Membrane Potential of Cells PDF 2019

The membrane potential of cells The text under the slides was written by Zoltan Varga 2019 This instructional material was prepared for the biophysics lectures held by the Department of Biophysics and Cell...

The membrane potential of cells The text under the slides was written by Zoltan Varga 2019 This instructional material was prepared for the biophysics lectures held by the Department of Biophysics and Cell Biology Faculty of Medicine University of Debrecen Hungary https://biophys.med.unideb.hu Connections with other lectures:  chemical potential  electrochemical potential  structure of biological membranes  membrane transport processes (passive and active transport, Na/K pump) The lecture serves as an introduction to understanding the electric properties of cells It demonstrates the significance of the membrane potential, the processes contributing to its development and its connection with ionic movements. 2 An electric potential difference (voltage) can be measured between the two sides of the membrane surrounding living cells, which is called membrane potential (MP). This is a historical name, but incorrect, since the potential is assigned to a single point in space, the potential difference measured between two points should be called voltage. But since we consider the potential of the external space to be zero, and the MP is defined as Em= i – e (internal minus external potential) the internal electric potential is numerically equal to the voltage. The resting MP of mammalian cells typically falls in the -50 - -80 mV (the voltage of a AA battery is 1.5 V = 1500 mV). The voltage is generated by the uneven distribution of charge carrying ions, which does not quickly equilibrate due to the selective permeability of the membrane. 3 The uneven ion distribution and thus the MP is regulated by the ion transport mechanisms. The active (pump) processes move ions against the electrochemical gradient (ECG), while the passive ones in the direction of the ECG. The effect is mutual: when ions cross the membrane, the charge distribution changes and the MP changes, but in turn, the MP affects the movement of charge carrying ions. E.g. if positive charges (e.g. Na+ ions) enter the cell, they cause depolarization, the MP shifts in the positive direction, while the entry of negative charges (e.g. Cl- ions) causes hyperpolarization, the MP shifts in the negative direction. On the other hand, a more negative MP means a greater driving force for Na+ entry, but smaller for Cl- entry. 4 The best known cellular function associated with MP changes is the action potential (AP). APs are primarily generated by nerve and muscle cells in response to appropriate stimuli and mean the change of the MP in time, characteristic for the particular cell. Its duration ranges from a few ms (neurons) to several hundred ms (cardiac AP). In neurons it functions to relay information, while in muscles it initiates contraction. However, in all other cell types, even in non-excitable cells, the MP has an important role in regulating various cellular functions. Such are e.g. the transport of materials (including exocytosis), cell division, volume regulation, etc. For example, if we use ion channel blockers on lymphocytes to prevent the regulation of the MP, the cells cannot divide. 5 The lipid bilayer membrane can be likened to a capacitor. The parallel-plate capacitor consists of two parallel metal plates, which are separated by an insulator (e.g. air). Connecting the capacitor to a battery will cause the accumulation of charges (Q) on the plates, one positive, the other negative. There will be a voltage V generated between the plates. The capacitor is characterized by its capacitance C = Q / V, 1 Farad = 1 Coulomb / 1 Volt. The good insulator lipid bilayer separates two good conductors (solutions full of ions), so charge accumulates on its two sides and a voltage is measured between the two sides, this is the MP. 6 You do not need to know the details of the above calculation. Its main point is that the charge accumulated on the two sides of the membrane that is sufficient to generate the MP is negligible compared to the total ion content of the cell. 7 Continuation of the previous calculation, you do not need to know the details either. Its main point continues the previous thought: to significantly change the MP (e.g. during an AP) the movement of only a very small amount of charge is sufficient, which does not measurably change the bulk IC or EC ion concentrations. The relatively large MP is generated by a very small charge excess. Based on the above rough estimation, if for 30000 IC cations there are 30001 anions, it is sufficient to generate the -70 mV MP. 8 Thus, the MP of cells is created by the uneven distribution of ions and the selective permeability of the membrane (if it were not selective, the concentrations would quickly equilibrate and the MP would disappear). The movement of ions across the membrane regulates the MP. 9 The figure shows the IC and EC concentrations of the main permeating ions. (You must know these values, many other subjects will require their