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Supplementary material to Lovmar et al.:
Modelling the erythromycin mechanism and the
resistance caused by the L22(Δ82-84) mutation
To explain the mechanism of resistance caused by the ribosomal protein mutation
L22(Δ82-84), we combined our model for inhibition of protein synthesis by
erythromycin (Figure S1) with a model for transport over the cell membranes (Figure
S2). Parameter values for simulating the increase in cell mass after 4 hrs with
different erythromycin concentrations (Figure 5C and 5D) are presented in Table S1.
1. Inhibition of protein synthesis by erythromycin
The model for erythromycin inhibition of protein synthesis (Figure S1) is a modified
version of a previous model (Lovmar et al., 2006), used to successfully account for
resistance conferred by cis-acting peptides (Lovmar et al., 2006; Tenson et al., 1996;
Vimberg et al., 2004).
Figure S1. The model for binding and translation inhibition by
erythromycin. The seven states used to model the inhibition of protein synthesis
caused by erythromycin. A 50S subunit with (50SM) or without (50S)
erythromycin bound initiate with the rate k to form initiated 70S complexes (RM1)
or (R1) respectively. Elongation of the first few amino acids is made with rate k1
independently of erythromycin. However, if no erythromycin is bound (R2) the
ribosome continue elongation and becomes refractory to the drug (Re) with the
rate k2, and finally a new protein is produced and the 50S is recycled with a rate
k3. In contrast, if the elongating ribosome contains erythromycin (RM2) it is
stalled until either erythromycin dissociates with a rate kd or peptidyl-tRNA drops
off and the erythromycin containing 50S is recycled with a rate k4. Erythromycin
associate with a second order rate constant ka and dissociates with the rate
constant kd.
The model includes seven states of the large ribosomal subunit (Figure S1), which are
defined by the following system of differential equations:
1
d 50SM 
dt
d  R1 
 ka   M f   50S  k4  RM 2   k  kd     50SM  ,
 k  50S  kd   RM1    k1  ka  M f       R1  ,
dt
d R 2 
 k1   R1   kd   RM 2    k2  ka  M f       R 2  ,
dt
d R e 
 k 2   R 2    k3      R e  ,
dt
d  RM1 
 k  50SM   ka   M f    R1    k1  kd      RM1  ,
dt
d  RM 2 
 k1   RM1   ka   M f    R2    k4  k d      RM 2  ,
dt
[S1]
A 50S ribosomal subunit may be either bound [50SM] or not bound [50S] to
erythromycin. It may also be in complex with a 30S subunit thus forming a ribosome
ready to initiate translation, either bound [RM1] or not bound [R1] to erythromycin.
The ribosome may be translating the first few codons either bound [RM2], or not
bound, but still susceptible, to erythromycin, [R2]. Without erythromycin, the
ribosome continues in elongation and become temporarily immune to erythromycin
[Re].
The rate constant of association and spontaneous dissociation of the antibiotic is ka
and kd, respectively. Association of the ribosomal subunits occurs with rate constant k
and translation of the first few codons occurs with rate constant k1. The rate constant
for translating the codon that makes the ribosome temporarily immune for
erythromycin binding is k2. The rate constant for completing synthesis of the protein
and recycling the ribosomal subunits is k3, and the rate constant of peptidyl-tRNA
drop-off from erythromycin bound, stalled ribosome is k4. In addition, all
concentrations are diluted by the cell growth rate μ. The total concentration of 50S
subunits [50S0] is kept constant and new 50S subunits are thus synthesized by rate
μ∙[50S0] and the free concentration of 50S subunits varies according to
[50S] = [50S0] - [50SM] - [R1] - [R2] - [RM1] - [RM2] - [Re].
The system expands by exponential growth with the growth rate μ, which is
proportional to the concentration of elongating ribosomes [Re] as defined by
(Ehrenberg and Kurland, 1984)

