Download Robustness

Robustness
in immune system modeling
and sepsis therapy
Rüdiger W. Brause
Introduction
Robustness, NOT evolvability or stability
for
 disturbances in ecosystems
 cell response to environmental or genetic change
 computer performance at input errors, disk failures,


network overload
resilience of a political institution during societal flux
viability of a technological product in wildly changing
markets
Robustness = aspect of structural stability
NiSIS Workshop, Mallorca 2006
R.Brause: Nature-inspired Robustness
sheet 2
Traditional Modelling
Modelling, e.g. modelling of biochemical pathways
Traditional time dynamic modeling
 fuzzy clustering stage
 dynamical interaction of the clusters by linear
differential equations based on the expression data
of selected genes

selection criterion: most simple network
But: after long evolutionary development, small genetic
mutations will not cause fatal changes any more.
NiSIS Workshop, Mallorca 2006
R.Brause: Nature-inspired Robustness
sheet 3
Example plasmid replication
Escherichia coli Col E1
plasmids = short DNA loops
• give resistance against toxics
and antibiotics
• replicated separately
• segregated on cell division
High plasmid replication:
longer bacteria replication time,
smaller fraction of population
No plasmid replication:
smaller fitness in the long run,
not in the short.
Modest plasmid replication regulation – how?
NiSIS Workshop, Mallorca 2006
R.Brause: Nature-inspired Robustness
sheet 4
Example: replication control pathways
Col E1 plasmid replication regulation loop
RNA I & RNA II & ROM
complex
Mean 38 copies for
binomial segregation
RNA I-modulator ROM
stable with
RNA I
&RNA II
Plasmid DNA
in unstable complex
Negative
feedback loop
Brendel, Perelson 1993
Prob plasmid free
cell = 7.3·10-12
Observed: much
higher !??
Plasmid DNA
in complex with short RNA II
Plasmid
DNA
Plasmid DNA
in complex with long RNA II
for replication
NiSIS Workshop, Mallorca 2006
R.Brause: Nature-inspired Robustness
sheet 5
Stochastic Petri net model
Col E1 plasmid replication
Goss, Peccoud 1999
Molecular interpretation of SPN terminology
SPN term
Place
Token
Marking
Transition
Input place
Output place
Weight function
To be enabled
To fire
Molecular interpretation
Molecular species
Molecule
Number of molecules
Reaction
Reactant
Product
Rate of reaction
For a reaction to be possible
For a reaction to occur
• Simulates the molecular motion
stochastically
• models timing of molecular reactions
NiSIS Workshop, Mallorca 2006
R.Brause: Nature-inspired Robustness
sheet 6
simulation results
COLE1 plasmid replication regulation loop
Adapts to mean value 19 per segregation
Variance enhancement: 2.3·10-8, factor 10,000!
bacterium: 3811 in 95% interval
NiSIS Workshop, Mallorca 2006
R.Brause: Nature-inspired Robustness
sheet 7
Simulation results
No ROM protein  double plasmids/bacterium
Kinetic parameters adapted for same plasmid mean like wild
type  bigger variance of mutant  2-6 fold plasmid loss !
No segregation variance assumed  variance is due to timing
NiSIS Workshop, Mallorca 2006
R.Brause: Nature-inspired Robustness
sheet 8
Sepsis and immune system
Infection and trauma: sepsis symptomes (fever, tachycardia, ..)
pro-inflammatory
time
anti-inflammatory
Problem SIRS, sept. shock
correction of overshooting reaction of immune system
Many factors involved (~80):



