7 Lojayn Salah Zaid R Al Najdawi Mohammad-Khatatbeh
Salam everyone, I made my best to make this sheet clear enough to be easily understood let the party begin :P Quick Revision about the previous lectures: - Cellular membrane separates two compartments (inside compartment from outside, intracellular fluid from extracellular fluid) which have different compositions. - The concentration of K + ions inside the cells is very high (higher than outside), on the other hand the concentration of Na + ions outside the cell is very high. (Higher than inside). - The Chemical gradient of Na + and K + ions causes the net movement of K + ions from inside to outside and Na + ions from outside to inside the cell. - There are two types of potentials: a) Chemical Potential: which is the concentration gradient. b) Electrical Potential: which is the electrical gradient (for example, the movement of K + will result in movement of (+) charges outside the cell and leaving behind (-) charges inside the cell. 1 P a g e The beginning of this lecture In the last lecture we have assumed that the cellular membrane is permeable only to potassium ions (K + ) and not permeable to other ions, by this assumption what will we get from the movement of that specific ion? And will that movement continue until reaching the same concentrations of ions? The answer of the second question is NO, by the diffusion of K + ions we are creating electrical potential across that flat membrane, which will be negative inside and positive outside, in fact the membrane here works as separator of charges, also here we are reaching electrochemical equilibrium.
Chemical potential drives force from inside to outside and Electrical potential drives force from outside to inside, but once we reach equilibrium, both chemical and electrical forces are in balance(also both potentials will be equal to each other at equilibrium). Electrochemical Equilibrium (or reversal Erev ) potentials For each ion: it is the membrane potential where the net flow through any open channels is 0. In other words, at Erev, the amount of ions that moves from inside to outside the cell will be equal to the amount of ions that moves from outside to inside the cell. If we have high activation of sodium channels we say that the potential created will be positive inside and negative outside the cell. -in resting state, Inside the cell is generally negative in relation to the outside of the cell. (see the figure) Note: The sign of the potential (+ or -) always refers to the inside of the cell, so at any time you see (-) sign it means that the charge inside the cell is negative and outside the cell is positive. Calculations of equilibrium potential: As we mentioned before we can measure the equilibrium potential for univalent ion and for many ions by using 2 equations: 2 P a g e
The First Equation: We use Nernst Equation when the plasma membrane is permeable only for univalent ion: E = equilibrium potential for univalent ion. Ci = concentration inside the cell. Co = concentration outside the cell. E (mv) = -61 * Log Ci Co In this lecture the doctor talked about the table below, which shows the calculated potentials (by using Nernst equation) for different ions (Na +, K +, Cl -, Ca +2 ), for example if the membrane is permeable only for chloride the potential created will be -80 and so on. - If the ion s movement through the membrane is only for K +, then the Nernst potential is equal to -94 (mv). - If the ion s movement through the membrane is only for Na +, then the Nernst potential is equal to +61 (mv). Let us assume that the membrane is permeable for both sodium and potassium ions (it has high permeability for K + and low permeability for Na + ), think about the potential, will it be closer to -94 or +61? Well, because the permeability for K + is about 100 times greater than Na +, then the potential will be closer to -94 and will be equal to -86 (mv). 3 P a g e
The Second equation: We know that our membrane can be permeable to more than one ion, so when more than one ion channel is present (and open) in the plasma membrane, the membrane potential can be calculated by using the Goldman-Hodgkin- Katz Equation : **Before we talk about this equation I want to remind you that Permeability refers to the ability of ions to cross the membrane easily, and is directly proportional to the total number of open channels for a given ion in the membrane. Vm is the membrane potential. R is the universal gas constant (8.314 J.K -1.mol -1 ). T is the temperature in Kelvin (K = C + 273.15). F is also constant = (96485 C.mol -1 ). pk, pna, pcl : are the relative membrane permeability for K+, Na+, and Cl-, respectively. [K + ]o, [K + ]i is the concentration of K + in the extracellular fluid (outside) and in the intracellular fluid (inside) respectively. [Na + ]o, [Na + ]i: is the concentration of Na + in the extracellular fluid (outside) and in the intracellular fluid (inside) respectively. [Cl - ]o, [Cl - ]i: is the concentration of Cl - in the extracellular fluid (outside) and in the intracellular fluid (inside) respectively. If you want to use in the equation the normal log, you have to multiply the equation by 2.303. In this equation, we predict that the movement of the cations (positively charged ions such as (Na + and K + ), will be out of the cell, down its electrochemical gradient. The situation is reversed for anions (negatively charged ions such as Cl ), where the ion movement will be inside the cell. In this equation if we assume that the membrane is not permeable for sodium and Chloride ions then we will return back to Nernst equation. 4 P a g e
Resting Membrane Potential: The human organism is composed of multiple cells, all of them with different components and therefore with different resting membrane potentials which we can define it as: - The unequal distribution of ions on the both sides of the cell membrane. - The voltage difference of quiescent cells. - The recorded membrane potential for a cell if there weren t any stimuli or conducting impulses across it (at resting conditions). - Determined by the concentrations of ions on both sides of the membrane. - A negative value, which means that there is an excess of negative charge inside of the cell, compared to the outside. - Because of the variety in permeability between cells there are different resting membrane potentials between tissues. There are three factors involved in establishing resting membrane potential: Activity of K + channels (permeability to K + ions). Activity of Na + channels (permeability to Na + ions). Na + / K + pumps. *) Example for resting membrane potential: For neurons the recorded resting membrane potential is about -90 (mv), this represents a potential difference between the inside to the outside when neuron is not active. Maybe some of us think that the main factor of establishing resting membrane potential is the high protein content inside cells, because they are negatively charged, in fact that is not true, because we have many ions that can neutralize these negatively 5 P a g e
charged particles of proteins, and that what we call Donnan s effect, which is the neutralization of charged particles near a semi-permeable membrane by other ions. Let us first remember signal transduction mechanisms by reading its pathway from the picture below: We know that sometimes we can change the permeability for some ions, for example activation of sodium and potassium channels: If we have activated sodium channels more Na + ions will move from outside to inside the cell this will change the membrane permeability for Na + ions resting membrane potential will be different we will get less negative membrane potential ( we mean by less negative: inside with regard to outside the cell). If the stimulus that cause the increase in the activity of sodium channels is over, the membrane potential will return to its resting state. Another example If we have activated potassium channels more K + ions will move from inside to outside the cell this will change the membrane permeability for K + ions resting membrane potential will be different we will get more negative membrane potential ( we mean by more negative: inside with regard to outside the cell). Changes in membrane potential (Polarization) can happen in two ways: - Depolarization stage: it is the stage when the membrane potential decreases (becomes less negative). For example if we activate the sodium channels Depolarization will happen. - Hyperpolarization stage: it is the change in membrane potential in opposite direction of depolarization (membrane potential will become more negative). For example if we 6 P a g e
activate the potassium channels Hyperpolarization will happen. ** Any change in permeability at Equilibrium Potential will not cause any change in the value of resting membrane potential. Na+ and K+ conductance at resting potentials: Conductance: Is the extent to which the membrane allows the ion to permeate, and controls the amount of ion crossing the membrane in response to the gradient. - At rest we have very high conductance for K + ions and very low conductance for Na + ions. Ohm s Law: Where V = Voltage in volts I = Current in amps R = Resistance in ohms G= conductance At any time you increase the resistance you ll decrease the conductance, and if you decrease the resistance you ll increase the conductance. 7 P a g e Sorry for any mistakes, Wish you best of luck Your colleague and friend: Lojayn Salah