ohms law explained
Transcription
ohms law explained
The plasma membrane separates two media of different ionic composition K+ are the predominant cations in the intracellular fluid Na+ are the predominant cations in the extracellular fluid. The main anions of the intracellular fluid are organic molecules (P-): negatively charged amino acids (glutamate and aspartate), proteins, nucleic acids, phosphates, etc… In the extracellular fluid the predominant anions are ClA marked difference between cytosolic and extracellular Ca2+ concentrations is also observed The plasma membrane separates two media of different ionic composition Intracellular and extracellular media are neutral ionic solutions: in each medium, the concentration of positive ions is equal to that of negative ions. Extracellular: [Na+]e + [K+]e + 2[Ca2+]e = 140 +3 + (2 x 1.5) = 146 mM and [Cl-]e = 146 mM Intracellular: [Na+]i + [K+]i + 2[Ca2+]i = 7 + 140 + 0.0002 = 147 mM but [Cl-]i = 7 mM In the intracellular compartment, other anions than chloride ions are present and compensate for the positive charges (HCO3-, PO42-, aminoacids, proteins, nucleic acids, etc …). The unequal distribution of ions across the neuronal plasma membrane is kept constant by active transport of ions Concentration gradients for Na+, K+, Ca2+ and Cl- ions are constant in the external and cytosolic compartments. Two hypotheses can explain this constancy: Na+, K+, Ca2+ and Cl- ions cannot cross the plasma membrane. In that case, concentration gradients need to be established only once in the lifetime. Plasma membrane is permeable to Na+, K+, Ca2+ and Cl- ions but there are mechanisms that continuously re-establish the gradients and maintain constant the unequal distribution of ions. The unequal distribution of ions across the neuronal plasma membrane is kept constant by active transport of ions When proteins are absent from a synthetic lipid bilayer, no movements of ions occur. The lipid bilayer is a barrier for the diffusion of ions and most polar molecules. When a axon is immerged in a bath containing a control concentration of radioactive *Na+ (24Na+), *Na+ constantly appear in the cytoplasm. This *Na+ influx is not affected by dinitrophenol (DNP), a blocker of ATP synthesis in mitochondria. It does not require energy expenditure. This is passive transport. But what are the mechanisms that maintain concentration gradients across neuronal membranes? The unequal distribution of ions across the neuronal plasma membrane is kept constant by active transport of ions When the reverse experiment is conducted, the axon is passively loaded with radioactive *Na+, and is transferred to a bath containing cold Na+. Measuring the quantity of *Na+ that appears in the bath per unit of time (d*Na+/dt, expressed in counts per minute) allows quantification of the efflux of *Na+. In the presence of dinitrophenol (DNP) this *Na+ efflux quickly diminishes to nearly zero. The process can be started up again by intracellular injection of ATP. Therefore the *Na+ efflux is active transport. Ionic composition of cytosol and extracellular compartments are maintained at the expense of a continuous basal metabolism that provides energy (ATP) utilized to actively transport ions and thus to compensate for their passive movements. (a) Effect of dinitrophenol on the outflux of *Na+ as a function of time (b) Passive and active Na+ fluxes are in opposite directions Ionic channels Ionic channels have a 3D structure that delimits an aqueous pore through which certain ions can pass. Each channel may be regarded as an excitable molecule as it is specifically responsive to a stimulus and can be in at least two different states: closed and open. Channel opening, the switch from the closed to the open state, is tightly controlled by: 1. a change in the membrane potential – these are voltage-gated channels; 2. the binding of an extracellular ligand, such as a neurotransmitter – these are ligand-gated channels, also called receptor channels or ionotropic receptors; 3. the binding of an intracellular ligand such as Ca2+ ions or a cyclic nucleotide; 4. mechanical stimuli such as stretch – these are mechanoreceptors. Membrane potential (Vm) The cell interior shows a negative potential (between –60 and –80 mV) with respect to the outside, which is taken as the zero reference potential. Membrane potential (Vm) is by convention the difference between the potential of the internal and external faces of the membrane (Vm = Vi - Vo). In the absence of ongoing electrical activity, this negative potential is termed the resting membrane potential (Vrest) Membrane potential (Vm) Vm varies: it can be more negative or hyperpolarized or less negative (depolarized) or even positive (also depolarized, the internal face is positive