2504:
1023:
43:
588:
2269:
657:
1298:
1973:
3072:
232:
2499:{\displaystyle {\begin{aligned}E_{X}&\approx {\frac {0.0267\ \mathrm {V} }{z}}\ln {\frac {X_{o}}{X_{i}}}\\&={\frac {26.7\ \mathrm {mV} }{z}}\ln {\frac {X_{o}}{X_{i}}}\\&\approx {\frac {61.5\ \mathrm {mV} }{z}}\log {\frac {X_{o}}{X_{i}}}&{\text{ since }}\ln 10\approx 2.303\end{aligned}}}
1018:{\displaystyle E_{m,\mathrm {K} _{x}\mathrm {\text{Na}} _{1-x}\mathrm {Cl} }={\frac {RT}{F}}\ln {\left({\frac {P_{\text{Na}}_{\mathrm {out} }+P_{\text{K}}_{\mathrm {out} }+P_{\text{Cl}}_{\mathrm {in} }}{P_{\text{Na}}_{\mathrm {in} }+P_{\text{K}}_{\mathrm {in} }+P_{\text{Cl}}_{\mathrm {out} }}}\right)}}
3283:
Current density has units of (Amperes/m). Molar flux has units of (mol/(s m)). Thus, to get current density from molar flux one needs to multiply by
Faraday's constant F (Coulombs/mol). F will then cancel from the equation below. Since the valence has already been accounted for above, the charge
3879:
3690:
1978:
The ionic charge determines the sign of the membrane potential contribution. During an action potential, although the membrane potential changes about 100mV, the concentrations of ions inside and outside the cell do not change significantly. They are always very close to their respective
1038:
2765:
1746:
3291:
There is such a current associated with every type of ion that can cross the membrane; this is because each type of ion would require a distinct membrane potential to balance diffusion, but there can only be one membrane potential. By assumption, at the
Goldman voltage
2904:
2120:
583:{\displaystyle E_{m}={\frac {RT}{F}}\ln {\left({\frac {\sum _{i}^{n}P_{M_{i}^{+}}_{\mathrm {out} }+\sum _{j}^{m}P_{A_{j}^{-}}_{\mathrm {in} }}{\sum _{i}^{n}P_{M_{i}^{+}}_{\mathrm {in} }+\sum _{j}^{m}P_{A_{j}^{-}}_{\mathrm {out} }}}\right)}}
3373:, not considered here which serve to balance each individual ion's current, so that the ion concentrations on either side of the membrane do not change over time in equilibrium.) If all the ions are monovalent—that is, if all the
2046:
3698:
3509:
1293:{\displaystyle E_{m,{\text{Na}}}={\frac {RT}{F}}\ln {\left({\frac {P_{\text{Na}}_{\mathrm {out} }}{P_{\text{Na}}_{\mathrm {in} }}}\right)}={\frac {RT}{F}}\ln {\left({\frac {_{\mathrm {out} }}{_{\mathrm {in} }}}\right)}}
1738:
2621:
2258:
649:
3192:
2175:
1968:{\displaystyle E_{X}=61.5\,\mathrm {mV} \cdot \log {\left({\frac {_{\mathrm {out} }}{_{\mathrm {in} }}}\right)}=-61.5\,\mathrm {mV} \cdot \log {\left({\frac {_{\mathrm {out} }}{_{\mathrm {in} }}}\right)}}
3498:
3278:
2274:
1688:
3128:
3364:
1377:
1428:
3067:{\displaystyle j_{\mathrm {A} }=\mu n_{\mathrm {A} }P_{\mathrm {A} }{\frac {\left_{\mathrm {out} }-\left_{\mathrm {in} }e^{n_{\mathrm {A} }\mu }}{1-e^{n_{\mathrm {A} }\mu }}}}
1484:
1597:
17:
3423:
1599:
is approximately 26.7 mV at human body temperature (37 °C); when factoring in the change-of-base formula between the natural logarithm, ln, and logarithm with base 10
2051:
1328:
2577:
According to
Goldman's model, only two factors influence the motion of ions across a permeable membrane: the average electric field and the difference in ionic
1558:
1536:
1506:
224:
200:
1990:
3874:{\displaystyle v=\sum _{\mathrm {cations\ C} }P_{\mathrm {C} }\left_{\mathrm {in} }+\sum _{\mathrm {anions\ A} }P_{\mathrm {A} }\left_{\mathrm {out} }}
3685:{\displaystyle w=\sum _{\mathrm {cations\ C} }P_{\mathrm {C} }\left_{\mathrm {out} }+\sum _{\mathrm {anions\ A} }P_{\mathrm {A} }\left_{\mathrm {in} }}
2797:
due to the electric field, which increases linearly with the electric field; Formally, it is multiplied by the drift velocity of the ions, with the
2581:
from one side of the membrane to the other. The electric field is assumed to be constant across the membrane, so that it can be set equal to
2760:{\displaystyle j_{\mathrm {A} }=-D_{\mathrm {A} }\left({\frac {d\left}{dz}}-{\frac {n_{\mathrm {A} }F}{RT}}{\frac {E_{m}}{L}}\left\right)}
1693:
31:
2183:
596:
3146:
2125:
3434:
107:
4203:
The membrane voltage is calculated interactively as the number of ions are changed between the inside and outside of the cell.
4186:
4121:
4072:
4030:
3988:
79:
3229:
86:
4226:
2802:
3288:
of each ion in the equation above, therefore, should be interpreted as +1 or -1 depending on the polarity of the ion.
4159:
126:
60:
93:
3369:(Although the current for each ion type considered here is nonzero, there are other pumps in the membrane, e.g.
1602:
3083:
2855:
64:
3307:
75:
2615:—in other words, the number of ions crossing per time and per area of the membrane—is given by the formula
4221:
2534:
4195:
4101:
4052:
4010:
3968:
1347:
2771:
1384:
155:
across a cell's membrane, taking into account all of the ions that are permeant through that membrane.
