J Biol Phys (2017) 43:315–318 DOI 10.1007/s10867-017-9445-8 ERRATUM
Erratum to: Computer model of unstirred layer and intracellular pH changes. Determinants of unstirred layer pH Roger Marrannes1
Published online: 20 March 2017 © Springer Science+Business Media Dordrecht 2017
Keywords Computer model · Unstirred layer pH · Intracellular pH · Proton transport · Buffer · Carbonic anhydrase · Disequilibrium pH · pH
Erratum to: J Biol Phys 39, 515–564 (2013) DOI 10.1007/s10867-013-9309-9 The author found an error in the computer program of the multicompartment model (J. Biol. Phys., 2013, 39:515–564). This error did not influence the flux clamp simulations of the extracellular unstirred layer and had thus no effect on Tables 1 to 5 and Figs. 1 to 10. However, this error, affecting the intracellular pH, had a small effect on the results of Figs. 11 and 12 and Table 6. After correction of the program, the simulations of Figs. 11 and 12 and Table 6 were repeated. The correct Figs. 11 and 12 and Table 6 are shown below. Note that the fluxes JHA , JCO2 and JHCO3 in Fig. 11 are expressed in the SI unit (mole m−2 s−1 ), whereas in its previous version they were expressed accidentally in the c.g.s. unit (mole cm−2 s−1 ). All equations and conclusions of the paper remain unchanged.
The online version of the original article can be found at http://10.1007/s10867-013-9309-9. Roger Marrannes
[email protected] 1
Kongostraat 135, 2300, Turnhout, Belgium
316
R. Marrannes 20 mM propionate
20 mM propionate
Catalysis
Catalysis
-3
20x10
-3
9x10
8
-
[ HCO3 ]
[A]
15 10 5
7 6 5
0 0
10
20
30
40
50
60
70
0
10
20
30
s
50
60
70
40
50
60
70
40
50
60
70
40
50
60
70
40
50
60
70
-3
1.1x10 1.0
-6
200x10
[ CO2 ]
150
[HA]
40 s
100 50
0.9 0.8 0.7
0 0
10
20
30
40
50
60
70
0
10
20
30
s
s
-6
4x10
-6
2.5x10 2.0 1.5 1.0 0.5 0.0
[ H2CO3 ]
3 jHA
2 1 0 -1 0
10
20
30
40
50
60
70
0
10
20
30
s
s 7.6
-6
3x10
7.4
jCO2
2 pH
1 0
7.2 7.0 6.8
-1
6.6 0
10
20
30
40
50
60
70
0
10
20
30 s
0 -10 -20 -30 -40
H2CO3 > CO2
jHCO3
-
s
-6
-50x10
0 -2 -4 -3
-6x10 0
10
20
30
40 s
50
60
70
0
10
20
30 s
Fig. 11 Transient changes after addition of an anion of a weak acid. The extracellular bulk solution was buffered with 5 mM bicarbonate at pH 6.8. 20 mM Cl− was replaced by 20 mM propionate (A) in the bulk solution, as indicated with a horizontal line. The unstirred layer was subdivided into 16 compartments. The Deh reaction was not catalyzed in the unstirred layer, except during a period indicated with the thick horizontal line, wherein the Deh reaction was catalyzed infinitely in compartment 16 (N ). The Deh reaction was infinitely catalyzed (in equilibrium) in the intracellular compartment. The graphs display the time course of [A], [HA], [HCO− 3 ], [CO2 ], [H2 CO3 ], pH, the fluxes jH A , jCO2 , jH CO3 and the rate of the Deh reaction in all compartments during the first 70 s of the simulation. The darker-grey color corresponds to a higher compartment number. The dashed curves represent the time course of the intracellular concentrations or pH, fluxes through the cell membrane or the time rate of the intracellular Deh reaction
Computer model of unstirred layer and intracellular...
