982

J. Theoretical Biology
 Experimental parameter values for
Tryptophan biosynthetic pathway in E.coli

Parameter Units Magnitude

D Operons/cell 1.3
Km mRNA/operon/sec 0.07
Ke Emzyme/mRNA/sec 0.28 Wild type -
K1, K2 1/sec 0.016, 0.0002
a1 = 1
KR Molar 1/1.73 x10-4
a2 = 0.01
KI Molar 10-4 (normal operon)
KI Molar 10-3 a3 = 0.01
(feedback resistant) g=4
KG Molar 10-6
r = 10
KD 1/sec 0.0002
KP Moles end-prod/ 10-8
enzyme molec/cell
litres/cell
March 6, 2017
 Three major regulatory schemes
Dual control through end-product Control by repressor- Control by endproduct
inhibition of enzyme activity and mediated repression of inhibition of enzyme
repressor- mediated repression of transcription alone activity
transcription of the operon.

E.coli and Salmonella Rhizobium Chromobacterium violecium,

Do pathways with
typhimurium different structuralLoose-repressing
leguminosarum designs show mutants
• distinct functional
(2 genes)dynamics, and of E.coli.
• degrees of robustness to environmental noise ?
 Two Negative feedback System
Repressor mediated repression and allosteric inhibition

• x ,y, z scaled concentrations of A,B, C

• γ the strength of repression of C on A
• n the co-operativity of repressor mediated repression
• g related to the utilization of end product in cellular processes
• α1, α2, α3 degradation rates of x, y and z
• β strength of enzyme inhibition of C on the enzyme E
• k related to the utilization of end product in cellular processes
 Experimental parameter values for
Tryptophan biosynthetic pathway in E.coli

Parameter Units Magnitude

D Operons/cell 1.3
Km mRNA/operon/sec 0.07 a1 = 1
Ke Emzyme/mRNA/sec 0.28 a2 = 0.01
K1, K2 1/sec 0.016, 0.0002
a3 = 0.01
KR Molar 1/1.73 x10-4
g=4
KI Molar 10-4 (normal operon)
KI Molar 10-3 r = 10
(feedback resistant)
β = 0.33
KG Molar 10-6
KD 1/sec 0.0002
KP Moles end-prod/ 10-8
enzyme molec/cell
litres/cell
 Analysis of the two negative feed back system
1. Behaviour of the normal pathway
Parameter values used are:
a1 =1; a2 = 0.01; a3 = 0.01; g = 4; γ = 10; β = 0.33; k= 0.0173

The pathway is stable under normal values of parameters

2. Changing the strength of repression:

No change in dynamics on 100-fold increase in γ,

but as repression strength increases
less tryptophan is synthesized.
3. Effect of sudden perturbation

In stable region: γ = 10.

No effect of perturbation.

The pathway is robust to random perturbation

in end product.
Pathway is stable under changes in parameters
Pathway is robust to random perturbations. ?
 Single Negative Feedback Pathway
Repressor mediated repression only - no or very low Enzyme inhibition

Where:
• x ,y, z are scaled concentrations of A,B, C
• γ is the strength of repression of C on A
• n is the co-operativity of repressor mediated repression
• g are related to the utilization of end product in cellular processes
• α1, α2 and α3 are degradation rates of x, y and z
Analysis of a pathway with two designs of Negative Feedback
1. Behaviour of the normal pathway:
Parameter values for the normal (wild type) pathway are:
γ =10 α1=1 α2=0.01 α3 =0.01 g=4 and n=2.

Single negative feedback Dual negative feedback

β = 0.33

There is stable synthesis of end product, as expected for the

single negative feedback system.
 Experimental parameter values for
Tryptophan biosynthetic pathway in E.coli

Parameter Units Magnitude

D Operons/cell 1.3
Km mRNA/operon/sec 0.07
Ke Emzyme/mRNA/sec 0.28 a1 = 1
K1, K2 1/sec 0.016, 0.0002
a2 = 0.01
KR Molar 1/1.73 x10-4
a3 = 0.01
KI Molar 10-4 (normal operon)
KI Molar 10-3 g=4
(feedback resistant)
r = 10
KG Molar 10-6
KD 1/sec 0.0002
KP Moles end-prod/ 10-8
enzyme molec/cell
litres/cell
2. Changing strength of repression, γ :
Stable steady state,γ =100 Bistability, γ =250

Limit cycle

Seperatrix

Equilibrium
point

Stable Limit Cycle,

γ = 500

On increasing repression, the system loses stability (via a sub-critical

Hopf bifurcation) and exhibits bistable behaviour for a range of
parameter values.
2. Changing the strength of repression:
Dual feedback Single feedback
Stable steady state Bistability
γ =100 γ =250

Stable Limit Cycle,

γ = 500
No change in dynamics
on 100-fold increase in γ.
Only endproduct conc.
is reduced

Change in dynamics with increase in γ. Same cell can show two

different functional dynamics on perturbation (no parameter change)
 3. Effect of random perturbation on dynamics

No effect

No effect.