1443:
1570:
3933:
3928:
3386:
2115:{\displaystyle F\approx {\frac {9.6\times 10^{4}\ \mathrm {J} }{\mathrm {mol} \cdot \mathrm {V} }}}
53:
3967:
Enderle, John (2005-01-01), Enderle, John D.; Blanchard, Susan M.; Bronzino, Joseph D. (eds.),
3938:
2541:
direction being perpendicular to the membrane. Assuming that the system is symmetrical in the
2177:
and the fact that one volt is equal to one joule of energy per coulomb of charge, the equation
100:
4151:
4144:
3948:
3923:
1306:
8:
2813:
163:
4206:
4113:
4064:
3980:
2790:
1543:
1521:
1509:
1491:
209:
185:
167:
2041:{\displaystyle R\approx {\frac {8.3\ \mathrm {J} }{\mathrm {K} \cdot \mathrm {mol} }}}
4155:
4117:
4068:
4026:
4022:
3984:
3901:
152:
4183:
4109:
4108:, Woodhead Publishing Series in Biomaterials, Woodhead Publishing, pp. 13–43,
4060:
4018:
3976:
3893:
3198:
1561:
159:
4190:
3943:
3201:
2810:
2806:
2510:
1029:
3913:
2841:
2798:
2571:
4215:
4051:
Enderle, John D. (2012-01-01), Enderle, John D.; Bronzino, Joseph D. (eds.),
4011:"Chapter 2 – Mechanisms of Ion Transport Across Cell Membranes and Epithelia"
3900:; in this case, the formula for the Goldman equation can be solved using the
2779:
2578:
4200:
3918:
2834:
171:
2598:
is the thickness of the membrane. For a given ion denoted A with valence
4180:
Includes a well-explained derivation of the
Goldman-Hodgkin-Katz equation
2823:
1431:
4150:(2nd ed.). Sunderland, Massachusetts: Sinauer Associates. pp.
1486:= the intracellular concentration of that ion (in moles per cubic meter)
4009:
Reuss, Luis (2008-01-01), Alpern, Robert J.; Hebert, Steven C. (eds.),
593:
This results in the following if we consider a membrane separating two
148:
4207:
Potential, Impedance, and
Rectification in Membranes by Goldman (1943)
3370:
2775:
4059:, Biomedical Engineering, Boston: Academic Press, pp. 747–815,
3975:, Biomedical Engineering, Boston: Academic Press, pp. 627–691,
42:
4177:
2848:
2563:
2822:
of the ion A (e.g., +1 for K, +2 for Ca and −1 for Cl), the
1733:{\displaystyle 26.7\,\mathrm {mV} \cdot 2.303=61.5\,\mathrm {mV} }
3885:
2522:
1339:
2253:{\displaystyle E_{X}={\frac {RT}{zF}}\ln {\frac {X_{o}}{X_{i}}}}
1979:
concentrations when the membrane is at their resting potential.
644:{\displaystyle \mathrm {K} _{x}\mathrm {Na} _{1-x}\mathrm {Cl} }
27:
Generalization of the Nernst equation for the membrane potential
2830:
2549:
directions (around and along the axon, respectively), only the
1513:
3187:{\displaystyle P_{\mathrm {A} }={\frac {D_{\mathrm {A} }}{L}}}
2782:
gradient, i.e., from high to low concentration. The constant
2170:{\displaystyle T=37\ ^{\circ }\mathrm {C} =310\ \mathrm {K} }
1335:
3493:{\displaystyle {\frac {FE_{m}}{RT}}=\mu =\ln {\frac {w}{v}}}
2794:
2606:
1331:
203:
4102:"2 - Physiological principles of electrical stimulation"
3973:
Introduction to
Biomedical Engineering (Second Edition)
1435:
4057:
Introduction to
Biomedical Engineering (Third Edition)
3273:{\displaystyle J_{A}=q_{\mathrm {A} }j_{\mathrm {A} }}
4100:
Bhadra, Narendra (2015-01-01), Kilgore, Kevin (ed.),
3701:
3512:
3437:
3389:
3310:
3232:
3149:
3086:
2907:
2624:
2272:
2186:
2128:
2054:
1993:
1749:
1696:
1605:
1573:
1546:
1524:
1494:
1446:
1387:
1379:= the selectivity for that ion (in meters per second)
1350:
1309:
1041:
660:
599:
235:
212:
188:
3380:equal either +1 or -1—this equation can be written
67:. Unsourced material may be challenged and removed.
4143:
4106:Implantable Neuroprostheses for Restoring Function
3873:
3684:
3492:
3417:
3358:
3272:
3186:
3122:
3066:
2759:
2498:
2252:
2169:
2114:
2040:
1967:
1732:
1682:
1591:
1552:
1530:
1500:
1478:
1430:= the extracellular concentration of that ion (in
1422:
1371:
1322:
1292:
1017:
643:
582:
218:
194:
4015:Seldin and Giebisch's The Kidney (Fourth Edition)
4213:
2553:direction need be considered; thus, the voltage
177:
4017:, San Diego: Academic Press, pp. 35–56,
1982:
1032:-like" but has a term for each permeant ion:
2793:of the ion A. The second term reflects the
3140:is the ionic permeability, defined here as
2521:Goldman's equation seeks to determine the
1683:{\displaystyle (^{-1}=\ln(10)=2.30258...)}
3123:{\displaystyle \mu ={\frac {FE_{m}}{RT}}}
2847:, which is the total charge of a mole of
2537:is used to describe the system, with the
1870:
1766:
1721:
1700:
127:Learn how and when to remove this message
4196:Goldman-Hodgkin-Katz Equation Calculator
3359:{\displaystyle J_{tot}=\sum _{A}J_{A}=0}
4141:
4050:
3966:
3428:whose solution is the Goldman equation
14:
4214:
4201:Nernst/Goldman interactive Java applet
4099:
1740:, a value often used in neuroscience.
