BIO THE ELECTRIC EGG. Upon fertilization, the eggs of many species undergo a rapid change in potential difference across their outer membrane. This change affects the physiological development of the eggs. The potential difference across the membrane is called the membrane potential, Vm, which is the potential inside the membrane minus the potential outside it. The membrane potential arises when enzymes use the energy available in ATP to expel three sodium ions (Na+) actively and accumulate two potassium ions (K+) inside the membrane—making the interior less positively charged than the exterior. For a sea urchin egg, Vm is about −70 mV; that is, the potential inside is 70 mV less than that outside. The egg membrane behaves as a capacitor with a capacitance of about 1 μF/cm2. The membrane of the unfertilized egg is selectively permeable to K+; that is, K+ can readily pass through certain channels in the membrane, but other ions cannot. When a sea urchin egg is fertilized, Na+ channels in the membrane open, Na+ enters the egg, and Vm rapidly increases to +30 mV, where it remains for several minutes. The concentration of Na+ is about 30 mmol/L in the egg’s interior but 450 mmol/L in the surrounding seawater. The K+ concentration is about 200 mmol/L inside but 10 mmol/L outside. A useful constant that connects electrical and chemical units is the Faraday number, which has a value of approximately 105 C/mol; that is, Avogadro’s number (a mole) of monovalent ions, such as Na+ or K+, carries a charge of 105 C.
24.73 How many moles of Na+ must m ove per unit area of membrane to change Vm from −70 mV to +30 mV, If we assume that the membrane behaves purely as a capacitor? (a) 10 −4 mol/cm2; (b) 10−9 mol/cm2; (c) 10−12 mol/cm2; (d) 10−14 mol/cm2.
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