Create RPE_Model_2022.m

Author: SchwartzNU

RPE/RPE_Model_2022.m

@@ -0,0 +1,82 @@
+% Model of RPE cells
+% How much does the input resistance change by just closing the gap
+% junctions?
+
+%% 2006 Fortier and Bagna
+%%% Equation 10
+
+% R1 = R11 * (Rj + Rn)/((Rj + Rn) - f*R11)
+% simplified: R = R11 * (Rj + R)/((Rj + R) - f*R11)
+
+%% solve algebraically
+% syms R R_I R_j;
+% eqn = R == RI * (R_j + R)/((R_j + R) - f*RI);
+% S = solve(eqn, RI);
+
+% RI = [R*(Rj + R)]/ [J + R + f*R]
+
+%% known values
+f = 6; % number of neighbors
+Rj = linspace(1, 10000, 1000)'; % range of gap junction resistance values to be tested
+R = [20, 200, 1000]; % measured input resistances tested
+
+
+%%
+
+RI_vals = nan(length(Rj), length(R)); % single cell input resistance values
+CC_vals = nan(length(Rj), length(R)); % coupling coefficient values
+
+for i = 1:length(R) % for each measured control resistance
+    r = R(i);
+    for j = 1:length(Rj) % for each gap junctional resistance
+        rj = Rj(j);
+        ri = (r*(rj+r)) / (rj + r + f*r);
+        
+        RI_vals(j, i) = ri;
+        cc = r / (rj + r);
+        CC_vals(j, i) = cc;
+    end
+end
+
+
+figure;
+subplot(2, 1, 1)
+plot(Rj, RI_vals, 'LineWidth', 2)
+xlabel('Rj (M Ohm)')
+ylabel('Input Resistance (M Ohm)')
+xlim([0 7500])
+legend(cellstr(num2str(R', ' Measured R=%-d')))
+subplot(2, 1, 2)
+plot(Rj, CC_vals, 'LineWidth', 2)
+xlabel('Rj (M Ohm)')
+ylabel('CC')
+xlim([0 7500])
+legend(cellstr(num2str(R', ' Measured R=%-d')))
+
+% 0.025 to 0.15 is the physiological range of coupling coefficients
+Ind = CC_vals > 0.025 & CC_vals < 0.15;
+RI_CC_vals = RI_vals;
+RI_CC_vals(~Ind) = nan;
+figure;
+hold on
+for x = 1:length(R)
+    scatter(Rj, RI_CC_vals(:, x), 'filled')
+end
+xlabel('Rj (M Ohm)')
+ylabel('Input R (M Ohm)')
+legend(cellstr(num2str(R', 'Measured R=%-d')))
+
+% plot in conductance
+figure;
+subplot(2, 1, 1)
+plot(1./Rj, RI_vals, 'LineWidth', 2)
+xlabel('Gj (m Seimens)')
+xlim([0 0.1]); ylim([0 500]);
+ylabel('Input Resistance (M Ohm)')
+legend(cellstr(num2str(R', ' Measured R=%-d')))
+subplot(2, 1, 2)
+plot(1./Rj, CC_vals, 'LineWidth', 2)
+xlabel('Gj (m Seimens)')
+xlim([0 0.1])
+ylabel('CC')
+legend(cellstr(num2str(R', ' Measured R=%-d')))