ve  [R e ]
0
,
[S2]
where ve is the average elongation rate of an uninhibited ribosome and ρ0 is the
concentration of amino acids incorporated in proteins. The system was solved with
the parameters in Table S1 by Euler’s method (Heath, 1997) using MATLAB 6.5
(The MathWorks, Inc., Natick, Massachusetts, U.S.A.).
The accumulated increase in cell density (“growth yield”), is calculated by numerical
integration of the growth rates µ according to
Vt  Vt  dt  e  dt ,
[S3]
2
where dt is a small time-step and Vt-dt and Vt is the total “cell volume” prior and after
time-step dt, respectively. To allow comparisons between the simulated growth yields
and OD measurements from cell cultures we also need to estimate how the total
intracellular concentration [M0] (= [Mf] + [50SM] + [RM1] + [RM2]) changes with
different erythromycin concentrations in the surrounding media [Mext] as seen in the
next section.
2. Drug flows into and out from gram negative bacteria
The cell envelope of gram-negative bacteria consists of two membrane layers
separated by the periplasmic space (Figure S2). The drug concentration, [Mp], in the
periplasmic space obeys the following differential equation
d MP 
dt

AC
A1C1
AC
 Mext    M P   2 2  Mf    M P   1 pump  M P     M P 

Vp
Vp
Vp
Here A1 and A2 are the areas of the outer and inner membranes, respectively. C1 and
C2 are the permeability of the outer and inner membrane, respectively. Cpump is the
efflux pump efficiency per outer membrane area, VP is the periplasmic volume,
assumed to be much smaller than the cytoplasmic volume VC. [Mext] is the drug
concentration in the growth medium and [Mf] the free drug concentration in the
cytoplasm. With the definitions cI = A1C1 / VC, cII = A1C2 / VC and cI = A1Cpump / VC,
the steady state solution to the differential equation can be written:
[M p ] 
cI   M ext   cII   M f 
V
cI  cII  cIII  P  
VC
[S4]
Figure S2. The model for the flow of inhibitor over the cell membranes in a
gram negative cell. Erythromycin diffuses over the outer membrane with a
permeability constant cI and over the inner membrane with a permeability
constant cII. In addition, erythromycin is actively pumped out over the outer
membrane with a rate constant cIII by the AcrAB-TolC efflux pump system.
The change in the total erythromycin concentration of the cytoplasm, [M0]
(= [Mf] + [50SM] + [RM1] + [RM2]), can be written:
d  M0 
dt
 cII   M P    Mf      M0 
3
[S5]
Inserting Eq. S4 into Eq. S5 gives the differential equation that connects the total
cytoplasmic erythromycin concentration [M0] to the erythromycin concentration in
the growth media.
d  M0 
dt


