(Diffusion & Equilibrium Potential) DR QAZI IMTIAZ RASOOL Electrical properties of cell membrane I (Diffusion & Equilibrium Potential) DR QAZI IMTIAZ RASOOL

OBJECTIVES Define diffusion potential of an ion and simply conclude how to calculate it Discuss the concept of charge separation. Explain the methods of calculation of equilibrium potential when the membrane is permeable to several ions. Define Donnan equilibrium and discuss its consequences Apply this knowledge to a practical instance.

BASICS FACTS Molecular Gradients (in mM) (in mM) outside 142 4 1-2 (pH 7.4) 28 110 1 5 inside (in mM) 14 140 0.5 10-4 (pH 7.2) 10 5-15 2 75 40 Na+ K+ Mg2+ Ca2+ H+ HCO3- Cl- SO42- PO3- protein Ions – Particles / molecules electrically charged Anions – Negatively charged particles Cations – Positively charged particles High permeability indicates that particle mass moves easily through a membrane. High conductance indicates that electrical charge moves easily through a membrane. Conductance is the inverse of electrical resistance. If the conductance of the membrane to a particular ion is low, then the resistance to movement of that ion across the membrane is high.

Lipid Bilayer Plasma membrane is selectively permeable CO2 O2 N2 halothane H2O urea ions glucose Fat-soluble molecules, such as glycerol, can diffuse through the membrane easily. They dissolve in the phospholipid bilayer and pass through it in the direction of the concentration gradient, from a high concentration to a low concentration. Water, oxygen and carbon dioxide can also diffuse through the bilayer, passing easily through the temporary small spaces between the 'tails' of the phospholipids. Plasma membrane is selectively permeable Impermeable membrane - membrane though which nothing can pass Freely permeable membrane - any substance can pass through it Selectively permeable membrane - permits free passage of some materials and restricts passage of others.Distinction may be based on size, electrical charge, molecular shape, lipid solubility Cells differ in their permeabilities; depending on what lipids and proteins are present in the membrane and how these components are arranged.

Diffusion lipid-soluble molecules move readily across the membrane (rate depends on lipid solubility) 2. H2O soluble molecules cross via channels or pores (a) (b)

Ion Channels Characteristics: 1. Ungated Determined by size, shape, distribution of charge, et 2.Gated voltage (e.g. voltage-dependent Na+ channels) chemically (e.g. nicotinic ACh receptor channels. in out Na+ and other ions Na+

Cell Membrane in resting state Ion concentrations Cell Membrane in resting state K+ Na+ Cl- A- Outside of Cell Inside of Cell Key words: ion concentrations; cell membrane; intracellular fluid; extracellular fluid; Na+; Cl-; K+

Cell Membrane is Semi-Permeable Cell Membrane at rest Na+ Cl- K+ A- Outside of Cell Inside of Cell (K+) can pass through to equalize its concentration Na+ and Cl- cannot pass through Result - inside is negative relative to outside - 55 to -100mv The hydrophobic membrane bilayer is a formidable barrier to inorganic ions and is also a poor conductor of electricity. Poor conductors are said to have a high resistance to electrical current, in this case, ionic current. On the other hand, ion channels act as molecular conductors of ions. They introduce a conductance pathway into the membrane and lower its resistance. The cell membrane is semi-permeable. That is, when the neuron is at rest, the cell membrane allows some ions (K+) to pass freely through the cell membrane, whereas other ions (such as Na+ and Cl-) cannot.

ELECTRICAL POTENTIAL=CHARGE SEPARATION In H2O, without a membrane hydrated Cl- is smaller than hydrated Na+ therefore faster: Hydration Shells Cl - - + - + - + - + - + - + - + - + - + Na + - + - + - + The resulting separation of charge is called an ELECTRICAL POTENTIAL IONS WITH SMALLER CRYSTAL RADIUS HAVE A HIGHER CHARGE DENSITY THE HIGHER CHARGE DENSITY ATTRACTS MORE WATER OF HYDRATION THUS THE SMALLER THE CRYSTAL RADIUS, THE LOWER THE MOBILITY IN WATER - + - + Cl- - + Na+

Basic Concepts Forces that determine ionic movement Volt;- A charge difference between 2 points in space Electrostatic forces Opposite charges attract Identical charges repel Concentration forces Diffusion – movement of ions through semipermeable membrane Osmosis – movement of water from region of high concentration to low

