This document discusses how intrinsic noise in biological systems can both help and hinder cellular processes. It summarizes that intrinsic noise arises from the small number of molecules involved in cellular reactions, causing stochasticity. While noise can cause unwanted variability, it can also be beneficial by creating phenotypic heterogeneity and allowing positive feedback mechanisms to diversify cellular responses. The document examines how cells regulate noise through feedback loops and synchronization, and how noise may drive oscillations in population-level models, suggesting it could operate cellular clocks.

1. Not All Quiet on the Biology Front
Somdeb Ghose
The Institute of Mathematical Sciences
Ronojoy Adhikari
The Institute of Mathematical Sciences
Soma Saha and Arti Dua
Indian Institute of Technology Madras

7. Not just an indecisive cat ...
"For it is simply a fact of observation that the
guiding principle in every cell is embodied in a
single atomic association existing only in one
copy (or sometimes two) and a fact of
observation that it results in producing events
which are paragons of orderliness [...] the
situation is unprecedented, it is unknown
anywhere else except in living matter."
Erwin Schrödinger
What is Life?
(Cambridge University Press, 1944)

8. Sources of noise
Extrinsic Intrinsic
Global effect Local effect
Random fluctuations in
environmental parameters
Temperature, pH
Fluctuations due to small
number of reacting molecules

9. Sources of noise
Extrinsic Intrinsic
Global effect Local effect
Random fluctuations in
environmental parameters
Temperature, pH
Fluctuations due to small
number of reacting molecules

10. Intrinsic noise
Cellular functions often involve chemical reactions between a small number
of molecules.
Inherent stochasticity
Reactions occur due to probabilistic collisions between randomly moving
molecules. Less the number of molecules, more is the randomness.
Discreteness
The numbers of molecular species increases or decreases by integer
amounts for each reaction event.

11. Intrinsic noise
Cellular functions often involve chemical reactions between a small number
of molecules.
Inherent stochasticity
Reactions occur due to probabilistic collisions between randomly moving
molecules. Less the number of molecules, more is the randomness.
Discreteness
The numbers of molecular species increases or decreases by integer
amounts for each reaction event.

12. Intrinsic noise
Cellular functions often involve chemical reactions between a small number
of molecules.
Inherent stochasticity
Reactions occur due to probabilistic collisions between randomly moving
molecules. Less the number of molecules, more is the randomness.
Discreteness
The numbers of molecular species increases or decreases by integer
amounts for each reaction event.

13. Stochastic gene expression
Gene expression
mRNADNA Protein
Transcription Translation

14. Stochastic gene expression
Gene expression
mRNADNA Protein
Transcription Translation
Noise

15. Stochastic gene expression
Gene expression
mRNADNA Protein
Transcription Translation
Noise

16. Phenotypic heterogeneity
Genotype
The full hereditary information of an organism, whether expressed or not.
Phenotype
The actual observed properties of an organism, including its morphology,
development, biophysical and biochemical characteristics, and behavioural
traits.
Wikipedia

17. Phenotypic heterogeneity
Elowitz et al, Science (2002)
No intrinsic noise

18. Phenotypic heterogeneity
Elowitz et al, Science (2002)
No intrinsic noise
With intrinsic noise

19. Phenotypic heterogeneity
Fingerprints of identical twins
Raser and O'Shea, Science (2005)

20. Phenotypic heterogeneity
Fingerprints of identical twins
Rainbow, on the right, and her
clone, Cc
Raser and O'Shea, Science (2005)

21. Twin roles of noise
Can be exploited for positive
gains
Nuisance Source of variability
Impediment to reliable
behaviour, requires regulation

22. Twin roles of noise
Can be exploited for positive
gains
Nuisance Source of variability
Impediment to reliable
behaviour, requires regulation

23. Adverse effects of noise
Development of embryos
Noise might prevent cells from cooperating and coordinating during embryo
development, causing mutations and thus disease in some individuals.
Ageing
Older cells show greater susceptibility to noise. For the heart, it may lead to
a gradual decrease in efficiency over time.
Bahar et al, Nature (2006)
Pearson, Nature (2008)

24. Adverse effects of noise
Development of embryos
Noise might prevent cells from cooperating and coordinating during embryo
development, causing mutations and thus disease in some individuals.
Ageing
Older cells show greater susceptibility to noise. For the heart, it may lead to
a gradual decrease in efficiency over time.
Bahar et al, Nature (2006)
Pearson, Nature (2008)

25. Regulation of noise
A simple negative feedback loop functions as a low-pass filter that attenuates
high-frequency noise, thus increasing stability.
Negative feedback
Gene expression control
Proteins called
transcription factors
either activate or
repress gene
expression
Becskei and Serrano, Nature (2000)