 c M   c  M  
ext
II
f
  cII   M f      M 0 
 cII   I
 c  c  c  VP   
 I II III V

C


[S6]
This equation (Eq. S6) is added as the seventh differential equation that completes the
system of differential equations in Eq. S1 which was used to simulate the bacterial
growth yield (Eq. S3) at different erythromycin concentrations [Mext].
3. Masking of resistance mutations in pump deficient mutants
An interesting feature of the model is that it captures the effect of resistance masking
by pump deficient mutants, which we noticed in our cell culture experiments. To
understand why this masking phenomenon occurs we can reformulate Eq. S6 as
d  M0 
dt
 cI  Q   Mext   cII  1  Q    M f      M 0 
[S7]
where
Q
cII
[S8]
V
cI  cII  cIII  P  
VC
First, we note that Q ≈ 1 in a pump deficient mutant (cIII = 0) and Q→0 as the value of
is cIII increases. Secondly, we note in Eq. S7 that there are one positive and two
negative terms that modulate the total intracellular concentration of erythromycin
[M0]. While the inflow to the cytoplasm depends on the erythromycin concentration
in the media [Mext], the outflow could either depend on the free cytoplasmic
concentration [Mf], the total cytoplasmic concentration [M0] or a combination of the
two. Efficient pumps (Q << 1) give a smaller positive [Mext]-term, i.e. efflux pumps
give resistance, but they also maximize the negative [Mf]-term so that the outflow
depends solely on the free concentration of erythromycin. In contrast, the dilution
term, which depends on the total cytoplasmic concentration [M0], dominates the
outflow in a pump deficient mutant (Q ≈ 1).
Thus, although a ribosome mutation can alter the erythromycin binding constants and
thereby increase [Mf], this “resistance mutation” is masked in a pump deficient
mutant, because the erythromycin outflow from the cytoplasm is independent of [Mf]
but depends only on the total concentration [M0].
4
References
Antoun, A., Pavlov, M.Y., Lovmar, M. and Ehrenberg, M. (2006) How initiation
factors tune the rate of initiation of protein synthesis in bacteria. Embo J, 25,
2539-2550.
Bremer, H. and Dennis, P.P. (1996) Modulation of Chemical Composition and Other
Parameters of the Cell by Growth Rate. In Neidhardt, F.C. (ed.), Escherichia
coli and Salmonella : cellular and molecular biology. ASM Press,
Washington, Vol. 2, pp. 1553-1569.
Ehrenberg, M. and Kurland, C.G. (1984) Costs of accuracy determined by a maximal
growth rate constraint. Quarterly Reviews of Biophysics, 17, 45-82.
Heath, M.T. (1997) Scientific computing : an introductory survey. McGraw-Hill, New
York.
Lovmar, M., Nilsson, K., Vimberg, V., Tenson, T., Nervall, M. and Ehrenberg, M.
(2006) The Molecular Mechanism of Peptide-mediated Erythromycin
Resistance. Journal of Biological Chemistry, 281, 6742-6750.
Tenson, T., DeBlasio, A. and Mankin, A. (1996) A functional peptide encoded in the
Escherichia coli 23S rRNA. Proc Natl Acad Sci U S A, 93, 5641-5646.
Vimberg, V., Xiong, L., Bailey, M., Tenson, T. and Mankin, A. (2004) Peptidemediated macrolide resistance reveals possible specific interactions in the
nascent peptide exit tunnel. Mol Microbiol, 54, 376-385.
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Table S1. Definitions and values of used parameters in the macrolide model.
Model parameter
Value
Reference
k = effective translation initiation rate
1 s-1
(Antoun et al., 2006)
5 s-1
(Bremer and Dennis, 1996)
20 s-1
(Bremer and Dennis, 1996)
k1 = rate constant for translation of the first
codons when the ribosome is susceptible for the
antibiotic
k2 = rate constant for translation of the codon
rendering the ribosome temporarily immune to
erythromycin
k3 = rate constant for translation beyond the 0.03 s-1
(Bremer and Dennis, 1996)
first codons and translation termination
k4 = drop-off rate constant of peptidyl-tRNA 0.1 s-1
(Lovmar, unpublished results)
ka = association rate constant of erythromycin
Table 1
Present work
k d = dissociation rate constant of erythromycin Table 1
Present work
from a stalled ribosome
cI = rate constant for diffusion over the outer 5∙10-4 s-1
membrane
cII = rate constant for diffusion over the inner 0.1 s-1
membrane
0 s-1 (tolC¯),
cIII = rate constant of erythromycin pumping 0.01 s-1 (acrB¯)
over the outer membrane.
1 s-1 (wt pumps)
VP / VC = the volume of the periplasm divided
by the volume of the cytoplasm (approximated
to be constant)
0.1
ve = ribosome elongation rate
20 s-1
(Bremer and Dennis, 1996)
0
2M
(Bremer and Dennis, 1996)
4∙10-5 M
(Bremer and Dennis, 1996)
= concentration of amino acids in proteins
50Stot  = total concentration of 50S
 Mext  = concentration of erythromycin in the
growth medium
0.6∙10-6-500∙10-6 M
(Fig. 5)
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