knowledge). K+ is the only ion whose IC concentration is higher than its EC concentration. The IC concentration of Cl- is highly variable among different cell types, but not that of the other ions. Ca2+ has a special role, since it functions as a second messenger in many signaling pathways (see later in cell biology). In resting cells the free cytosolic Ca2+ concentration is very low, but in response to certain signals (e.g. in muscles just before contraction) it increases many fold due to Ca 2+ ions released from intracellular stores or entering from outside. Thus it is the only one of the main permeating ions whose concentration can significantly change in the cell. The resting MP of cells is typically between -50 and -80 mV, but in some cells it can be more negative or significantly more positive, depending on the presence of transporters required for their functions. 10 If no charges are crossing the membrane, the MP does not change. The MP is also constant if within unit time the same amount of charge leaves as enters, that is, the net flux is zero. This can happen in two ways: 1. For each individual ion the net flux is zero, that is, within unit time the same number of K+ ions leave passively as enter, and the same is true for Na+ and other ions. This means a thermodynamic equilibrium, because the equilibrium remains without energy investment and the ion concentrations do not change in time. Since the electrochemical potential of each ion is equal on the two sides, each ion is in thermodynamic equilibrium. Such are the Nernst and Donnan equilibria. 2. The net flux is zero for all ions combined, but not for the individual ions. For example, if a K+ ion leaves and a Na+ enters, the net flux is 0, but not for the individual ion species. With time the number of K + ions decreases and that of Na+ ions increases without energy investment. This situation can only be maintained by active transport mechanisms (pumps). In this case, at a given MP only one ion species may be at equilibrium (but most often none of them are), and since the others are not at equilibrium, they are “trying” to cross the membrane, which can only be compensated by the ion pumps. In living cells this scenario is relevant and is described by the GHK equation to be detailed in the next slides. 11 Let us look at a simple arrangement, where we have a single permeating ion. On the left side of the beaker we put a KCl solution of 100 mM concentration, on the right a 10 mM KCl solution. The membrane only allows the permeation of K+ ions. Due to the concentration gradient K+ flows from left to right, but Cl- cannot follow. Because of this an excess of positive charges starts to build up on the right, which pushes K+ ions back from right to left. The greater the electric potential difference (voltage) between the two sides, the greater the “driving force” from right to left. At a given voltage the two opposing driving forces (concentration gradient vs. electric potential gradient) become equal and equilibrium is reached. This voltage is the equilibrium or Nernst potential of the given ion. The net flow of K + ions stops, that is why this is an equilibrium! The concentrations DO NOT equilibrate! There is a small positive charge excess on the right and a small negative excess on the left. But this does not measurably change the original ion concentrations! 12 Examining the previous arrangement, let us write the electrochemical potential (ECP) of the permeating K+ ions on the two sides: μ K  μ 0K  RTlnc K  zF  This consists of the standard chemical potential 0K (since we are interested in the difference between the two sides and this term is on both sides, it will cancel out), a term dependent on the K+ ion concentration (RT ln cK), and a term dependent on the electric potential (zF, z – the charge of the ion in e0 units, F – Faraday’s constant,  - electric potential). At Nernst equilibrium RT ln cK is greater on the left, while zF is greater on the right, that is how equilibrium is possible. Writing the difference in ECP between the two sides, and because of the criterion of equilibrium making it equal to zero, we get: [K] I Δμ K  RTln  zFΔ   0 [K] II Expressing  from here, which is the electric potential difference (=voltage = MP) between the two sides, we get the voltage that keeps balance with a 10-fold concentration difference for a monovalent ion (at a given temperature). The calculation shows that here the equilibrium potential of K+ is -59 mV, the side with the higher K+ concentration being more negative. The net flow of K+ between the sides is 0. (You must be able to substitute values in the Nernst equation and perform this calculation!) 