In stable region: γ=100 In oscillatory region: γ=500

Bistable region: γ=250.

No effect Change in
dynamics Large
Small
perturbation. perturbation

Effect of perturbation depends on strength of perturbation.

3. Effect of sudden perturbation ROBUSTNESS
Dual feedback Single feedback

In stable region: In oscillatory

γ=100. region: γ=500.
No effect. No effect.

In stable region: γ = 10.

No effect of perturbation.
The pathway is robust to
random perturbation
in end product. In bistable region: γ=250.
Effect of perturbation depends on strength of
perturbation.
 For wild type parameters!
!n = 2, a1 = 1.0,!
!a2 = a3 = 0.01,!
!g= 4, γ = 10
!
The steady state values are!
!A=0.5,!
!B=866.5!
!C=0.03.!
 Prediction for
Tryptophan (Z) synthesis in
over-production normal strain (r=10) for
of Tryptophan different values of g

in reduced inhibition
background
g Z

almost doubles production

Predicted mutations –
• Reduced Asase binding to Trp
• Reduced incorporation of Trp in
protein synthesis
Time (x 102 )
Prospect of the using pathway modelling for improvement in food
production through prediction of useful genetic modifications
March 7, 2017
 MODELLING BIOCHEMICAL PATHWAYS
Three complementary approaches

REVERSE ENGINEERING LARGE NETWORKS

Model existing pathways based on Construction & analysis of

information derived from – functionally related pathways
• Genome sequences from large scale gene
• Protein sequences expression and protein
interaction data using network
• Biochemical & Genetic information
theory

FORWARD ENGINEERING

‘Rational Network Design’

Artificial genetic and enzymatic
networks with specific
properties constructed based
on mathematical models
 Any NETWORK is composed of a large set of units
interacting among themselves, and can be studied using
Graph Theory.

Many biological processes (e.g., metabolic networks,

protein-protein interaction networks, gene regulatory
networks, …) underlying specific biological functions have
been described using graphs.

The idea is to understand macroscopic properties of

these systems using global parameters that may have
relevance to their functions.
 Genetic Networks

Networks are constructed based on data from

biochemistry, molecular biology, genetics,
microarray and proteomics experiments

Attempt to find motifs and modules

that make-up complex networks
 Design principles in transcriptional regulatory
networks that control gene expression
Network motifs found in the E. coli transcriptional regulation network

Transcription factor X regulates a second

transcription factor Y, and both jointly
regulate one or more operons Z1 ...Zn

Example of a feed forward loop

(L-arabinose utilization)

A single transcription factor, X,

regulates a set of operons Z1 ...Zn.
X is usually auto-regulatory.

Example of a SIM system

(Arginine biosynthesis)

Network motifs in the transcriptional regulation network of E. coli. Nature Genetics, (2002)
A set of operons Z1 ...Zm are each regulated by a combination of a set
of input transcription factors, X1 ...Xn .

DORs are defined by an algorithm that detects dense regions of

connections, with a high ratio of connections to transcription factors.

Example of a DOR (stationary phase response).

Part of the network of direct transcriptional interactions in the E.
coli data set, represented using network motifs
 METHODS used in this study
Transcriptional interaction database
Data from RegulonDB (v. 3.2, XML format)
Algorithms for detecting network motifs
The transcriptional network was represented as a connectivity matrix, M,
such that Mij = 1 if operon j encodes a transcription factor that
transcriptionally regulates operon i, and Mij = 0 otherwise.
DOR detection
Algorithm for detecting dense regions of interactions in the network used a
(non-metric) distance measure between operons k and j, based on the
number of transcription factors regulating both operons.
Generation of randomized networks
For a stringent comparison to randomized networks, networks were
generated with precisely the same number of operons, interactions,
transcription factors and number of incoming and outgoing edges for each
node as in the real E. coli network.
Mathematical model of network motif dynamics
Boolean kinetics and differential equations were used.
 Papers related to methodology

McAdams, H.H. & Arkin, A. Simulation of prokaryotic genetic circuits.

Ann..Rev.Biophys. Biomol. Struct. 27, 199–224 (1998).

McAdams, H.H. & Shapiro, L. Circuit simulation of genetic networks.

Science 269, 650–656 (1995).

Newman, M.E., Strogatz, S.H. & Watts, D.J. Random graphs with arbitrary
degree distributions and their applications. Phys. Rev. E 64, 026118 (2001).

Salgado, H. et al. RegulonDB (version 3.2): transcriptional regulation and

operon organization in Escherichia coli K-12. Nucl. Acids Res. 29, 72–74
(2001).