26. Regulation of noise
A simple negative feedback loop functions as a low-pass filter that attenuates
high-frequency noise, thus increasing stability.
Negative feedback
Gene expression control
Proteins called
transcription factors
either activate or
repress gene
expression
Becskei and Serrano, Nature (2000)

27. Biochemical timekeeping
At the level of the cell
Cells must know when to divide and die
If not, it could lead to cancer
At the level of the organism
They must adhere to the 24-hr circadian rhythm
If not, they run the risk of becoming a

28. Biochemical timekeeping
At the level of the cell
Cells must know when to divide and die
If not, it could lead to cancer
At the level of the organism
They must adhere to the 24-hr circadian rhythm
If not, they run the risk of becoming a grad student

29. Cellular clock
Repressilator
Toy model of cellular clock,
developed in E. coli
Produces oscillations in protein
concentration through a negative
feedback cycle.
TetR
λcI LacI
Elowitz and Leibler, Nature (2000)Elowitz and Leibler, Nature (2000)

30. Cellular clock
Repressilator
Toy model of cellular clock,
developed in E. coli
Produces oscillations in protein
concentration through a negative
feedback cycle.
Not robust to noise
TetR
λcI LacI
Elowitz and Leibler, Nature (2000)

31. Noise regulation and synchronization
Quorum Sensing
Individual repressilators are coupled via
exchange of signaling molecules called
autoinducers.
Garcia-Ojalvo et al, PNAS (2004)

32. Noise regulation and synchronization
Quorum Sensing
Individual repressilators are coupled via
exchange of signaling molecules called
autoinducers.
At sufficient bacterial concentration, all
repressilators get synchronized
Garcia-Ojalvo et al, PNAS (2004)

33. Noise regulation and synchronization
Quorum Sensing
Individual repressilators are coupled via
exchange of signaling molecules called
autoinducers.
At sufficient bacterial concentration, all
repressilators get synchronized
Garcia-Ojalvo et al, PNAS (2004) Danino et al, Nature (2010)

34. Exploitation of noise
Activation of a positive feedback loop allows the transcription factor ComK in
B. Subtilis to promote itself, resulting in higher competence (ability to take up
DNA from the environment for repair and development). The positive
feedback creates a bimodal population distribution, thus increasing survival
probability.
Lowering the noise decreases the fraction of population crossing the
competence threshold, and is thus counterproductive.
Thattai and van Oudenaarden, PNAS (2001)
Ozbudak et al, NatGenet (2002)
Raj and van Oudenaarden, Cell (2008)
Positive feedback

35. Bacterial persistence
E. coli bacteria before antibiotic
E. coli bacteria after antibiotic
Balaban et al, Science (2004)

36. Bacterial persistence
E. coli bacteria before antibiotic
E. coli bacteria after antibiotic
Balaban et al, Science (2004)

37. Eye of a fruitfly
Scattered pattern of
photoreceptors in the
developing retina of the fruitfly
Drosophila.
The random switching on and
off of the spineless gene
causes this distribution, where
some photoreceptors are
sensitive to blue light, while
others are sensitive to green
light.
Wernet et al, Nature (2006)

38. A quick refresher ...
Small number of molecules give rise to intrinsic noise
This in turn causes phenotypic heterogeneity, where clones or identical
twins have different physical characteristics
Transcriptional regulation and negative feedback loops control noise. Cellular
clocks band together to overcome noise using quorum sensing.
Phenotypic heterogeneity and population bimodality due to positive feedback
mechanisms allow organisms to survive or to see better

39. Enzyme kinetics
Enzymes are biochemical catalysts. Their job is to ensure that critical
biological processes such as metabolism run on time.

40. Enzyme kinetics
Enzymes are biochemical
catalysts. Their job is to
ensure that critical
biological processes such
as metabolism run on
time.
Mechanism
In the simplest model,
enzymes form complexes
with substrates, which
then dissociate into
products, thus
regenerating the enzyme
One enzymatic turnover

41. Deterministic mass action kinetics
Michaelis-Menten equation
Product formation rates are given, in the limit of
a very large number of molecules, by the classic
Michaelis-Menten (MM) rate equation

42. Deterministic mass action kinetics
Michaelis-Menten equation
Product formation rates are given, in the limit of
a very large number of molecules, by the classic
Michaelis-Menten (MM) rate equation
A Lineweaver-Burk plot of [E0
]/v
vs 1/[S] will be linear
Lineweaver and Burk, JAmChemSoc (1934)

43. Single enzyme kinetics
Stochastic turnovers form a renewal process, where successive intervals
are independent and identically distributed.
Xie and Lu, JBiolChem (1999)
Kou et al, JPhysChemB (2005)
English et al, NatChemBio (2006)
A reinterpreted MM equation holds
Here is the mean of the intervals
between turnovers. A plot of vs
1/[S] will again be linear.