4008:
1434:per cubic meter, to match the other
141:Goldman–Hodgkin–Katz voltage equation
18:Goldman–Hodgkin–Katz voltage equation
4095:
4093:
4091:
4089:
4053:"Chapter 12 – Bioelectric Phenomena"
3301:, the total current density is zero
65:adding citations to reliable sources
36:
2886:with the boundary conditions (0) =
166:, and the Medicine Nobel laureates
24:
4114:10.1016/b978-1-78242-101-6.00002-1
4065:10.1016/b978-0-12-374979-6.00012-5
3981:10.1016/b978-0-12-238662-6.50013-6
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3531:
3528:
3525:
3264:
3252:
3217:of the ion multiplied by the flux
3173:
3156:
3077:where ÎĽ is a dimensionless number
3050:
3020:
3003:
3000:
2990:
2975:
2972:
2969:
2959:
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2914:
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2017:
2010:
1951:
1948:
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1814:
1811:
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1702:
1470:
1467:
1457:
1454:
1451:
1414:
1411:
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1398:
1395:
1392:
1372:{\displaystyle P_{\mathrm {ion} }}
1363:
1360:
1357:
1276:
1273:
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1168:
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1126:
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870:
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827:
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775:
706:
703:
674:
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614:
602:
566:
563:
560:
490:
487:
418:
415:
345:
342:
339:
32:Goldman–Hodgkin–Katz flux equation
25:
4238:
4184:Nernst/Goldman Equation Simulator
4171:
4086:
1423:{\displaystyle _{\mathrm {out} }}
4023:10.1016/b978-012088488-9.50005-x
1479:{\displaystyle _{\mathrm {in} }}
41:
4178:Subthreshold membrane phenomena
1592:{\displaystyle {\frac {RT}{F}}}
52:needs additional citations for
4135:
4044:
4002:
3960:
3888:are considered, terms such as
2874:; integrating both sides from
2774:, which gives the flux due to
2770:The first term corresponds to
2122:, (assuming body temperature)
1943:
1929:
1910:
1896:
1839:
1825:
1806:
1792:
1677:
1668:
1662:
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1637:
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1462:
1447:
1403:
1388:
1268:
1252:
1233:
1217:
1163:
1147:
1118:
1102:
990:
974:
947:
931:
904:
888:
862:
846:
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800:
770:
754:
555:
536:
482:
463:
410:
391:
334:
315:
13:
1:
3954:
3418:{\displaystyle w-ve^{\mu }=0}
2809:. The constants here are the
2516:
1330:= the membrane potential (in
182:The GHK voltage equation for
1538:= the temperature in kelvins
178:Equation for monovalent ions
158:The discoverers of this are
7:
4146:Nerve and Muscle Excitation
3907:
2535:Cartesian coordinate system
147:, is used in cell membrane
10:
4243:
1983:Calculating the first term
29:
4227:Electrochemical equations
3884:If divalent ions such as
2898:, one gets the solution
2807:electrophoretic mobility
2803:Stokes–Einstein relation
30:Not to be confused with
3969:"Bioelectric Phenomena"
2772:Fick's law of diffusion
143:, sometimes called the
3875:
3686:
3494:
3419:
3360:
3274:
3188:
3124:
3068:
2854:This is a first-order
2761:
2533:across a membrane. A
2500:
2254:
2171:
2116:
2042:
1969:
1734:
1684:
1593:
1554:
1532:
1502:
1480:
1424:
1373:
1324:
1294:
1019:
645:
584:
513:
440:
368:
292:
220:
196:
3892:appear, which is the
3876:
3687:
3495:
3420:
3361:
3275:
3189:
3125:
3069:
2762:
2574:across the membrane.
2501:
2255:
2172:
2117:
2043:
1970:
1735:
1685:
1594:
1555:
1533:
1503:
1481:
1425:
1374:
1325:
1323:{\displaystyle E_{m}}
1295:
1020:
646:
585:
499:
426:
354:
278:
221:
197:
3949:Saltatory conduction
3934:Hodgkin–Huxley model
3929:Hindmarsh–Rose model
3924:GHK current equation
3699:
3510:
3435:
3387:
3308:
3230:
3147:
3084:
2905:
2801:expressed using the
2622:
2270:
2184:
2126:
2052:
1991:
1747:
1694:
1603:
1571:
1544:
1522:
1492:
1444:
1385:
1348:
1307:
1039:
658:
597:
233:
210:
202:monovalent positive
186:
61:improve this article
1564:(coulombs per mole)
553:
533:
480:
460:
408:
388:
332:
312:
164:Columbia University
4222:Physical chemistry
4189:2010-08-08 at the
3939:Morris–Lecar model
3871:
3823:
3743:
3682:
3637:
3554:
3490:
3415:
3356:
3339:
3270:
3210:equals the charge
3184:
3120:
3064:
2791:diffusion constant
2757:
2496:
2494:
2263:can be reduced to
2250:
2167:
2112:
2038:
1965:
1730:
1680:
1589:
1562:Faraday's constant
1550:
1528:
1510:ideal gas constant
1498:
1476:
1420:
1369:
1320:
1290:
1015:
641:
580:
539:
519:
466:
446:
394:
374:
318:
298:
216:
192:
168:Alan Lloyd Hodgkin
76:"Goldman equation"
4123:978-1-78242-101-6
4074:978-0-12-374979-6
4032:978-0-12-088488-9
3990:978-0-12-238662-6
3902:quadratic formula
3817:
3791:
3737:
3708:
3631:
3605:
3548:
3519:
3488:
3463:
3330:
3182:
3118:
3062:
2737:
2720:
2688:
2570:component of the
2475:
2474: since
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2438:
2425:
2405:
2375:
2362:
2342:
2312:
2302:
2248:
2218:
2161:
2141:
2110:
2082:
2036:
2008:
1958:
1854:
1587:
1553:{\displaystyle F}
1531:{\displaystyle T}
1501:{\displaystyle R}
1283:
1259:
1224:
1201:
1178:
1154:
1144:
1109:
1099:
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1008:
981:
971:
938:
928:
895:
885:
853:
843:
807:
797:
761:
751:
728:
688:
573:
262:
219:{\displaystyle A}
195:{\displaystyle M}
153:Resting potential
151:to determine the
137:
136:
129:
111:
16:(Redirected from
4234:
4166:
4165:
4149:
4142:Junge D (1981).