compared to the external face). At rest, Vm is in the range -80/ -50 mV. But when neurons are active, Vm varies between –90 mV and +30 mV. Since nerve cells communicate through rapid (ms) or slow (s) changes in their membrane potential, it is important to understand Vrest first. The electrochemical gradient To predict the direction of the passive diffusion of ions through an open channel, both the concentration gradient of the ion and the membrane potential have to be known. The resultant of these electrochemical gradient. two forces is called the To understand what the electrochemical gradient is for a particular ion, the concentration gradient and the electrical gradient will first be explained separately. Ions passively diffuse down their concentration gradient If Vm = 0 mV, ions will diffuse according to their concentration gradient only. Na+, Ca2+ and Cl- will diffuse passively towards the intracellular medium (when Na+, Ca2+ or Cl- permeable channels are open) as a result of their concentration gradient. In contrast, K+ will move from the intracellular medium to the extracellular one (when K+ permeable channels are open). Equation de Nernst : gradient de concentration Sous l’influence du gradient de concentration, un cation passe du compartiment A vers B produisant un excès de charges + dans le compartiment B et un excès de charges – dans le compartiment A Le travail (W) nécessaire pour le déplacement d’un ion dépend de la constante des gaz parfaits R = 8,314 joules/mole/°K de la température absolue T° Kelvin = T° Celsius + 273 des concentrations dans chaque compartiment [cation]A & [cation]B W1 = R x T x Ln [cation]B [cation]A Equation de Nernst : gradient électrique Le transfert des cations de A vers B polarise la membrane et crée un gradient électrique (ou électrostatique) de B vers A qui tend à s’opposer au gradient de concentration Le travail (W) électrostatique s’opposant à la diffusion de l’ion dépend : de la valence de l’ion : Z de la quantité d’électricité que représente un ion gramme F = Faraday = 96500 coulombs de la force électromotrice générée : E W2 = z.F.E Le flux ionique né d’un gradient de concentration est auto-limité par le gradient électrique qu’il génère Equation de Nernst : potentiel d’équilibre Le flux ionique, né d’un gradient de concentration, est auto-limité par le gradient électrique qu’il génère [cation]B W1 = R.T.Ln W2 = z.F.E [cation]A z.F.E = [cation]Ext R.T Eion = R.T.Ln Ln z.F [cation]B B = EXTERNE A = INTERNE [cation]A Ln = 2,3 log10 ou Eion = 2,3 [cation]Int A 20°C : 2,3 R.T z.F [cation]Ext R.T log z.F [cation]Int [cation]Ext = 58,2 Eion = 58,2 x log [cation]Int Equation de Nernst : gradient de diffusion Le déplacement d’une molécule chargée (ion inorganique) entre deux compartiments C1 et C2 génère un potentiel électrique E. L’équilibre ou il n’y a pas de mouvement net de la molécule chargée est décrit par l’équation de Nernst Equation de Nernst: C1 C2 = e EZF/RT E: différence de potentiel Z: charge de l’ion F: constante de Faraday (96520 Coulombs) T: température absolue (273+C) R: Constante des gaz parfaits, égale à 8,314570 J.K-1.mol-1 La somme du gradient de concentration et du gradient électrique = Gradient électrochimique ou de diffusion (driving force) C’est la résultante des forces ou gradients qui déterminent le sens de passage d’un ion à travers le membrane Equation de Nernst : potentiel d’équilibre d’un ion Equation de Nernst: RT E= Ln ZF C1 Potentiel d’équilibre : le flux passif net d’un ion à travers la membrane est nul. C2 A 20°C: RT/F = 25 mV; En base 10 avec Z = +1 RT/ZF= 58 Pour le K : EK = 58 log 3/140 = - 96mV Pour le Na: ENa = 58 log 140/14 = + 58 mV Pour le Cl: ECl = -58 log144/14 = - 58 mV Pour le Ca: ECa = 29 Log 1/10-4 = + 116mV The passive diffusion of ions through an open channel creates a current – To know the direction of passive diffusion of a particular ion and how many of these ions diffuse per unit of time, the direction and intensity of the net flux of ions (number of moles per second) through an open channel have to be measured. Usually the net flux (fnet) is not measured. – The electrical counterpart of this net flux, the ionic current, is measured instead. The passive diffusion of ions through an open channel creates a current • Passive diffusion of ions through an open channel is a movement of charges through a resistance (resistance here is a measure of the difficulty of ions moving through the channel pore). • Movement of charges through a resistance is a current. Through a single channel the current is called ‘single-channel current’ or ‘unitary current’, iion. The relation between fnet and iion is: iion = fnet zF Loi d’Ohm • The amplitude of iion is expressed in ampères (A) which are coulombs per seconds (C s–1). F is