317
20 mM propionate
7.0 pH
a
pH0 intracellular pH unstirred layer pH (pHN) steady state pHN with same transmembrane fluxes (pHNSF)
7.2
6.8 6.8
6.6
pH
pH
7.2 7.0 6.8
6.4
6.6 6.4 6.2
120
160
200
240
1920 1960 2000 2040
s
6.2 0
500
1000
s
1500
2000 s
2500
3000
7.6
b
pH0 intracellular pH unstirred layer pH (pH N) steady state pH N with same transmembrane fluxes (pH NSF)
7.4 7.2
3500
pH
7.0 6.8 7.6
6.6
6.8
6.4
6.6
7.2
pH
pH
7.4
7.0
6.2
6.8
6.2
6.0 120
6.0 0
500
6.4
160 200 s
1000
240
1500
1920 1960 2000 2040 s
2000 s
2500
3000
3500
Fig. 12 Interpretation of the unstirred layer pH transients. The extracellular bulk solution was buffered with 5 mM bicarbonate at pH 6.8. 20 mM Cl− was replaced by 20 mM propionate in the bulk solution during 1800 s, as indicated with a horizontal line. The unstirred layer was subdivided into 16 compartments. The graphs display the pH in the extracellular bulk compartment (pH0 , grey), the pH in compartment 16 close to the cell membrane (pHN , black curve) and the intracellular pH (dashed curve) as a function of time. The pH of compartments 1–15 is not displayed. The full circles represent the steady-state pHN , calculated with the multicompartment model in flux clamp mode with the same transmembrane fluxes and extracellular bulk concentrations as during the simulation at that time point. The insets display the same at a more expanded time scale and also the time course of the pH in all unstirred layer compartments. The same simulation parameters were used as in Fig. 11, see also Table 4. The intracellular Deh reaction was catalyzed infinitely. a The Deh reaction was catalyzed infinitely in compartment 16 (N), but not catalyzed in the other unstirred layer compartments. b The Deh reaction was not catalyzed in the unstirred layer
318
R. Marrannes
Table 6 Comparison of transient pHN maximum with steady state pHN with same transmembrane fluxes Case Time pH0 pHNmax pHNSF % diff. β
[HCO3− ]0 [TH B ]0 pKH B DH B/B
Catalysis Other
1
45.5 7.4
7.491
7.490
1.5 0.01 25
0
N
2
22.3 7.4
7.768
7.763
1.2 0.01 25
0
–
3
34.6 6.8
6.907
6.910
−2.0 0.01 25
0
N
4
18.2 6.8
7.165
7.150
3.9 0.01 25
0
–
5
37.4 6.8
7.184
7.174
2.6 0.01 5
0
all
6
37.4 6.8
7.184
7.174
2.6 0.01 5
0
N
7
20.3 6.8
7.572
7.501
9.2 0.01 5
0
–
8
39.3 6.8
7.128
7.174
−13.9 3.85 5
0
9
39.4 6.8
7.124
7.171
−14.6 0.01 5
15
6.12
1E-22
all
10
30.3 6.8
7.052
7.062
−3.8 0.01 5
15
6.12
1.25E-9
all
11
22.4 6.8
7.486
7.977
−71.6 3.85 5
0
12
26.3 6.8
7.272
7.397
−26.6 0.01 0
10
6.8
6.20E-10 all
13
23.5 6.8
7.181
7.213
−8.5 0.01 0
10
6.8
1.25E-9
14
48.5 6.8
7.308
7.470
−31.8 3.85 5
0
15
53.0 6.8
7.193
7.210
−4.4 0.01 0
10
all
– all – 6.8
6.20E-10 all
* *
Erratum to: Computer model of unstirred layer and intracellular pH changes. Determinants of unstirred layer pH Roger Marrannes1
Published online: 20 March 2017 © Springer Science+Business Media Dordrecht 2017
Keywords Computer model · Unstirred layer pH · Intracellular pH · Proton transport · Buffer · Carbonic anhydrase · Disequilibrium pH · pH
Erratum to: J Biol Phys 39, 515–564 (2013) DOI 10.1007/s10867-013-9309-9 The author found an error in the computer program of the multicompartment model (J. Biol. Phys., 2013, 39:515–564). This error did not influence the flux clamp simulations of the extracellular unstirred layer and had thus no effect on Tables 1 to 5 and Figs. 1 to 10. However, this error, affecting the intracellular pH, had a small effect on the results of Figs. 11 and 12 and Table 6. After correction of the program, the simulations of Figs. 11 and 12 and Table 6 were repeated. The correct Figs. 11 and 12 and Table 6 are shown below. Note that the fluxes JHA , JCO2 and JHCO3 in Fig. 11 are expressed in the SI unit (mole m−2 s−1 ), whereas in its previous version they were expressed accidentally in the c.g.s. unit (mole cm−2 s−1 ). All equations and conclusions of the paper remain unchanged.