4139:
4133:
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4130:
4097:
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3255:
3242:
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3199:electric current
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2256:
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2236:
2227:
2219:
2217:
2209:
2201:
2196:
2195:
2176:
2174:
2173:
2168:
2166:
2159:
2152:
2147:
2146:
2139:
2121:
2119:
2118:
2113:
2111:
2109:
2108:
2100:
2088:
2087:
2080:
2079:
2078:
2062:
2047:
2045:
2044:
2039:
2037:
2035:
2034:
2020:
2014:
2013:
2006:
2001:
1974:
1972:
1971:
1966:
1964:
1963:
1959:
1957:
1956:
1955:
1954:
1941:
1940:
1927:
1926:
1925:
1924:
1908:
1907:
1894:
1878:
1860:
1859:
1855:
1853:
1852:
1851:
1850:
1837:
1836:
1823:
1822:
1821:
1820:
1804:
1803:
1790:
1774:
1759:
1758:
1739:
1737:
1736:
1731:
1729:
1708:
1689:
1687:
1686:
1681:
1652:
1651:
1621:
1620:
1598:
1596:
1595:
1590:
1588:
1583:
1575:
1559:
1557:
1556:
1551:
1537:
1535:
1534:
1529:
1507:
1505:
1504:
1499:
1485:
1483:
1482:
1477:
1475:
1474:
1473:
1460:
1429:
1427:
1426:
1421:
1419:
1418:
1417:
1401:
1378:
1376:
1375:
1370:
1368:
1367:
1366:
1334:, equivalent to
1329:
1327:
1326:
1321:
1319:
1318:
1299:
1297:
1296:
1291:
1289:
1288:
1284:
1282:
1281:
1280:
1279:
1266:
1265:
1260:
1257:
1250:
1249:
1248:
1247:
1231:
1230:
1225:
1222:
1215:
1202:
1197:
1189:
1184:
1183:
1179:
1177:
1176:
1175:
1174:
1161:
1160:
1155:
1152:
1146:
1145:
1142:
1135:
1134:
1133:
1132:
1116:
1115:
1110:
1107:
1101:
1100:
1097:
1090:
1077:
1072:
1064:
1059:
1058:
1057:
1054:
1024:
1022:
1021:
1016:
1014:
1013:
1009:
1007:
1006:
1005:
1004:
988:
987:
982:
979:
973:
972:
969:
960:
959:
958:
945:
944:
939:
936:
930:
929:
926:
917:
916:
915:
902:
901:
896:
893:
887:
886:
883:
876:
875:
874:
873:
860:
859:
854:
851:
845:
844:
841:
832:
831:
830:
814:
813:
808:
805:
799:
798:
795:
786:
785:
784:
768:
767:
762:
759:
753:
752:
749:
742:
729:
724:
716:
711:
710:
709:
701:
700:
689:
686:
683:
682:
677:
650:
648:
647:
642:
640:
632:
631:
620:
611:
610:
605:
589:
587:
586:
581:
579:
578:
574:
572:
571:
570:
569:
552:
547:
535:
534:
532:
527:
512:
507:
495:
494:
493:
479:
474:
462:
461:
459:
454:
439:
434:
424:
423:
422:
421:
407:
402:
390:
389:
387:
382:
367:
362:
350:
349:
348:
331:
326:
314:
313:
311:
306:
291:
286:
276:
263:
258:
250:
245:
244:
225:
223:
222:
217:
201:
199:
198:
193:
160:David E. Goldman
145:Goldman equation
132:
125:
121:
118:
112:
110:
69:
45:
37:
21:
4242:
4241:
4237:
4236:
4235:
4233:
4232:
4231:
4212:
4211:
4191:Wayback Machine
4174:
4169:
4162:
4140:
4136:
4128:
4126:
4124:
4098:
4087:
4079:
4077:
4075:
4049:
4045:
4037:
4035:
4033:
4007:
4003:
3995:
3993:
3991:
3965:
3961:
3957:
3944:Nernst equation
3910:
3858:
3857:
3847:
3842:
3841:
3837:
3836:
3829:
3828:
3824:
3796:
3795:
3778:
3777:
3767:
3762:
3761:
3757:
3756:
3749:
3748:
3744:
3713:
3712:
3700:
3697:
3696:
3672:
3671:
3661:
3656:
3655:
3651:
3650:
3643:
3642:
3638:
3610:
3609:
3589:
3588:
3578:
3573:
3572:
3568:
3567:
3560:
3559:
3555:
3524:
3523:
3511:
3508:
3507:
3480:
3455:
3448:
3444:
3440:
3438:
3436:
3433:
3432:
3403:
3399:
3388:
3385:
3384:
3379:
3344:
3340:
3334:
3315:
3311:
3309:
3306:
3305:
3300:
3287:
3263:
3262:
3258:
3251:
3250:
3246:
3237:
3233:
3231:
3228:
3227:
3223:
3216:
3209:
3172:
3171:
3167:
3165:
3155:
3154:
3150:
3148:
3145:
3144:
3139:
3110:
3103:
3099:
3095:
3093:
3085:
3082:
3081:
3049:
3048:
3044:
3043:
3039:
3032:
3019:
3018:
3014:
3013:
3009:
2999:
2998:
2989:
2985:
2984:
2968:
2967:
2958:
2954:
2953:
2952:
2950:
2943:
2942:
2938:
2931:
2930:
2926:
2913:
2912:
2908:
2906:
2903:
2902:
2897:
2889:
2821:
2788:
2743:
2739:
2728:
2724:
2722:
2712:
2701:
2700:
2696:
2695:
2693:
2680:
2670:
2666:
2662:
2660:
2659:
2655:
2648:
2647:
2643:
2630:
2629:
2625:
2623:
2620:
2619:
2614:
2604:
2589:
2561:
2532:
2519:
2511:Nernst equation
2493:
2492:
2472:
2470:
2462:
2458:
2452:
2448:
2446:
2426:
2419:
2417:
2408:
2407:
2399:
2395:
2389:
2385:
2383:
2363:
2356:
2354:
2345:
2344:
2336:
2332:
2326:
2322:
2320:
2303:
2296:
2294:
2287:
2281:
2277:
2273:
2271:
2268:
2267:
2242:
2238:
2232:
2228:
2226:
2210:
2202:
2200:
2191:
2187:
2185:
2182:
2181:
2162:
2148:
2142:
2138:
2127:
2124:
2123:
2104:
2090:
2089:
2083:
2074:
2070:
2063:
2061:
2053:
2050:
2049:
2024:
2016:
2015:
2009:
2002:
2000:
1992:
1989:
1988:
1985:
1947:
1946:
1942:
1936:
1932:
1928:
1914:
1913:
1909:
1903:
1899:
1895:
1893:
1889:
1888:
1871:
1843:
1842:
1838:
1832:
1828:
1824:
1810:
1809:
1805:
1799:
1795:
1791:
1789:
1785:
1784:
1767:
1754:
1750:
1748:
1745:
1744:
1722:
1701:
1695:
1692:
1691:
1644:
1640:
1616:
1612:
1604:
1601:
1600:
1576:
1574:
1572:
1569:
1568:
1545:
1542:
1541:
1523:
1520:
1519:
1493:
1490:
1489:
1466:
1465:
1461:
1450:
1445:
1442:
1441:
1407:
1406:
1402:
1391:
1386:
1383:
1382:
1356:
1355:
1351:
1349:
1346:
1345:
1314:
1310:
1308:
1305:
1304:
1272:
1271:
1267:
1261:
1256:
1255:
1251:
1237:
1236:
1232:
1226:
1221:
1220:
1216:
1214:
1210:
1209:
1190:
1188:
1167:
1166:
1162:
1156:
1151:
1150:
1141:
1137:
1136:
1122:
1121:
1117:
1111:
1106:
1105:
1096:
1092:
1091:
1089:
1085:
1084:
1065:
1063:
1053:
1046:
1042:
1040:
1037:
1036:
994:
993:
989:
983:
978:
977:
968:
964:
951:
950:
946:
940:
935:
934:
925:
921:
908:
907:
903:
897:
892:
891:
882:
878:
877:
866:
865:
861:
855:
850:
849:
840:
836:
820:
819:
815:
809:
804:
803:
794:
790:
774:
773:
769:
763:
758:
757:
748:
744:
743:
741:
737:
736:
717:
715:
702:
690:
685:
684:
678:
673:
672:
665:
661:
659:
656:
655:
633:
621:
613:
612:
606:
601:
600:
598:
595:
594:
559:
558:
554:
548:
543:
528:
523:
518:
514:
508:
503:
486:
485:
481:
475:
470:
455:
450:
445:
441:
435:
430:
425:
414:
413:
409:
403:
398:
383:
378:
373:
369:
363:
358:
338:
337:
333:
327:
322:
307:
302:
297:
293:
287:
282:
277:
275:
271:
270:
251:
249:
240:
236:
234:
231:
230:
211:
208:
207:
187:
184:
183:
180:
133:
122:
116:
113:
70:
68:
58:
46:
35:
28:
23:
22:
15:
12:
11:
5:
4240:
4230:
4229:
4224:
4210:
4209:
4204:
4198:
4193:
4181:
4173:
4172:External links
4170:
4168:
4167:
4160:
4134:
4122:
4085:
4073:
4043:
4031:
4001:
3989:
3958:
3956:
3953:
3952:
3951:
3946:
3941:
3936:
3931:
3926:
3921:
3916:
3914:Bioelectronics
3909:
3906:
3882:
3881:
3867:
3864:
3861:
3855:
3850:
3845:
3840:
3832:
3827:
3820:
3814:
3811:
3808:
3805:
3802:
3799:
3794:
3790:
3784:
3781:
3775:
3770:
3765:
3760:
3752:
3747:
3740:
3734:
3731:
3728:
3725:
3722:
3719:
3716:
3711:
3707:
3704:
3693:
3692:
3678:
3675:
3669:
3664:
3659:
3654:
3646:
3641:
3634:
3628:
3625:
3622:
3619:
3616:
3613:
3608:
3604:
3598:
3595:
3592:
3586:
3581:
3576:
3571:
3563:
3558:
3551:
3545:
3542:
3539:
3536:
3533:
3530:
3527:
3522:
3518:
3515:
3501:
3500:
3487:
3484:
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3476:
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3406:
3402:
3398:
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3377:
3367:
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3355:
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3347:
3343:
3337:
3333:
3329:
3324:
3321:
3318:
3314:
3296:
3285:
3281:
3280:
3266:
3261:
3254:
3249:
3245:
3240:
3236:
3221:
3214:
3207:
3195:
3194:
3181:
3175:
3170:
3164:
3158:
3153:
3137:
3131:
3130:
3116:
3113:
3106:
3102:
3098:
3092:
3089:
3075:
3074:
3058:
3052:
3047:
3042:
3038:
3035:
3028:
3022:
3017:
3012:
3005:
3002:
2996:
2992:
2988:
2983:
2977:
2974:
2971:
2965:
2961:
2957:
2946:
2941:
2934:
2929:
2925:
2922:
2916:
2911:
2895:
2887:
2819:
2799:drift velocity
2786:
2768:
2767:
2755:
2750:
2746:
2742:
2736:
2731:
2727:
2718:
2715:
2710:
2704:
2699:
2692:
2686:
2683:
2677:
2673:
2669:
2665:
2658:
2651:
2646:
2642:
2639:
2633:
2628:
2612:
2602:
2585:
2572:electric field
2557:
2528:
2518:
2515:
2507:
2506:
2491:
2488:
2485:
2482:
2479:
2471:
2465:
2461:
2455:
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2445:
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2437:
2432:
2429:
2422:
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2413:
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2402:
2398:
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2388:
2382:
2379:
2374:
2369:
2366:
2359:
2353:
2350:
2348:
2346:
2339:
2335:
2329:
2325:
2319:
2316:
2311:
2306:
2299:
2293:
2290:
2288:
2284:
2280:
2276:
2275:
2261:
2260:
2245:
2241:
2235:
2231:
2225:
2222:
2216:
2213:
2208:
2205:
2199:
2194:
2190:
2165:
2158:
2155:
2151:
2145:
2137:
2134:
2131:
2107:
2103:
2099:
2096:
2093:
2086:
2077:
2073:
2069:
2066:
2060:
2057:
2033:
2030:
2027:
2023:
2019:
2012:
2005:
1999:
1996:
1984:
1981:
1976:
1975:
1962:
1953:
1950:
1945:
1939:
1935:
1931:
1923:
1920:
1917:
1912:
1906:
1902:
1898:
1892:
1887:
1884:
1881:
1877:
1874:
1869:
1866:
1863:
1858:
1849:
1846:
1841:
1835:
1831:
1827:
1819:
1816:
1813:
1808:
1802:
1798:
1794:
1788:
1783:
1780:
1777:
1773:
1770:
1765:
1762:
1757:
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1728:
1725:
1720:
1717:
1714:
1711:
1707:
1704:
1699:
1679:
1676:
1673:
1670:
1667:
1664:
1661:
1658:
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1643:
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1365:
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1354:
1343:
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1301:
1300:
1287:
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933:
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920:
914:
911:
906:
900:
890:
881:
872:
869:
864:
858:
848:
839:
835:
829:
826:
823:
818:
812:
802:
793:
789:
783:
780:
777:
772:
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756:
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732:
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708:
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366:
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336:
330:
325:
321:
317:
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305:
301:
296:
290:
285:
281:
274:
269:
266:
261:
257:
254:
248:
243:
239:
215:
191:
179:
176:
135:
134:
49:
47:
40:
26:
9:
6:
4:
3:
2:
4239:
4228:
4225:
4223:
4220:
4219:
4217:
4208:
4205:
4202:
4199:
4197:
4194:
4192:
4188:
4185:
4182:
4179:
4176:
4175:
4163:
4161:0-87893-410-3
4157:
4153:
4148:
4147:
4138:
4125:
4119:
4115:
4111:
4107:
4103:
4096:
4094:
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4076:
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4054:
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4016:
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3992:
3986:
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3920:
3917:
3915:
3912:
3911:
3905:
3903:
3899:
3895:
3891:
3887:
3853:
3848:
3838:
3825:
3792:
3788:
3773:
3768:
3758:
3745:
3709:
3705:
3702:
3695:
3694:
3667:
3662:
3652:
3639:
3606:
3602:
3584:
3579:
3569:
3556:
3520:
3516:
3513:
3506:
3505:
3504:
3485:
3482:
3477:
3474:
3471:
3468:
3465:
3459:
3456:
3449:
3445:
3441:
3431:
3430:
3429:
3412:
3409:
3404:
3400:
3396:
3393:
3390:
3383:
3382:
3381:
3376:
3372:
3353:
3350:
3345:
3341:
3335:
3331:
3327:
3322:
3319:
3316:
3312:
3304:
3303:
3302:
3299:
3295:
3289:
3259:
3247:
3243:
3238:
3234:
3226:
3225:
3224:
3220:
3213:
3206:
3203:
3200:
3179:
3168:
3162:
3151:
3143:
3142:
3141:
3136:
3114:
3111:
3104:
3100:
3096:
3090:
3087:
3080:
3079:
3078:
3056:
3045:
3040:
3036:
3033:
3026:
3015:
3010:
2994:
2986:
2981:
2963:
2955:
2939:
2927:
2923:
2920:
2909:
2901:
2900:
2899:
2893:
2885:
2881:
2877:
2873:
2869:
2865:
2861:
2857:
2852:
2850:
2846:
2843:
2839:
2836:
2833:), the molar
2832:
2828:
2825:
2818:
2815:
2812:
2808:
2804:
2800:
2796:
2792:
2785:
2781:
2780:concentration
2777:
2773:
2753:
2748:
2740:
2734:
2729:
2725:
2716:
2713:
2708:
2697:
2690:
2684:
2681:
2675:
2667:
2663:
2656:
2644:
2640:
2637:
2626:
2618:
2617:
2616:
2611:
2608:
2601:
2597:
2593:
2588:
2584:
2580:
2579:concentration
2575:
2573:
2569:
2565:
2560:
2556:
2552:
2548:
2544:
2540:
2536:
2531:
2527:
2524:
2514:
2512:
2509:which is the
2489:
2486:
2483:
2480:
2477:
2463:
2459:
2453:
2449:
2443:
2440:
2435:
2420:
2414:
2412:
2400:
2396:
2390:
2386:
2380:
2377:
2372:
2357:
2351:
2349:
2337:
2333:
2327:
2323:
2317:
2314:
2309:
2297:
2291:
2289:
2282:
2278:
2266:
2265:
2264:
2243:
2239:
2233:
2229:
2223:
2220:
2214:
2211:
2206:
2203:
2197:
2192:
2188:
2180:
2179:
2178:
2156:
2153:
2143:
2135:
2132:
2129:
2101:
2075:
2071:
2067:
2064:
2058:
2055:
2021:
2003:
1997:
1994:
1980:
1960:
1937:
1933:
1904:
1900:
1890:
1885:
1882:
1879:
1867:
1864:
1861:
1856:
1833:
1829:
1800:
1796:
1786:
1781:
1778:
1775:
1763:
1760:
1755:
1751:
1743:
1742:
1741:
1718:
1715:
1712:
1709:
1697:
1690:, it becomes
1674:
1671:
1665:
1659:
1656:
1653:
1648:
1645:
1634:
1628:
1625:
1622:
1617:
1613:
1584:
1580:
1577:
1563:
1547:
1540:
1525:
1518:
1515:
1511:
1495:
1488:
1440:
1437:
1433:
1381:
1352:
1344:
1341:
1337:
1333:
1315:
1311:
1303:
1302:
1285:
1262:
1227:
1211:
1206:
1203:
1198:
1194:
1191:
1185:
1180:
1157:
1138:
1112:
1093:
1086:
1081:
1078:
1073:
1069:
1066:
1060:
1050:
1047:
1043:
1035:
1034:
1033:
1031:
1010:
984:
965:
961:
941:
922:
918:
898:
879:
856:
837:
833:
810:
791:
787:
764:
745:
738:
733:
730:
725:
721:
718:
712:
697:
694:
691:
679:
669:
666:
662:
654:
653:
652:
628:
625:
622:
607:
575:
549:
544:
540:
529:
524:
520:
515:
509:
504:
500:
496:
476:
471:
467:
456:
451:
447:
442:
436:
431:
427:
404:
399:
395:
384:
379:
375:
370:
364:
359:
355:
351:
328:
323:
319:
308:
303:
299:
294:
288:
283:
279:
272:
267:
264:
259:
255:
252:
246:
241:
237:
229:
228:
227:
213:
205:
189:
175:
173:
169:
165:
161:
156:
154:
150:
146:
142:
131:
128:
120:
109:
106:
102:
99:
95:
92:
88:
85:
81:
78: –
77:
73:
72:Find sources:
66:
62:
56:
55:
50:This article
48:
44:
39:
38:
33:
19:
4145:
4137:
4127:, retrieved
4105:
4078:, retrieved
4056:
4046:
4036:, retrieved
4014:
4004:
3994:, retrieved
3972:
3962:
3919:Cable theory
3897:
3889:
3883:
3502:
3427:
3374:
3368:
3297:
3293:
3290:
3282:
3218:
3211:
3204:
3196:
3134:
3132:
3076:
2891:
2883:
2879:
2875:
2871:
2867:
2863:
2859:
2858:of the form
2853:
2844:
2837:
2835:gas constant
2826:
2816:
2783:
2769:
2609:
2599:
2595:
2591:
2586:
2582:
2576:
2567:
2558:
2554:
2550:
2546:
2542:
2538:
2529:
2525:
2520:
2508:
2262:
1986:
1977:
1567:
1512:(joules per
1027:
651:-solutions:
592:
206:species and
181:
172:Bernard Katz
157:
144:
140:
138:
123:
114:
104:
97:
90:
83:
71:
59:Please help
54:verification
51:
3371:Na/K-ATPase
2860:y' = ay + b
2824:temperature
2805:applied to
4216:Categories
4129:2020-10-23
4080:2020-10-23
4038:2020-10-23
3996:2020-10-23
3955:References
2840:, and the
2517:Derivation
1675:2.30258...
226:negative:
149:physiology
87:newspapers
3849:−
3793:∑
3710:∑
3663:−
3607:∑
3521:∑
3478:
3469:μ
3405:μ
3394:−
3332:∑
3088:μ
3057:μ
3037:−
3027:μ
2982:−
2924:μ
2849:electrons
2778:down the
2776:diffusion
2691:−
2641:−
2487:≈
2481:
2444:
2415:≈
2381:
2318:
2292:≈
2224:
2144:∘
2102:⋅
2068:×
2059:≈
2022:⋅
1998:≈
1938:−
1905:−
1886:
1880:⋅
1865:−
1782:
1776:⋅
1710:⋅
1660:
1646:−
1629:
1623:
1516:per mole)
1207:
1082:
985:−
857:−
734:
695:−
626:−
550:−
530:−
501:∑
428:∑
405:−
385:−
356:∑
280:∑
268:
117:June 2010
4187:Archived
3908:See also
2594:, where
2564:integral
3886:calcium
3202:density
2866:= and
2862:, with
2842:faraday
2831:kelvins
2814:valence
2789:is the
2566:of the
2562:is the
2523:voltage
1340:coulomb
1028:It is "
101:scholar
4158:
4120:
4071:
4029:
3987:
3894:square
3816:
3736:
3630:
3547:
3503:where
2878:=0 to
2811:charge
2605:, its
2424:
2361:
2301:
2298:0.0267
2160:
2140:
2081:
2007:
1987:Using
1514:kelvin
1508:= the
1438:units)
1336:joules
1030:Nernst
103:
96:
89:
82:
74:
4152:33–37
2890:and (
2870:= d/d
2490:2.303
1713:2.303
1432:moles
1332:volts
204:ionic
108:JSTOR
94:books
4156:ISBN
4118:ISBN
4069:ISBN
4027:ISBN
3985:ISBN
3197:The
3133:and
2894:) =
2829:(in
2795:flux
2607:flux
2545:and
2421:61.5
2358:26.7
1868:61.5
1764:61.5
1719:61.5
1698:26.7
1338:per
170:and
139:The
80:news
4110:doi
4061:doi
4019:doi
3977:doi
3896:of
2896:out
2856:ODE
2441:log
2157:310
2065:9.6
2004:8.3
1883:log
1779:log
1626:exp
1614:log
162:of
63:by
4218::
4154:.
4116:,
4104:,
4088:^
4067:,
4055:,
4025:,
4013:,
3983:,
3971:,
3904:.
3475:ln
2888:in
2868:y'
2851:.
2513:.
2484:10
2478:ln
2378:ln
2315:ln
2221:ln
2136:37
2072:10
2048:,
1666:10
1657:ln
1618:10
1560:=
1436:SI
1258:Na
1223:Na
1204:ln
1153:Na
1143:Na
1108:Na
1098:Na
1079:ln
1055:Na
980:Cl
970:Cl
894:Na
884:Na
852:Cl
842:Cl
760:Na
750:Na
731:ln
687:Na
265:ln
174:.
4164:.