the Faraday constant (96 500 C) • z is the valence of the ion (+1 for Na+ and K+, –1 for Cl–, +2 for Ca+); and fnet is the net flux of the ion in mol s–1. Loi d’Ohm A current is expressed following Ohm’s law: U = RI I is the current through a resistance R and U is the difference of potential between the two ends of the resistance. For currents carried by ions, I is called iion, the current that passes through the resistance of the channel pore which has a resistance R (called rion). Loi d’Ohm • But what is U in biological systems? • U is the force that makes ions move in a particular direction; it is the electrochemical gradient for the considered ion and is also called the driving force: U = Vm – Eion Loi d’Ohm Loi d’Ohm According to Ohm’s law, the current iion through a single channel is derived from: (Vm – Eion) = rion . iion so: iion = (1/rion)( Vm - Eion) = gion (Vm - Eion) Loi d’Ohm gion is the reciprocal of resistance: it’s the conductance of the channel. It is a measure of the ease of flow of ions (flow of current) through the channel pore. Whereas resistance is expressed in ohms (Ω), conductance is expressed in siemens (S). Loi d’Ohm iion is negative when it represents an inward flux of positive charges (cations) iion is positive when it represents an outward flux of positive charges. Passive diffusion of ions according to (a) their concentration gradient only, or (b) to membrane potential (electrical gradient) only (Vm = –30 mV). Loi d’Ohm In fact, several channels of the same type are open at the same time. e.g.: the total current of Na+ channels INa that crosses the membrane at time t is the sum of the unitary currents iNa at time t: INa = Npo iNa Npo is therefore the number of open Na+ channels in the membrane at time t); and iNa is the unitary Na+ current. More generally: Iion = Npo iion Loi d’Ohm By analogy, the total conductance of the membrane for a particular ion is: Gion = Npo gion and from iion = gion (Vm - Eion) : Iion = Gion (Vm - Eion) Iion and iion can be measured experimentally : • iion is the current measured from a patch of membrane where only one channel of a particular type is present. • Iion is the current measured from a whole cell membrane where N channels of the same type are present. Roles of ionic currents Ionic currents have two main functions: • Ionic currents change the membrane potential: – either they depolarize the membrane – or repolarize it or hyperpolarize it, depending on the charge carrier. • These terms are in reference to resting potential. Roles of ionic currents Roles of ionic currents • Changes of membrane potential are signals. – A depolarization can be an action potential or a postsynaptic excitatory potential (EPSP). – An hyperpolarization can be a postsynaptic inhibitory potential (IPSP). Ionic currents increase the concentration of a particular ion in the intracellular medium. • Example of Ca2+ current : – It is always inward. It transiently and locally increases the intracellular concentration of Ca2+ ions and contributes to the triggering of Ca2+dependent events such as secretion or contraction. A particular membrane potential, the resting membrane potential Vrest • In the absence of ongoing electrical activity (when the neuron is not excited or inhibited by the activation of its afferents) its membrane potential is termed the resting membrane potential (Vrest). • For some neurons, Vrest is stable (silent neurons) for others it is not (pacemaker neurons for example). The theory of Vrest : Julius Bernstein (1902) 1. Vrest is due to selective permeability of the membrane to one ionic species only and that nerve excitation developed when such selectivity was transiently lost. 2. under resting conditions the cell membrane permeability is minimal to Na+, Cland Ca2+ while it is high to K+. 3. K+ moves outwards following its concentration gradient ([K+]i is 50 times higher than [K+]e): positive charges are thus subtracted from the intracellular medium and there is an accumulation of negative charges at the intracellular side of the membrane and positive charges at the external side of the membrane. 4. These positive charges will oppose further outward movements of K+ until an equilibrium is reached when the concentration gradient for K+ cancels the drive exerted by the electrical gradient. 5. This is by definition the equilibrium potential EK. Hence, at Vm = EK, although K+ keeps moving in and out of the cell, there is no net change in its concentration across the membrane. Establishment of Vrest in a cell where most of the channels open are K+ channels. Suppose that at t = 0 and cell potential Vm = 0 mV (a), K+ ions will move outwards due to their concentration gradient (b). Loss of intracellular K+ induces a negative potential (Vm) as Vm = EK (c).