1. Stochastic Modelling of Survival of E. Coli
E U NIVERS
K I
IC
TÄ
R
VO N GUE
TM
exposed to Methyglyoxal Stress
AG DE BU
O
TT
R
O
G
Jens Karschau1,2,3,4, Camila de Almeida2,3, Morgiane Richard2,3, Samantha Miller2, Ian R. Booth2, Andreas Kremling1, Alessandro de Moura3
MAX−PLANCK−INSTITUT
1Max-Planck-Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany.
DYNAMIK KOMPLEXER
TECHNISCHER SYSTEME 2School of Medical Sciences, University of Aberdeen, Aberdeen, UK.
MAGDEBURG
3School Natural Sciences & Computing Sciences, University of Aberdeen, UK.
4Otto-von-Guericke-Universität Magdeburg, Germany.
1. Introduction 5 Experimental Results
Damage
1
log(surviving fraction) [-]
Increasing methylglyoxal (MG) concen- 5.1. Survival Assay
●
trations slow the growth of E. coli, and
●
.1
- - - - -
MJF335 (kdp , kup , kefB , kefC , gsh ) was ex-
●
for [MG]>0.3mM cells are killed [1].
● Repair enyzme
posed to MG stress. The number of surviving
It is known that MG attacks guanine
●
0.01
bases in the DNA [2]. We established cells was determined. The death rate (k=1/T) to
●
a model which assumes that the cell
●
MG exposure was determined according to
0 10 20 30
1
will die due to double-strand breaks. time [min]
●
 ⋅t 
. The rate was compared to power
T
S =e Fig. 4: Survival curves for MJF335 exposed to methylglyoxal.
Those strand breaks are caused by simul- (●) 0.3mM, (■) 0.5mM, (♦) 0.7mM, ( ) 0.9mM
●
Fig. 1: Creation of double-strand breaks
laws of the powers 1.5, 2 and 3 (see Fig. 5).
taneous initiation of repair of 2 opposed damaged bases. The relationship
●
log(normalized rate)
1
between the MG concentration and the survival time was investigated with a 2
=c
1 3
T
1
=c
10
stochastic and a deterministic model. Experimental results support those
T
findings. Furthermore the effect of habituation to MG was investigated.
2. Modelling assumptions 1 1.5
=c
T
Growth is inhibited for MG concentrations higher than 0.3mM
– 0
10
1
2 3 4
log(normalized concentration)
MG attacks guanine bases, which are assumed to be evenly distributed on
– Fig 5: The rates were taken from 3 independent experiments (+) ( ) ( ). The rates and the concentration were normalized by the
*
smallest value. Dotted lines show upper and lower boundary for scaling parameter 1.5 or 3.
the DNA
5.2. Habituation
Death is due to two closely opposed single-strand breaks forming a double-
–
When cells habituate, they increase their ability to repair; SOS-response. This is
●
strand break (L≈10bp). Breaks occur at the time of repair when
triggered by single-stranded DNA and inhibited by DNA damage. ne ≠const.
endonuclease cleaves the DNA ⋅n r
dne
=   
⋅n d⋅ne ⋅n  ⋅ne 7
r
ne n r n d

dt
The number of repair enzymes is assumed to be constant.
–
binding succesful repair enzyme removal
SOS response
There is no detoxification of MG.
–
0.7mM
4
0.7mM
x 10
4
3. Model structure 3.5 100
20
# of damaged bases
Damaged base
# of repair enzymes
Base bound to
# of damaged bases
Damage 3
# of repair enzymes
Binding
Normal (nd) repair enzyme (nr) 2.5 15
base 200
Repair enzyme 2
Methylglyoxal
(ne) 10
(M) 1.5
Ligation 1
5
Fig. 2: Block diagram of damage and repair processes.
0.5
A modified Gillespie algorithm [3] was used for the stochastic model.
● 0 0 0 0
0 50 100 150 0 50 100 150
time [min] time [min]
The following ODE system is used for an analytical investigation: Fig 7: ODE model with habituation (starting with 0mM at t=0). Fig 8: ODE model with habituation (starting with 0.1mM at t=0).
●
dn d dn r MJF335 was exposed to a 0.1mM methylglyoxal during preculture growth at an
●
=   1
⋅N⋅M ⋅nd⋅ne =⋅nd⋅ne ⋅n 2
dt   OD650=0.2. After 50 min the cells were exposed to 0.7mM methylglyoxal.
r
dt damage creation
binding binding succesful repair
1
= ne  n r 3
 
NE
log(Surviving fraction)
total number of enzymes free bound 0.1
4. Results 0.01
⋅N⋅M
⋅N
nd = 5
For the steady-state (Ne=const.): n r =  ⋅M 4 0.001
⋅N
●
⋅ N E ⋅M 
 0.001
⋅ln 2 0 10 20 30 40 50 60
2
T= 2 ⋅M 6
Then the survival time, T, results in: time [min]
●
 ⋅L⋅N Fig. 6: Survival curves for habituated vs. not habituated cells. MFJ335 was exposed to (●) 0.1mM methylglyoxal in preculture or
(♦) not. Then treated with 0.7mM methylglyoxal.
6. Conclusions
T follows a power law to the power of 2
There must be a minimum number of repair enzymes, so eq. (5) is positive.
●
Fittings of a stochastic simulation show the same result
The survival time follows a power law (Fig. 3 and Fig. 5) to the power of 2.
●
log(death rate (1/T)) [-]
1 Experiments show decreased killing for habituated cells.
-1 ●
2.13
10 =7.8e5⋅M
T
7. Future directions
Experimental investigation of the dynamics of double-stranded breaks
●
-2
10
Experimental monitoring enzyme level in vivo during expose to MG
●
Include effects on guanine rich regions in the stochastic model
●
Investigation of the change in steady-state conditions and modification of
●
-4 -3
10 10
equation (7) for the habituation model.
log(MG) [-]
Fig 3: (─) Fit of ( ) stochastic simulation.
[1] G. P. Ferguson et al, Methylglyoxal production in bacteria: suicide or survival?, Archives of Microbiology, 170:209-219, 1998
[2] P. J. Thornalley, Protecting the genome: defence against nucleotide glycation and emerging role of glyoxalase I overpression
More extensive results and analysis can be found in [4].
multidrug resistance in cancer chemotherapy, Biochemical Society Transactions, 31:1372-1377, 2003
[3] D. J. Wilkinson, Stochastic modelling for Systems Biology, CRC Press, 2006
[4] J. Karschau, Stochastic modelling of survival of E.coli exposed to methylglyoxal stress, Studienarbeit, September 2008