tumor necrose factor TNF-, interleucin IL-1, IL-6, IL-8
IL-4, IL-10, IL-11, IL-13, TGF-, IL-1 receptor antagonists,…
…….
NiSIS Workshop, Mallorca 2006
R.Brause: Nature-inspired Robustness
sheet 9
Immune system pathways
Suppression of single mediators, e.g. TNF, do not influence
SIRS  Existence of multiple redundant mediator pathways
Example: cluster state modelling of cellular immune response
Guthke, Thies, Möller 2003
MHC-II
STAT1
IL-1
NiSIS Workshop, Mallorca 2006
R.Brause: Nature-inspired Robustness
sheet 10
Simple sepsis model
Preferred modeling strategy: make it simple!
make clusters
choose clusters representatives
model state dynamics between representatives as simple as
possible
Example protein interaction map of pheromone cell response B
Steffe, Petti, Aach, D‘haeseleer, Church 2002
start
signal
protein
target
70 proteins, 354 pathways
NiSIS Workshop, Mallorca 2006
score > median
R.Brause: Nature-inspired Robustness
top 15
graph, node size =S path scores
sheet 11
State dynamic modeling: example
1) P'(t) ~ P
2) P'(t) ~ (Pmax–P)
3) P'(t) ~ –M×P
P athogen cells will be increased by cell splitting
4) M'(t) ~ M×P
The number of macrophages will grow when a “combat
indicator” is produced when they destroy the pathogen.
Therefore, they grow with the probability of macrophages and
pathogens at the same place
Macrophages die at constant rate
5) M'(t) ~ –M
A limit of resources exist with concentration Pmax =1.
P will also decrease by macrophages and pathogens at the
same place
6) M'(t) ~ M×D
There is a cell damage D which is caused by inflammation.
Like the pathogens, the macrophages grow with the
probability of being at the same place:
7) M'(t) ~ (1-M)
A limit of resources exist for macrophages
8) D'(t) ~ –D
The cell damage is repaired with a certain rate
9) D'(t) ~ h(M-q)
Additional damage is indicated by a sigmoid function h() of
the number of macrophages where q is a threshold
NiSIS Workshop, Mallorca 2006
R.Brause: Nature-inspired Robustness
sheet 12
Modeling by ODE
Setting up ordinary differential equations
P'(t) = 1P(1–P) – 2MP
1) +2) +3) i>0
M'(t) = –1M +M(1–M)(2P+ 3D) 4) +5)+6)+7) i>0
D'(t) = –1D + 2h((M–q)/3)
8) + 9)
i>0
Fitting parameter values to measurements
damage
macrophages
pathogen cells
NiSIS Workshop, Mallorca 2006
R.Brause: Nature-inspired Robustness
sheet 13
Range of parameters
Problem: determination of parameters by observations
Experience: long adaptation, 3 may also be negative
System becomes instable,
but instabilities also fulfil the requirements !
NiSIS Workshop, Mallorca 2006
R.Brause: Nature-inspired Robustness
sheet 14
Problems
Static approach:




Which genes (proteins) should be in one cluster?
How should the cluster number be chosen?
How should the score be designed?
Alternatives with small score difference: which one to choose?
Dynamic approach:
 How many variables (clusters should be chosen?
 What values for coupling coefficients should be chosen?
NiSIS Workshop, Mallorca 2006
R.Brause: Nature-inspired Robustness
sheet 15
Proposition: robustness constraint
Select robust pathway modeling
predict new signalling pathways compared to
literature
identify previously unknown members of
documented pathways
identify relevant groups of interacting proteins
Robustness Criteria

fault tolerance: random faults should not propagate and
impede essential system functions

inherent stability: no system deviation by noise or
random input, even by internal component change
NiSIS Workshop, Mallorca 2006
R.Brause: Nature-inspired Robustness
sheet 16
Nature inspired robustness
Nature inspired heuristics
 Parallel redundancy : different pathways with
same effect
 adaptive negative feedback
Nature inspired mathematical progress
• stability (qualitative aspect)
• sensitivity (quantitative aspect)
• redundancy (structural aspect)
of differential equations needed.
Complexity research: degrees of freedom, number of parameters !
NiSIS Workshop, Mallorca 2006
R.Brause: Nature-inspired Robustness
sheet 17