4112::
4063::
4021::
3979::
3898:e
3890:e
3866:t
3863:u
3860:o
3854:]
3844:A
3839:[
3831:A
3826:P
3819:A
3813:s
3810:n
3807:o
3804:i
3801:n
3798:a
3789:+
3783:n
3780:i
3774:]
3769:+
3764:C
3759:[
3751:C
3746:P
3739:C
3733:s
3730:n
3727:o
3724:i
3721:t
3718:a
3715:c
3706:=
3703:v
3677:n
3674:i
3668:]
3658:A
3653:[
3645:A
3640:P
3633:A
3627:s
3624:n
3621:o
3618:i
3615:n
3612:a
3603:+
3597:t
3594:u
3591:o
3585:]
3580:+
3575:C
3570:[
3562:C
3557:P
3550:C
3544:s
3541:n
3538:o
3535:i
3532:t
3529:a
3526:c
3517:=
3514:w
3486:v
3483:w
3472:=
3466:=
3460:T
3457:R
3450:m
3446:E
3442:F
3413:0
3410:=
3401:e
3397:v
3391:w
3378:A
3375:n
3354:0
3351:=
3346:A
3342:J
3336:A
3328:=
3323:t
3320:o
3317:t
3313:J
3298:m
3294:E
3286:A
3284:q
3265:A
3260:j
3253:A
3248:q
3244:=
3239:A
3235:J
3222:A
3219:j
3215:A
3212:q
3208:A
3205:J
3180:L
3174:A
3169:D
3163:=
3157:A
3152:P
3138:A
3135:P
3115:T
3112:R
3105:m
3101:E
3097:F
3091:=
3051:A
3046:n
3041:e
3034:1
3021:A
3016:n
3011:e
3004:n
3001:i
2995:]
2991:A
2987:[
2976:t
2973:u
2970:o
2964:]
2960:A
2956:[
2945:A
2940:P
2933:A
2928:n
2921:=
2915:A
2910:j
2892:L
2884:L
2882:=
2880:z
2876:z
2872:z
2864:y
2845:F
2838:R
2827:T
2820:A
2817:n
2787:A
2784:D
2754:)
2749:]
2745:A
2741:[
2735:L
2730:m
2726:E
2717:T
2714:R
2709:F
2703:A
2698:n
2685:z
2682:d
2676:]
2672:A
2668:[
2664:d
2657:(
2650:A
2645:D
2638:=
2632:A
2627:j
2613:A
2610:j
2603:A
2600:n
2596:L
2592:L
2590:/
2587:m
2583:E
2568:z
2559:m
2555:E
2551:z
2547:y
2543:x
2539:z
2530:m
2526:E
2464:i
2460:X
2454:o
2450:X
2436:z
2431:V
2428:m
2401:i
2397:X
2391:o
2387:X
2373:z
2368:V
2365:m
2352:=
2338:i
2334:X
2328:o
2324:X
2310:z
2305:V
2283:X
2279:E
2244:i
2240:X
2234:o
2230:X
2215:F
2212:z
2207:T
2204:R
2198:=
2193:X
2189:E
2164:K
2154:=
2150:C
2133:=
2130:T
2106:V
2098:l
2095:o
2092:m
2085:J
2076:4
2056:F
2032:l
2029:o
2026:m
2018:K
2011:J
1995:R
1961:)
1952:n
1949:i
1944:]
1934:X
1930:[
1922:t
1919:u
1916:o
1911:]
1901:X
1897:[
1891:(
1876:V
1873:m
1862:=
1857:)
1848:n
1845:i
1840:]
1834:+
1830:X
1826:[
1818:t
1815:u
1812:o
1807:]
1801:+
1797:X
1793:[
1787:(
1772:V
1769:m
1761:=
1756:X
1752:E
1727:V
1724:m
1716:=
1706:V
1703:m
1678:)
1672:=
1669:)
1663:(
1654:=
1649:1
1642:]
1638:)
1635:1
1632:(
1610:[
1607:(
1585:F
1581:T
1578:R
1548:F
1526:T
1496:R
1471:n
1468:i
1463:]
1458:n
1455:o
1452:i
1448:[
1415:t
1412:u
1409:o
1404:]
1399:n
1396:o
1393:i
1389:[
1364:n
1361:o
1358:i
1353:P
1342:)
1316:m
1312:E
1286:)
1277:n
1274:i
1269:]
1263:+
1253:[
1245:t
1242:u
1239:o
1234:]
1228:+
1218:[
1212:(
1199:F
1195:T
1192:R
1186:=
1181:)
1172:n
1169:i
1164:]
1158:+
1148:[
1139:P
1130:t
1127:u
1124:o
1119:]
1113:+
1103:[
1094:P
1087:(
1074:F
1070:T
1067:R
1061:=
1051:,
1048:m
1044:E
1011:)
1002:t
999:u
996:o
991:]
975:[
966:P
962:+
956:n
953:i
948:]
942:+
937:K
932:[
927:K
923:P
919:+
913:n
910:i
905:]
899:+
889:[
880:P
871:n
868:i
863:]
847:[
838:P
834:+
828:t
825:u
822:o
817:]
811:+
806:K
801:[
796:K
792:P
788:+
782:t
779:u
776:o
771:]
765:+
755:[
746:P
739:(
726:F
722:T
719:R
713:=
707:l
704:C
698:x
692:1
680:x
675:K
670:,
667:m
663:E
638:l
635:C
629:x
623:1
618:a
615:N
608:x
603:K
576:)
567:t
564:u
561:o
556:]
545:j
541:A
537:[
525:j
521:A
516:P
510:m
505:j
497:+
491:n
488:i
483:]
477:+
472:i
468:M
464:[
457:+
452:i
448:M
443:P
437:n
432:i
419:n
416:i
411:]
400:j
396:A
392:[
380:j
376:A
371:P
365:m
360:j
352:+
346:t
343:u
340:o
335:]
329:+
324:i
320:M
316:[
309:+
304:i
300:M
295:P
289:n
284:i
273:(
260:F
256:T
253:R
247:=
242:m
238:E
214:A
190:M
130:)
124:(
119:)
115:(
105:·
98:·
91:·
84:·
57:.
34:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