13 The easily understandable naïve model of the Nernst equilibrium. The slide is self- explanatory. The boys represent K+ ions and the girls the Cl- ions. The border guard only allows the passage of boys. 14 If an ion is permeating, then its electrochemical gradient (not its concentration gradient, since it has a charge!) will determine which direction it will flow. In order to decide which direction a given ion will flow through an open ion channel, two values must be compared: the equilibrium (Nernst) potential calculated from the concentrations and the actual MP of the cell. If the two values are equal, the ion is in equilibrium, the “driving force” is zero. The greater the difference between the MP and the Nernst potential, the greater the driving force for the ion. In the figure above: the concentration of K+ ions inside is 140 mM, outside 5 mM. From this the Nernst equation gives an equilibrium potential of -89 mV. If the MP of the cell is more positive than that (e.g. -60 mV) then K+ flows out of the cell (hyperpolarizes), at -89 mV it is at equilibrium, at an MP more negative than that (e.g. -120 mV) it flows into the cell (depolarizes). Of course the charge of the ion must be considered as well. Following a different logic, the direction of ion flow is always such that it shifts the MP toward the equilibrium potential of the given ion. For example, at a MP = -60 mV, the MP must be shifted negative to approach -89 mV. To achieve this, the positively charged K+ ions must flow out of the cell. The Nernst equation can also be written with the EC concentration in the numerator, but in this case the negative sign is not needed at the front due to the nature of the logarithm function. 15 16 Thus, if K+ were the only permeating ion, then the MP would be -89 mV, if it was Na+, it would be +70 mV. 17 In living cells the membrane is permeable to more ion species at the same time and since each has a different equilibrium potential, obviously all of them cannot be at equilibrium at the same time. Most often none of them is at equilibrium, that is, the MP is not equal to any of the equilibrium potentials. Thus, if ion channels selective for a given ion open, the ion will flow according to its electrochemical gradient. The Nernst equation only contains the ion concentrations as the factors determining the MP. According to this, the MP could only change significantly (e.g. as during an AP from -80 to +50 mV) if the ion concentrations would drastically change. This cannot and does not happen in living cells, thus the Nernst equation is not suitable for determining the MP of living cells. 18 19 The GHK equation resembles the Nernst equation, but contains the concentrations of the three main permeating ions, as well as their instantaneous permeabilities across the membrane. (Notice that the Cl- concentrations are swapped due to its negative charge.) In an extreme case when pK is very high (many K+ channels are open), and pNa = pCl =0 (all Na+ and Cl- channels are closed), then the GHK equation reduces to the Nernst equation, that is MP = EK. 20 The GHK simulator shown in the lecture can be downloaded from here: http://www.nernstgoldman.physiology.arizona.edu/ The top left panel shows the ion concentrations and permeabilities for an average cell, which gives a -63 mV MP. The other figures show that if the permeability of a single ion is made dominant over the others, then the MP shifts close to the equilibrium potential of that ion (the GHK equation reduces to the Nernst equation). Direction of current flow: bottom right panel> If the MP= -63 mV initially and pCl increases, then since the MP is more negative than the Cl equilibrium potential (E Cl = -47 mV), and since the Cl- ion is negative, it will flow out of the cell (the overly negative inner space pushes it out). The MP will approach ECl, that is, it will shift in the positive direction (-63 --> -47 mV). Alternative explanation: the leaving negative charges make the inside of the cell more positive and the MP shifts in the positive direction. 21 The cells contain numerous macromolecules, which are charged, but are unable to cross the membrane. These attract permeating counter ions from the EC space. The uneven ion distribution thus created generates a voltage between the two sides, this is the Donnan potential. 22 23 If we start from 100 mM K+ + 100 mM non-permeating anions on the IC side and 100 mM KCl on the EC side, then the ion distribution shown on the bottom figure will be formed passively. This is the Donnan equilibrium. Both the K+ and Cl- ions are in equilibrium. 24 If we write the Nernst equation either for the K+ ions or for the Cl- ions we get the same value for the Donnan potential. Notice that the total IC ion concentration has risen from 200 mM to 266 mM, which creates a significant osmotic gradient and causes water entry into the cell. 25 In normally functioning cells the active ion pumps decrease the IC ion concentrations and keep the cells far from the Donnan equilibrium. In such cells the contribution of the Donnan potential to the MP is minimal. Cells with deficient pump functions (e.g. low ATP) approach the Donnan equilibrium and since the developing osmotic gradient causes cell swelling, it can lead to the lysis of the cell. 26 27 28  Review questions How is the cellular membrane potential generated and what is its significance? What are the main permeating ions and what is there distribution like? What is the relationship between the movement of ions and the membrane potential? What does the Nernst equation describe? What does the GHK equation describe? How does the Donnan equilibrium develop? 29