ELECTRONEUTRAL DIFFUSSION LOW SALT CONC; HIGH SALT CONC; + - + - + - + - + - + - + - + - BARRIER SEPARATES THE TWO SOLUTIONS

ELECTRONEUTRAL DIFFUSSION HIGH SALT CONC; LOW SALT + - BARRIER REMOVED + - All potentials result from ions moving across membranes. Two forces on ions: Diffusion (from high to low concentration); Electrical (toward opposite charge and away from like charge). Each ion that can flow through channels reaches equilibrium between two forces. Equilibrium potential for each ion determined by Nernst Equation. K+ make - potentials; Na+ make + potentials. CHARGE SEPARATION = ELECTRICAL POTENTIAL

Diffusion Potentials(DP) is the potential difference generated across a membrane when a charged solute (an ion) diffuses down its concentration gradient. ( caused by diffusion of ions.) can be generated only if the membrane is permeable to that ion. FEATURES;-1. if not permeable to the ion, no DP will be generated no matter how large a conc; gradient is present. 2. magnitude/Unit =, measured in mV, 3. depends on the size of the concentration gradient, where the concentration gradient is the driving force. 4. Sign of the DP depends on the charge of the diffusing ion. 5. DP are created by the movement of only a few ions, and they do not cause changes in the concentration of ions in bulk solution. Diffusion Potentials A diffusion potential is the potential difference generated across a membrane when a charged solute (an ion) diffuses down its concentration gradient. Therefore, a diffusion potential is caused by diffusion of ions. It follows, then, that a diffusion potential can be generated only if the membrane is permeable to that ion. Furthermore, if the membrane is not permeable to the ion, no diffusion potential will be generated no matter how large a concentration gradient is present. The magnitude of a diffusion potential, measured in millivolts (mV), depends on the size of the concentration gradient, where the concentration gradient is the driving force. The sign of the diffusion potential depends on the charge of the diffusing ion. Finally, as noted, diffusion potentials are created by the movement of only a few ions, and they do not cause changes in the concentration of ions in bulk solution.

2.More –ve particles in than out EQUILIBRIUM POTENTIAL (EP) EP(electrochemical equilibrium), is the DIFFUSION POTENTIAL that exactly balances or opposes the tendency for diffusion down the concentration difference. At the chemical and electrical driving forces acting on an ion are equal and opposite, FEATURES;- 1.Membrane is polarized 2.More –ve particles in than out 3. Bioelectric Potential i.e,battery Potential for ion movement Current EQUILIBRIUM POTENTIAL (EP) The concept of equilibrium potential is simply an extension of the concept of diffusion potential. If there is a concentration difference for an ion across a membrane and the membrane is permeable to that ion, a potential difference (the diffusion potential) is created. Eventually, net diffusion of the ion slows and then stops because of that potential difference. In other words, if a cation diffuses down its concentration gradient, it carries a positive charge across the membrane, which will retard and eventually stop further diffusion of the cation. If an anion diffuses down its concentration gradient, it carries a negative charge, which will retard and then stop further diffusion of the anion. The equilibrium potential is the diffusion potential that exactly balances or opposes the tendency for diffusion down the concentration difference. At electrochemical equilibrium, the chemical and electrical driving forces acting on an ion are equal and opposite, and no further net diffusion occurs. The following examples of a diffusing cation and a diffusing anion illustrate the concepts of equilibrium potential and electrochemical equilibrium

At Electrochemical Equilibrium: 4.Concentration gradient for the ion is exactly balanced by the electrical gradient 5.No net flux of the ion 6.No requirement for any sort of energy-driven pump to maintain the concentration gradient

Electrical potential (EMF) + - - - - - - - - - - - - - - - - - - - - - - - + - - - When will the negatively charged molecules stop entering the cell? - - - - - - - - - - - - - - - - - - - - - - - - - - In this case we’re changing the electrical potential across the membrane and see what happens to the concn gradient of the ion. In reality, the concentraction gradient is changed various cellular processes which determines the Nernst potential. - - The Nernst potential (equilibrium potential) is the theoretical intracellular electrical potential that would be equal in magnitude but opposite in direction to the concentration force.

