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Extracellular charge adsorption influences intracellular electrochemical homeostasis in amphibian skeletal muscle.

Mehta AR, Huang CL, Skepper JN, Fraser JA - Biophys. J. (2008)

Bottom Line: The membrane potential measured by intracellular electrodes, E(m), is the sum of the transmembrane potential difference (E(1)) between inner and outer cell membrane surfaces and a smaller potential difference (E(2)) between a volume containing fixed charges on or near the outer membrane surface and the bulk extracellular space.First, analytic equations were developed to calculate the influence of charges constrained within a three-dimensional glycocalyceal matrix enveloping the cell membrane outer surface upon local electrical potentials and ion concentrations.Electron microscopy confirmed predictions of these equations that extracellular charge adsorption influences glycocalyceal volume.

View Article: PubMed Central - PubMed

Affiliation: Physiological Laboratory, University of Cambridge, Cambridge, United Kingdom.

ABSTRACT
The membrane potential measured by intracellular electrodes, E(m), is the sum of the transmembrane potential difference (E(1)) between inner and outer cell membrane surfaces and a smaller potential difference (E(2)) between a volume containing fixed charges on or near the outer membrane surface and the bulk extracellular space. This study investigates the influence of E(2) upon transmembrane ion fluxes, and hence cellular electrochemical homeostasis, using an integrative approach that combines computational and experimental methods. First, analytic equations were developed to calculate the influence of charges constrained within a three-dimensional glycocalyceal matrix enveloping the cell membrane outer surface upon local electrical potentials and ion concentrations. Electron microscopy confirmed predictions of these equations that extracellular charge adsorption influences glycocalyceal volume. Second, the novel analytic glycocalyx formulation was incorporated into the charge-difference cellular model of Fraser and Huang to simulate the influence of extracellular fixed charges upon intracellular ionic homeostasis. Experimental measurements of E(m) supported the resulting predictions that an increased magnitude of extracellular fixed charge increases net transmembrane ionic leak currents, resulting in either a compensatory increase in Na(+)/K(+)-ATPase activity, or, in cells with reduced Na(+)/K(+)-ATPase activity, a partial dissipation of transmembrane ionic gradients and depolarization of E(m).

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Comparison of GD and GC predictions of the relationship between Σg and E2. The predicted relationship between Σg and E2 is similar whether using GC theory (solid diamonds) or a GD approach (open triangles). However, GD theory suggests that only certain values of Σg are possible at steady state, as greater initial magnitudes of Σg would result in osmotic swelling of the charged matrix, and hence, reduction in steady-state Σg. This is reflected by the “bunching” of the GD points at higher magnitudes of Σg. This occurs because although each model was initiated with the same 20 evenly spaced values of Σg (GC model) by choosing values of zX(g) that gave equal starting values of FzX(g)[X]g (GD model), the steady-state values of FzX(g)[X]g are osmotically determined in the GD model, whereas Σg is fixed in the GC model.
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fig3: Comparison of GD and GC predictions of the relationship between Σg and E2. The predicted relationship between Σg and E2 is similar whether using GC theory (solid diamonds) or a GD approach (open triangles). However, GD theory suggests that only certain values of Σg are possible at steady state, as greater initial magnitudes of Σg would result in osmotic swelling of the charged matrix, and hence, reduction in steady-state Σg. This is reflected by the “bunching” of the GD points at higher magnitudes of Σg. This occurs because although each model was initiated with the same 20 evenly spaced values of Σg (GC model) by choosing values of zX(g) that gave equal starting values of FzX(g)[X]g (GD model), the steady-state values of FzX(g)[X]g are osmotically determined in the GD model, whereas Σg is fixed in the GC model.

Mentions: The theoretical approach presented here was developed because the glycocalyx is thick enough in skeletal muscle (some 40–80 nm) to require consideration as a three-dimensional volume rather than as a two-dimensional layer. The GD approach derived in Methods thus incorporates the concept of an osmotically determined glycocalyx volume. With this approach, the glycocalyx charge density (Σg) and potential (E2) are dependent variables influenced by the charge valency/osmole of the glycocalyx (zX(g)). Fig. 2 demonstrates this predicted relationship between E2 and zX(g) for a compartment with a stable osmotic content of molecules (Xg) of mean charge valency/osmole zX(g), but which has a volume determined by osmotically driven water movements and thus a variable concentration of Xg at steady state. The influence of osmotic water movements may be seen by comparison of the predictions of this GD-based approach with those of classical GC theory. To permit comparison of the relationship between the three-dimensional GD approach derived here and two-dimensional GC theory, Appendix 1 shows a derivation of the GC equation using conservation principles similar to those used to derive the GD-based equations. It shows that the novel GD equations reduce to a classical GC function in the limit of an adsorptive layer of zero thickness. Thus, Fig. 3 plots E2 against Σg from both the GC equation and the GD approach derived here, demonstrating an identical predicted relationship between Σg and E2 by each approach. However, because Σg = FzX(g)[X]g and [X]g decreases as the magnitude of zX(g) increases (Eq. 12), Σg is constrained to a limited range of values at steady state in GD theory. Thus, although both approaches demonstrate a similar relationship between Σg and E2, GD theory additionally suggests a limitation on the physically possible values of Σg. This limitation derives from the alterations in glycocalyceal volume predicted by the GD approach after changes in the value of zX(g).


