Supplementary information
Optimality in the zonation of ammonia detoxification in rodent liver
Martin Bartl1,2,3,§,, Michael Pfaff4,2,§, Ahmed Ghallab5,6,§, Dominik Driesch2, Sebastian
G. Henkel2, Jan G. Hengstler5, Stefan Schuster7, Christoph Kaleta8,1, Rolf Gebhardt9,
Sebastian Zellmer10,9,#* and Pu Li3,#
Supplementary Table 1:
Calculated numerical values of optimal zonation for enzyme activities of glutaminase
(eG), key enzyme carbamoyl phosphate synthetase (eCPS) and glutamine synthetase
(eGS), with a maximal relative activity of two. In addition the corresponding metabolite
concentrations of ammonia (cNH4), urea (cUREA) and glutamine (cGLN) are given in mM.
compartment
eG
input -
eCPS
eGS
-
-
cNH4
cUREA
cGLN
0.1707
0
0.4583
1
2
0
0
0.1913629
0
0.4313031
2
1.9908437
0.0091562
0
0.2090841
0.0001608
0.4075083
3
0.4031500
1.5968499
0
0.1844905
0.0233949
0.4033759
4
0
2
0
0.1563514
0.0464632
0.4033759
5
0
2
0
0.1334526
0.0647120
0.4033759
6
0
2
0
0.1148187
0.0791171
0.4033759
7
0
2
0
0.0996699
0.0904580
0.4033759
8
0
2
0
0.0873869
0.0993540
0.4033759
9
0
2
0
0.0774809
0.1062941
0.4033759
10
0
2
0
0.0695687
0.1116614
0.4033759
11
0
2
0
0.0633533
0.1157529
0.4033759
12
0
2
0
0.0586085
0.1187947
0.4033759
13
0
0
2
0.0259229
0.1187947
0.4347796
Supplementary Text S1: Sensitivity analysis of optimal zonation
For the sensitivity analysis a weighting factor α (correspondingly α=0.5 for the main
article) is introduced in the objective function with

min   c 2NH 4,Output  (1  )  (cGLN,Re g  cGLN,Output )2
e

(Eq. 1S)
and β is introduced for different maximum enzyme activity constraints
eGS, j  eG, j  eC, j  , j  1, ..., n
(Eq. 2S)
The corresponding optimal zonations were obtained by repeating the computation for
each studied value. The different weighting of the formulated physiological tasks
Bartl et al. Optimality in the zonation …
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resulted in moderate changes for the optimal zonation (cf. Supplementary Fig. 1S).
However, if α is chosen to 1 or 0 the zonation completely disappeared (not shown).
For different maximum enzyme activity constraints (cf. Supplementary Fig 2S) we
obtained a more sensitive zonation (compared to α) where the results of the main
article could be in principle obtained in the region of emax±25%. Furthermore, a
sensitivity analysis for ammonia concentrations in the blood flow is shown in
Supplementary Fig 3S).
Supplementary Figure 1S: Sensitivity analysis of optimal zonation for the
physiological tasks formulated in the objective function (3). Here the analysis is
based on introducing the weighting factor α (value are given in the center).
Supplementary Figure 2S: Sensitivity analysis of optimal zonation due to maximum
enzyme activity constraints (2). Here the analysis is based on introducing β for
different enzyme activity constraints emax (values are given in the center).
Supplementary Figure 3S: Sensitivity analysis of optimal zonation in the case of
ammonia detoxification. Here the analysis is based on different ammonia
concentrations in the blood inflow (values in mM were given in the center).
Supplementary Figure 4S: Optimal zonation in the case of repeated starvations.
Here the analysis is based on different glutamine concentrations in the blood inflow
to model repeated starvations (values in mM are given in the center). The model
predicts that the GS positive zone (pericentral) increases during starvation.
Supplementary Figure 5S: Predicted optimal zonation in the case of regeneration
after CCl4-intoxication with higher ammonia input concentrations (time series data
were taken from Schliess et al. (2014) with doubled ammonia input concentrations).
The obtained results were again mapped to two ideal hexagonal lobules, showing on
the left the enzyme activity distribution for Glnase, CPS and GS by equivalent areas
and on the right the corresponding metabolite concentrations for ammonia, urea and
glutamine. The time points (in days) after intoxication are given in the center.
Bartl et al. Optimality in the zonation …
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Supplementary Figure 6S: Optimal zonation for the refined model variant of a rat
liver lobule based on a previous model (Toepfer et al. 2007; Zellmer et al. 2007).
Input concentrations for glutamine, ammonia, urea and the glutamine regulation were
taken from Häussinger (1983). The obtained results were mapped to an ideal
hexagonal lobule for the reason of intuitive understanding of computed tissue
properties (assuming 16 hepatocytes in average from the periportal to the pericentral
region). The portal veins correspond idealized to 3 edges of the hexagonal lobule
while the central vein is located in the center. (A) The obtained enzyme activity
distribution along the liver lobule for glutaminase (G), carbamoyl phosphate
synthetase (CPS) and glutamine synthetase (GS). The fractions of enzyme activities
are illustrated with the equivalent area in each hexagon. (B) The corresponding
metabolite concentrations along the liver lobule for glutamine, ammonia and urea.
References
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ammonia detoxification during liver damage and regeneration. Hepatology 60(6):2040-2051
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Zellmer S, Toepfer S, Driesch D, et al. Modelling of hepatic glutamine metabolism. In: Allgöwer F, Reuss M
(eds) Proc 2nd Conference Foundations of Systems Biology in Engineering, Stuttgart, Germany, 9 – 12
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