Calculating equilibrium potential The Nernst Equation - at which an ion will be in electrochemical equilibrium. At this potential: total energy inside = total energy outside Electrical Energy Term: zFV Chemical Energy Term: RT.ln[Ion] Z is the charge, 1 for Na+ and K+, 2 for Ca2+ and Mg2+, -1 for Cl- F is Faraday’s Constant = 9.648 x 104 Coulombs / mole R is the Universal gas constant = 8.315 Joules / °Kelvin * mole T is the absolute temperature in °Kelvin Equilibrium potential (mV) , Eion = Relation of diffusion potential to the concentration difference…… resulting in Nernst (equilibrium) potential For any univalent ion at body temperature of 37° C EMF (mV)= +/-61log (Conc.inside/Conc.outside) Calculate for K+ and Na+ K= -61log(140/4) Na= -61log(14/142) Sign is –ve shows the polarity inside the cell. Nernst equation - the electrical potential for a single ion to prevent it from having any net movement across the cell membrane (equilibrium potential, Eion) For potassium If Ko = 5 mM and Ki = 140 mM EK = -61 log(140/4) EK = -61 log(35) EK = -94 mV For Sodium If Nao = 142 mM and Nai = 14 mM EK = -61 log(14/142) EK = -61 log(0.1) EK = +61 mV EK = -90mV ENa = +60mv

CAPACITANCE 1. Cell membranes form an insulating barrier that acts like a parallel plate capacitor (1 μF /cm2) 2. Only a small number of ions must cross the membrane to create a significant voltage difference 3. Bulk neutrality of internal and external solution 4. Cells need channels to regulate their volume 5. Permeable ions move toward electrochemical equilibrium 6. Eion =calculated as NERST POTENTIAL 7. Electrochemical equilibrium does not depend on permeability, only on the concentration gradient

The membrane potential Electrical properties The membrane potential difference of -50 to +120mV In the resting state, the intracellular space contains more negative ions than the extracellular space

THE MEMBRANE POTENTIAL Extracellular Fluid Intracellular Fluid K+ Na+ Sodium channel is less open causing sodium to be slower M E B R A N Potassium channel is more open causing potassium to be faster - + MEMRANE POTENTIAL (ABOUT 90 -120 mv)

Electrochemical gradients and cellular transport of molecules Electrochemical gradients and cellular transport of molecules. A, Because glucose is uncharged, the electrochemical gradient is determined solely by the concentration gradient for glucose across the cell membrane. As shown, the glucose concentration gradient would be expected to drive glucose into the cell. B, Because K+ is charged, the electrochemical gradient is determined by both the concentration gradient and the membrane voltage (Vm). The energy in the concentration gradient, determined from the Nernst equation, is 90.8 mV (driving K+ out of the cell). The membrane voltage of -60 mV will drive K+ into the cell. The electrochemical gradient, or the net driving force, is 30.8 mV, which will drive K+out of the cell. The compartments are electroneutral, but there is a concentration gradient Diffusion of ions from [1] do [2] Hydration envelope (water molecules are bound to ions) Na+ (more) a Cl- (less)  faster diffusion of Cl- against (!) concentration gradient  Transient voltage appears across the two compartments  Diffusion potential

Membrane potential Cell membrane acts as a barrier--ICF from mixing with ECF 2 solutions have different concentrations of their ions. Furthermore, this difference in concentrations leads to a difference in charge of the solutions.. Therefore,+ve ions will tend to gravitate towards -ve solution. Likewise, -ve ions will tend to gravitate towards +ve solution. Then the difference between the inside voltage and outside voltage is determined membrane potential. When a membrane is permeable to several different ions, DP developed depends on: 1.Polarity of the electrical charge of ions. 2. Permeability of the membrane (P) to each ion. 3. Concentration of each ion in two compartments separated by the membrane. MP is calculated by Goldman-Hodgkin-Katz equation. Cell membrane acts as a barrier which prevents the inside solution (intracellular fluid) from mixing with the outside solution (extracellular fluid). These two solutions have different concentrations of their ions. Furthermore, this difference in concentrations leads to a difference in charge of the solutions. This creates a situation whereby one solution is more positive than the other. Therefore, positive ions will tend to gravitate towards the negative solution. Likewise, negative ions will tend to gravitate towards the positive solution. To quantify this property, one would like to somehow capture this relative positivity (or negativity). To do this, the outside solution is set as the zero voltage. Then the difference between the inside voltage and the zero voltage is determined. For example, if the outside voltage is 100 mV, and the inside voltage is 30 mV, then the difference is 70 mV. This difference is what is commonly referred to as the membrane potential. Example: The membrane potential of the large nerve fibers in resting state (when they do not transmits the signals) is about -90 mV.