Duda, R.O. & Hart, P.E. Pattern Classification and Scene Analysis (Wiley, New
York, 1973).

Kannan, R., Tetali, P. & Vempala, S. Simple Markov-chain algorithms for

generating bipartite graphs and tournaments. Random Structures and
Algorithms 14, 293–308 (1999).
 LARGE NETWORKS

Construction & analysis of

functionally related pathways
using network theory
 Metabolic pathways – scales of description Amino acid
biosynthesis
pathways

Aromatic amino acid

biosynthesis pathway

Tryptophan
biosynthesis
pathway
 Biosynthesis of Aromatic Amino Acids
Erythrose 4-Phosphate
Negative
Phosphoenolpyruvate Feedback

Deoxy-h acid 7 phosphate

Dehydroquinic acid
Shikimic acid
Not in
Chorismic acid B. subtilis

Prephanic acid Anthranilic acid

Phenylpyruvic acid

Phenylalanine Tyrosine Tryptophan

Variation in regulation of the same pathway in different microorganisms

 Tryptophan biosynthesis pathway

Chorismate
Reaction Network Anthranilate synthase Enzyme network
R1 (EC:4.1.3.27)
C0 C1: Anthranilate
R1 Anthranilate phospho- EC:4.1.3.27
R2 ribosyltransferase (EC:2.4.2.18)
C1
C1 C2: N-(5-phospho-D-ribosyl)-anthranilate
R2 R3 Phosphoribosyl anthranilate EC:2.4.2.18
isomerase (EC:5.3.1.24)
C2
C2 C3: 1-(2-Carboxyphenylamino)-1-
deoxy-D-ribulose 5-phosphate EC:5.3.1.24
R3
Indole-3-glycerol-phosphate C3
C3 R4 synthase (EC:4.1.1.48)
EC:4.1.1.48
R4 C4: Indoleglycerol phosphate
C4
C4 R5 Tryptophan synthase alpha
R5 (EC:4.2.1.20a) EC: 4.2.1.20a
C5: Indole C5
C5 R6 Tryptophan synthase beta
EC: 4.2.1.20b
R6 (EC:4.2.1.20b)

Tryptophan
C6
Nodes: Metabolite Nodes: : Reaction
Edges:Reaction Edges: Metabolite
 Network parameters
• Degree: The number nodes connected to
Degree = 3
• Shortest path: The minimum number of nodes to
pass to reach another node
• Closeness centrality: It is the reciprocal of the
mean number of nodes to pass from one node to all
other nodes. It indicates how long it takes for
informa9on to pass from one node to another
• Betweenness centrality: The propor9on of
shortest paths passing from one node to another
that passes through a node. It shows how important
a node is in connec9ng other nodes
• Clustering coefficient: The propor9on of Clustering coeff = 2/3
connec9ons exis9ng between the neighbours of a
node. It shows how densely connected a network is
 AROMATIC AMINO ACID BIOSYNTHESIS - 4 parts
QA
NAD+
E4P ASPSA
NADH , H+
DAHP DHQ ADH
HPAP
PEP DKFP
H2O

PI

PI

NH3, NADH, H+

H2O, NAD+
H2O

Bacteria SHK Archaea

ATP

ADP
PRPP

SHKP
PP3

PEP
PI
PRAA AA
3PSME PHEN
PI CO2, H2O
CHA Asp
CPAD5P PHPYR 4HPP
CO2, H2O OA
Glu Glu
IGP AGN
AKG AKG
T3P1 H2O, CO2
Phe Tyr
INDOLE

Tetrahydr-
obiopterin

biopterin
Dihydro-
Serine

+ H2O
H2O

+ O2
145
Trp
 Aromatic
Amino Acid
Biosynthesis

+
Connected
pathways

Kyoto
Encyclopedia
of Genes and
Genomes

http://www.genome.jp/kegg/
Pathways connected to TTP in E. coli
ID Pathway Combined nodes
eco00020 Citrate cycle 43

eco00030 Pentose phosphate pathway 50

eco00230 Purine metabolism 109

eco00250 Alanine, aspartate and glutamate metabolism 51

eco00270 Cysteine and methionine metabolism 55

eco00480 Glutathione metabolism 41

eco00562 Inositol phosphate metabolism 26

eco00750 Vitamin B6 metabolism 39

eco00770 Pantothenate and CoA biosynthesis 44

eco00970 Aminoacyl-tRNA biosynthesis 35

eco01210 2-Oxocarboxylic acid metabolism 61

eco01230 Biosynthesis of amino acids 108

 Combined networks
TTP + Alanine,
aspartate &
glutamate
metabolism
Nodes - 51
Edges -323

TTP + Aminocycl-
tRNA biosynthesis
Nodes - 35
Edges - 72

Combined network
Nodes - 321
Edges -1479