Extracellular charge adsorption influences intracellular electrochemical homeostasis in amphibian skeletal muscle.

Mehta AR, Huang CL, Skepper JN, Fraser JA - Biophys. J. (2008)

Comparison of GD and GC predictions of the relationship between Σg and E2. The predicted relationship between Σg and E2 is similar whether using GC theory (solid diamonds) or a GD approach (open triangles). However, GD theory suggests that only certain values of Σg are possible at steady state, as greater initial magnitudes of Σg would result in osmotic swelling of the charged matrix, and hence, reduction in steady-state Σg. This is reflected by the “bunching” of the GD points at higher magnitudes of Σg. This occurs because although each model was initiated with the same 20 evenly spaced values of Σg (GC model) by choosing values of zX(g) that gave equal starting values of FzX(g)[X]g (GD model), the steady-state values of FzX(g)[X]g are osmotically determined in the GD model, whereas Σg is fixed in the GC model.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2480687&req=5

fig3: Comparison of GD and GC predictions of the relationship between Σg and E2. The predicted relationship between Σg and E2 is similar whether using GC theory (solid diamonds) or a GD approach (open triangles). However, GD theory suggests that only certain values of Σg are possible at steady state, as greater initial magnitudes of Σg would result in osmotic swelling of the charged matrix, and hence, reduction in steady-state Σg. This is reflected by the “bunching” of the GD points at higher magnitudes of Σg. This occurs because although each model was initiated with the same 20 evenly spaced values of Σg (GC model) by choosing values of zX(g) that gave equal starting values of FzX(g)[X]g (GD model), the steady-state values of FzX(g)[X]g are osmotically determined in the GD model, whereas Σg is fixed in the GC model.
Mentions: The theoretical approach presented here was developed because the glycocalyx is thick enough in skeletal muscle (some 40–80 nm) to require consideration as a three-dimensional volume rather than as a two-dimensional layer. The GD approach derived in Methods thus incorporates the concept of an osmotically determined glycocalyx volume. With this approach, the glycocalyx charge density (Σg) and potential (E2) are dependent variables influenced by the charge valency/osmole of the glycocalyx (zX(g)). Fig. 2 demonstrates this predicted relationship between E2 and zX(g) for a compartment with a stable osmotic content of molecules (Xg) of mean charge valency/osmole zX(g), but which has a volume determined by osmotically driven water movements and thus a variable concentration of Xg at steady state. The influence of osmotic water movements may be seen by comparison of the predictions of this GD-based approach with those of classical GC theory. To permit comparison of the relationship between the three-dimensional GD approach derived here and two-dimensional GC theory, Appendix 1 shows a derivation of the GC equation using conservation principles similar to those used to derive the GD-based equations. It shows that the novel GD equations reduce to a classical GC function in the limit of an adsorptive layer of zero thickness. Thus, Fig. 3 plots E2 against Σg from both the GC equation and the GD approach derived here, demonstrating an identical predicted relationship between Σg and E2 by each approach. However, because Σg = FzX(g)[X]g and [X]g decreases as the magnitude of zX(g) increases (Eq. 12), Σg is constrained to a limited range of values at steady state in GD theory. Thus, although both approaches demonstrate a similar relationship between Σg and E2, GD theory additionally suggests a limitation on the physically possible values of Σg. This limitation derives from the alterations in glycocalyceal volume predicted by the GD approach after changes in the value of zX(g).

Bottom Line: The membrane potential measured by intracellular electrodes, E(m), is the sum of the transmembrane potential difference (E(1)) between inner and outer cell membrane surfaces and a smaller potential difference (E(2)) between a volume containing fixed charges on or near the outer membrane surface and the bulk extracellular space.First, analytic equations were developed to calculate the influence of charges constrained within a three-dimensional glycocalyceal matrix enveloping the cell membrane outer surface upon local electrical potentials and ion concentrations.Electron microscopy confirmed predictions of these equations that extracellular charge adsorption influences glycocalyceal volume.

View Article: PubMed Central - PubMed

Affiliation: Physiological Laboratory, University of Cambridge, Cambridge, United Kingdom.

ABSTRACT
The membrane potential measured by intracellular electrodes, E(m), is the sum of the transmembrane potential difference (E(1)) between inner and outer cell membrane surfaces and a smaller potential difference (E(2)) between a volume containing fixed charges on or near the outer membrane surface and the bulk extracellular space. This study investigates the influence of E(2) upon transmembrane ion fluxes, and hence cellular electrochemical homeostasis, using an integrative approach that combines computational and experimental methods. First, analytic equations were developed to calculate the influence of charges constrained within a three-dimensional glycocalyceal matrix enveloping the cell membrane outer surface upon local electrical potentials and ion concentrations. Electron microscopy confirmed predictions of these equations that extracellular charge adsorption influences glycocalyceal volume. Second, the novel analytic glycocalyx formulation was incorporated into the charge-difference cellular model of Fraser and Huang to simulate the influence of extracellular fixed charges upon intracellular ionic homeostasis. Experimental measurements of E(m) supported the resulting predictions that an increased magnitude of extracellular fixed charge increases net transmembrane ionic leak currents, resulting in either a compensatory increase in Na(+)/K(+)-ATPase activity, or, in cells with reduced Na(+)/K(+)-ATPase activity, a partial dissipation of transmembrane ionic gradients and depolarization of E(m).

Show MeSH
Related in: MedlinePlus