Membrane Potential: Goldman Equation NOTE: P’ = permeability P = permeability At rest: PK: PNa: PCl = 1.0 : 0.4 : 0.45 Net potential movement for all ions Known Vm:Can predict direction of movement of any ion ~ In general, the resting potential of most vertebrate cells is dominated by high permeability to K+, which accounts for the observation that the resting Vm is typically close to EK. The resting permeability to Na+ and Ca2+ is normally very low. Skeletal muscle cells, cardiac cells, and neurons typically have resting membrane potentials ranging from -60 to -90 mV. As, excitable cells generate action potentials by transiently increasing Na+ or Ca2+ permeability and thus driving Vm in a positive direction toward ENa or ECa. A few cells, such as vertebrate skeletal muscle fibers, have high permeability to Cl-, which therefore contributes to the resting Vm. This high permeability also explains why the Cl- equilibrium potential in skeletal muscle is essentially equivalent to the resting potential Membrane Potential Depends on Ionic Concentration Gradients and Permeabilities Body_ID: HC006007 In the preceding section, we discussed how to use the GHK current equation to predict the current carried by any single ion, such as K+ or Na+. If the membrane is permeable to the monovalent ions K+, Na+, and Cl--and only to these ions-the total ionic current carried by these ions across the membrane is the sum of the individual ionic currents: Body_ID: P006037 The individual ionic currents given by Equation 6-7 can be substituted into the right-hand side of Equation 6-8. Note that for the sake of simplicity, we have not considered currents carried by electrogenic pumps or other ion transporters; we could have added extra "current" terms for such electrogenic transporters. At the resting membrane potential (i.e., Vm is equal to Vrev), the sum of all ion currents is zero (i.e., Itotal = 0). When we set Itotal to zero in the expanded Equation 6-8 and solve for Vrev, we get an expression known as the GHK voltage equation or the constant-field equation: Body_ID: P006038 Because we derived Equation 6-9 for the case of Itotal = 0, it is valid only when zero net current is flowing across the membrane. This zero net current flow is the steady-state condition that exists for the cellular resting potential, that is, when Vm equals Vrev. The logarithmic term of Equation 6-9 indicates that resting Vm depends on the concentration gradients and the permeabilities of the various ions. However, resting Vm depends primarily on the concentrations of the most permeant ion. Contribution of Ions to Membrane Potential

Equivalent electrical circuit model RMP Em = (EK * gK) + (ENa * gNa) + (ECl * gCl) gNa + gK + gCl With unequal distribution of ions and differential resting conductances to those ions, We can use the Nernst equation and Ohm’s law in an equivalent circuit model to predict a stable resting membrane potential of -75 mV, as is seen in many cells NB, this is a steady state and not an equilibrium, since K+ and Na+ are not at their equilibrium potentials; there is a continuous flux of those ions at the RMP more complete model provides energy-dependent pump to counter the steady flux of ions add voltage-gated K+ and Na+ channels for electrical signaling add ligand-gated (e.g. synaptic conductances) obviously, much greater complexity could be imagined

Chord Conductance Equation W. J. Lederer -- Cardiac electrophysiology Chord Conductance Equation Vm = EK+ +ENa+ + ECl-.... Vm = membrane potential, not equal to Eion; Weighted avg of equilibrium potentials of all ions to which membrane is permeable Esp. K+, Na+, Cl-; changes in ECF K+ alters RMP in all cells How and why do we define chord conductance? - March 2001 For type of channel at a single time, we can define the conductance through the channel as the inverse of the resistance - i.e. g=I/V. However, at a microscopic level channels behave in a stochastic and binary way, and so we cannot predict the behaviour of individual channels in this way. The chord conductance is a measure of the permeability of all of one type of channel for a particular cell, allowing us to predict the actual amount of current that will flow across the whole membrane. Chord conductance rises rapidly for the VONaC as it responds to depolarisation - if we were to measure it after a brief period at a higher potential, we would see it decrease as the permeability decreases. This is described by the equation shown under the graph on page 8 - the net current is equal to the potential difference available to drive it multiplied by the conductance through the channels. The most important things to take from this are that chord conductance lets us describe the macroscopic behaviour of the channels, giving an indication of the permeability of a class of channels for a given voltage. If we have described the response of chord conductance to changing potential difference, we can predict the current that will flow through a channel at any given time. Note that this is complicated in the case of the sodium channel, because chord conductance in this case is also a complex function of time (as activation and inactivation occur at different rates).