44. Multiple enzyme kinetics
Master Equation Simulate using Doob-Gillespie
Monte Carlo algorithm
ka
= k1
[S]
Actual enzyme kinetics involves finite, but small, number of enzyme and
substrate molecules. Molecular noise thus dictates affairs
Saha, SG, Dua, Adhikari,
PhysRevLett (2011)

45. Nonrenewal process
Waiting times are not identically
distributed and are multiexponential
Saha, SG, Dua, Adhikari,
PhysRevLett (2011)

46. Breakdown of MM equation
Blue curve corresponds to
single enzyme, where MM
equation holds
Saha, SG, Dua, Adhikari,
PhysRevLett (2011)

47. Breakdown of MM equation
Blue curve corresponds to
single enzyme, where MM
equation holds
Red and green curves are for
multiple enzymes. Here MM
equation breaks down.
Saha, SG, Dua, Adhikari,
PhysRevLett (2011)

48. Anticorrelation and Regulation?
Waiting times are
anticorrelated. A longer interval
is likely to be followed by a
shorter one, and vice versa.
Anticorrelation reduces the
variance in the product
turnovers and creates a
regulatory effect, thus ensuring
a uniform turnover rate at
steady state.
Might be a possible mechanism
for ensuring robustness against
noise in gene expression.
Saha, SG, Dua, Adhikari,
PhysRevLett (2011)

49. Anticorrelation and Regulation?
Waiting times are
anticorrelated. A longer interval
is likely to be followed by a
shorter one, and vice versa.
Anticorrelation reduces the
variance in the product
turnovers and creates a
regulatory effect, thus ensuring
a uniform turnover rate at
steady state.
Might be a possible mechanism
for ensuring robustness against
noise in gene expression.
Saha, SG, Dua, Adhikari,
PhysRevLett (2011)

50. Anticorrelation and Regulation?
Waiting times are
anticorrelated. A longer interval
is likely to be followed by a
shorter one, and vice versa.
Anticorrelation reduces the
variance in the product
turnovers and creates a
regulatory effect, thus ensuring
a uniform turnover rate at
steady state.
Might be a possible mechanism
for ensuring robustness against
noise in gene expression.
Saha, SG, Dua, Adhikari,
PhysRevLett (2011)

51. Can noise drive cellular clocks?
Test system
We test the effects of intrinsic noise at the population level, using a model
of epidemic spreading
Our test system is closed to the outside.
It is inhabited by a small number of individuals to ensure sufficient noise
strength.

52. Can noise drive cellular clocks?
Test system
We test the effects of intrinsic noise at the population level, using a model
of epidemic spreading
Our test system is closed to the outside.
It is inhabited by a small number of individuals to ensure sufficient noise
strength.

53. Can noise drive cellular clocks?
Test system
We test the effects of intrinsic noise at the population level, using a model
of epidemic spreading
Our test system is closed to the outside.
It is inhabited by a small number of individuals to ensure sufficient noise
strength.

54. SIRS epidemic model

55. Deterministic analysis
System of ordinary differential equations
Has one endemic fixed point, which can
either be a stable focus (underdamped)
or a stable node (overdamped)
SG, Adhikari, PhysRevE (2010)

56. Deterministic analysis
System of ordinary differential equations
Has one endemic fixed point, which can
either be a stable focus (underdamped)
or a stable node (overdamped)
No sustained oscillations in the
deterministic case
SG, Adhikari, PhysRevE (2010)

57. Stochastic analysis
Master equation
Simulate using DGMC algorithm
SG, Adhikari, PhysRevE (2010)

58. Stochastic analysis
Master equation
Simulate using DGMC algorithm
Noise-induced sustained
oscillations in the stochastic
case
SG, Adhikari, PhysRevE (2010)

59. Regularity of oscillations
Regularity is maximum at intermediate noise value
Noise is essential for stable oscillations
SG, Adhikari, PhysRevE (2010)

60. Noise-operated cellular clocks?
Oscillations are generated due to noise instead of inspite of noise.
Noise-induced oscillations seen in a simple model, albeit at a
population-level one.
Possible applications at cellular level?

61. That's all, folks!
Thanks for listening to this noisy presentation!
Ronojoy Adhikari Arti Dua