The online version of the original article can be found at http://10.1007/s10867-013-9309-9. Roger Marrannes
[email protected] 1
Kongostraat 135, 2300, Turnhout, Belgium
316
R. Marrannes 20 mM propionate
20 mM propionate
Catalysis
Catalysis
-3
20x10
-3
9x10
8
-
[ HCO3 ]
[A]
15 10 5
7 6 5
0 0
10
20
30
40
50
60
70
0
10
20
30
s
50
60
70
40
50
60
70
40
50
60
70
40
50
60
70
40
50
60
70
-3
1.1x10 1.0
-6
200x10
[ CO2 ]
150
[HA]
40 s
100 50
0.9 0.8 0.7
0 0
10
20
30
40
50
60
70
0
10
20
30
s
s
-6
4x10
-6
2.5x10 2.0 1.5 1.0 0.5 0.0
[ H2CO3 ]
3 jHA
2 1 0 -1 0
10
20
30
40
50
60
70
0
10
20
30
s
s 7.6
-6
3x10
7.4
jCO2
2 pH
1 0
7.2 7.0 6.8
-1
6.6 0
10
20
30
40
50
60
70
0
10
20
30 s
0 -10 -20 -30 -40
H2CO3 > CO2
jHCO3
-
s
-6
-50x10
0 -2 -4 -3
-6x10 0
10
20
30
40 s
50
60
70
0
10
20
30 s
Fig. 11 Transient changes after addition of an anion of a weak acid. The extracellular bulk solution was buffered with 5 mM bicarbonate at pH 6.8. 20 mM Cl− was replaced by 20 mM propionate (A) in the bulk solution, as indicated with a horizontal line. The unstirred layer was subdivided into 16 compartments. The Deh reaction was not catalyzed in the unstirred layer, except during a period indicated with the thick horizontal line, wherein the Deh reaction was catalyzed infinitely in compartment 16 (N ). The Deh reaction was infinitely catalyzed (in equilibrium) in the intracellular compartment. The graphs display the time course of [A], [HA], [HCO− 3 ], [CO2 ], [H2 CO3 ], pH, the fluxes jH A , jCO2 , jH CO3 and the rate of the Deh reaction in all compartments during the first 70 s of the simulation. The darker-grey color corresponds to a higher compartment number. The dashed curves represent the time course of the intracellular concentrations or pH, fluxes through the cell membrane or the time rate of the intracellular Deh reaction
Computer model of unstirred layer and intracellular...
317
20 mM propionate
7.0 pH
a
pH0 intracellular pH unstirred layer pH (pHN) steady state pHN with same transmembrane fluxes (pHNSF)
7.2
6.8 6.8
6.6
pH
pH
7.2 7.0 6.8
6.4
6.6 6.4 6.2
120
160
200
240
1920 1960 2000 2040
s
6.2 0
500
1000
s
1500
2000 s
2500
3000
7.6
b
pH0 intracellular pH unstirred layer pH (pH N) steady state pH N with same transmembrane fluxes (pH NSF)
7.4 7.2
3500
pH
7.0 6.8 7.6
6.6
6.8
6.4
6.6
7.2
pH
pH
7.4
7.0
6.2
6.8
6.2
6.0 120
6.0 0
500
6.4
160 200 s
1000
240
1500
1920 1960 2000 2040 s
2000 s
2500
3000
3500
Fig. 12 Interpretation of the unstirred layer pH transients. The extracellular bulk solution was buffered with 5 mM bicarbonate at pH 6.8. 20 mM Cl− was replaced by 20 mM propionate in the bulk solution during 1800 s, as indicated with a horizontal line. The unstirred layer was subdivided into 16 compartments. The graphs display the pH in the extracellular bulk compartment (pH0 , grey), the pH in compartment 16 close to the cell membrane (pHN , black curve) and the intracellular pH (dashed curve) as a function of time. The pH of compartments 1–15 is not displayed. The full circles represent the steady-state pHN , calculated with the multicompartment model in flux clamp mode with the same transmembrane fluxes and extracellular bulk concentrations as during the simulation at that time point. The insets display the same at a more expanded time scale and also the time course of the pH in all unstirred layer compartments. The same simulation parameters were used as in Fig. 11, see also Table 4. The intracellular Deh reaction was catalyzed infinitely. a The Deh reaction was catalyzed infinitely in compartment 16 (N), but not catalyzed in the other unstirred layer compartments. b The Deh reaction was not catalyzed in the unstirred layer
318
R. Marrannes
Table 6 Comparison of transient pHN maximum with steady state pHN with same transmembrane fluxes Case Time pH0 pHNmax pHNSF % diff. β
[HCO3− ]0 [TH B ]0 pKH B DH B/B
Catalysis Other
1
45.5 7.4
7.491
7.490
1.5 0.01 25
0
N
2
22.3 7.4
7.768
7.763
1.2 0.01 25
0
–
3
34.6 6.8
6.907
6.910
−2.0 0.01 25
0
N
4
18.2 6.8
7.165
7.150
3.9 0.01 25
0
–
5
37.4 6.8
7.184
7.174
2.6 0.01 5
0
all
6
37.4 6.8
7.184
7.174
2.6 0.01 5
0
N
7
20.3 6.8
7.572
7.501
9.2 0.01 5
0
–
8
39.3 6.8
7.128
7.174
−13.9 3.85 5
0
9
39.4 6.8
7.124
7.171
−14.6 0.01 5
15
6.12
1E-22
all
10
30.3 6.8
7.052
7.062
−3.8 0.01 5
15
6.12
1.25E-9
all
11
22.4 6.8
7.486
7.977
−71.6 3.85 5
0
12
26.3 6.8
7.272
7.397
−26.6 0.01 0
10
6.8
6.20E-10 all
13
23.5 6.8
7.181
7.213
−8.5 0.01 0
10
6.8
1.25E-9
14
48.5 6.8
7.308
7.470
−31.8 3.85 5
0
15
53.0 6.8
7.193
7.210
−4.4 0.01 0
10
all
– all – 6.8
6.20E-10 all
* *