Passive distribution Donnan equilibrium The ratio of positively charged permeable ions equals the ratio of negatively charged permeable ions Start Equilibrium II I II I K+ [K+] = [K+] Donnan Effect When an ion on one side of a membrane cannot diffuse through the membrane, the distribution of other ions to which the membrane is permeable is affected in a predictable way. For example, the negative charge of a nondiffusible anion hinders diffusion of the diffusible cations and favors diffusion of the diffusible anions. Consider the following situation, in which the membrane (m) between compartments X and Y is impermeable to charged proteins (Prot–) but freely permeable to K+ and Cl–. Assume that the concentrations of the anions and of the cations on the two sides are initially equal. Cl– diffuses down its concentration gradient from Y to X, and some K+ moves with the negatively charged Cl– because of its opposite charge. Therefore Furthermore, that is, more osmotically active particles are on side X than on side Y. Donnan and Gibbs showed that in the presence of a nondiffusible ion, the diffusible ions distribute themselves so that at equilibrium their concentration ratios are equal: Cross-multiplying, This is the Gibbs–Donnan equation. It holds for any pair of cations and anions of the same valence. The Donnan effect on the distribution of ions has three effects in the body introduced here and discussed below. First, because of charged proteins (Prot–) in cells, there are more osmotically active particles in cells than in interstitial fluid, and because animal cells have flexible walls, osmosis would make them swell and eventually rupture if it were not for Na, K ATPase pumping ions back out of cells. Thus, normal cell volume and pressure depend on Na, K ATPase. Second, because at equilibrium the distribution of permeant ions across the membrane (m in the example used here) is asymmetric, an electrical difference exists across the membrane whose magnitude can be determined by the Nernst equation. In the example used here, side X will be negative relative to side Y. The charges line up along the membrane, with the concentration gradient for Cl– exactly balanced by the oppositely directed electrical gradient, and the same holds true for K+. Third, because there are more proteins in plasma than in interstitial fluid, there is a Donnan effect on ion movement across the capillary wall. Cl- [Cl-] = [Cl-]

Donnan Equilibrium Mathematically expressed: Another way of saying the number of positive charges must equal the number of negative charges on each side of the membrane

A- A- Passive Distribution BUT, in real cells there are a large number of negatively charged, impermeable molecules (proteins, nucleic acids, other ions) call them A- Start Equilibrium II I A- II I A- K+ [K+] > [K+] Cl- [Cl-] < [Cl-]

Donnan potential: [K+]I = [A-]I + [Cl-]I [K+]II = [Cl-]II I II A- Equilibrium [K+]I = [A-]I + [Cl-]I II I - + A- [K+] > [K+] [K+]II = [Cl-]II [Cl-] < [Cl-] If [A-]I is large, [K+]I must also be large A=phosphate anions+ protiens macromolecules +’ve = -’ve +’ve = -’ve space-charge neutrality

EXAMPLE The product of Diffusible Ions is the same on the two sides of a membrane. 33 K+ 33 Cl- 67 K+ 50 Pr - 17 Cl- Step 2 66 Osmoles 134 Osmoles 50 K+ 50 Cl- Initial 100 Osmoles Final 33 ml 67 ml Total Volume 100 ml Ions Move H2O moves Proteins are not only large, osmotically active, particles, but they are also negatively charged anions. Proteins influence the distribution of other ions so that electrochemical equilibrium is maintained 41 41

Human Potentials Strong potentials in muscles--EMG, ECG (electromyogram and electrocardiogram). Weaker potentials from brain--EEGs. Evoked potentials allow study of changes. Computer averaging allows study of deep brain potentials: Event-related potentials in sensory systems and cognition.