Physics of Biological Membrane PDF

# Physics of Biological Membrane ## Electrolytes - Electrolytes are inorganic compounds, where water is often necessary for the ionization or molecule split. - The dissolved compounds in liquids (water) are broken down into ions. - Ions are atoms, which have accepted more electrons (negative charge...

# Physics of Biological Membrane ## Electrolytes - Electrolytes are inorganic compounds, where water is often necessary for the ionization or molecule split. - The dissolved compounds in liquids (water) are broken down into ions. - Ions are atoms, which have accepted more electrons (negative charges Ion) or lost electrons (positive charges Ion). - When solid NaCl is dissolved in water, water splits the NaCl molecules into free Na+ and Cl- ions. - The solution so formed is called an electrolyte. - The ions in electrolyte solution are more free to move (have a higher mobility) than in solids. - Living tissue is electrically an electrolytic conductor, where both intracellular and extracellular liquids contain ions free to migrate. - Electrolyte solution has positive and negative ions, if two electrodes with potential difference are inserted into this electrolyte solution, ion will be attracted to the electrode with opposite charge. - The positively charged ions move toward the cathode while the negatively charged ions move toward the anode. - Therefore an electric field forms between the two electrodes and such movement of ions conducts an electric current through the electrolyte solution. ## Cell Membrane - The basic building block of the human body is the living cell, and a prerequisite for its life is that it is surrounded by an electrolyte solution. - Cells appear as a transparent medium when viewed through a light microscope. - In living tissue important communication control is implemented by hormones and nerves. - Some cells are not excitable: - the cells of adipose and connective tissue or blood. - They are passive, not under nerve control, and only weakly polarized. - However, nerve, muscle and gland cells are polarized and excitable; within a 1/1000 second (1 m second) such cells may react on trigger signals such as electrical, mechanical or chemical energy. - The excitation of a cell is accompanied by an action potential. - The action potential is the basic bioelectric event and signal source in the body. - The cell is normally surrounded by a membrane, which act as partition to separate the interior of the cell from its surrounded medium. - The membrane is a bi-layer lipid membrane (BLM). - The membrane of a living cell is a most complex and dynamic system. - The structure of the membrane is composed of lipids and proteins with minute pores distributed through the membrane, it is a major barrier to ion flux. - Embedded in the membrane are channels, ion pumps and...etc. ## Electrical Properties of Cell Membrane ### Membrane Viscosity - The viscosity of a fluid will be constant regardless of the flow field if the temperature and the density are invariant. - Fluids that consist of small molecules, such as air and water, have low viscosity comparing with blood viscosity. | Temperature (C°) | Water Viscosity (Pa-s) | |---|---| | 30 | 0.797 x 10-3 | | 40 | 0.653 × 10-3 | | Temperature(C°) | blood Viscosity (Pa-s) | |---|---| | 37 | 3×10-3 to 4×10-3 | - Blood is a liquid that consists of plasma and particles, such as the red blood cells. - The viscosity of blood thus depends on the viscosity of the plasma, in combination with the hematocrit. - Physical studies have shown that the membrane exists in a liquid-crystalline state, where the viscosity of biological membrane ranges from 0.2 poise (or 0.02Pa.s = 20cP) and upwards at physiological temperatures of 37C⁰. ### Resistance - The resistor is a circuit component that opposes current flow. - Resistance (R) is measured in units of ohm(Ω). - The relation between current (I) and voltage (V) is given by Ohm's law: - $V = IR$ - $R = \rho \frac{l}{A}$ - Where - l = length of the conductor - A = cross-sectional area. - p = specific resistance (resistivity). - Materials that present a very small resistance to current flow are called conductors. - Materials with a very large resistance are called insulators. - In the aqueous environment of the body, salt and various other molecules dissociate into positive and negative ions. - As a result, body fluids are relatively good conductors of electricity. - Still, these fluids are not nearly as conductive as metals. - The electrical resistivity of the internal fluid is relatively higher than the external fluid, which is due to its relatively high specific resistance, a smaller volume and so a narrow cross-sectional area, but the plasma membrane offers the highest resistance that range between 10-2-10-5 ohms.cm-2. - Consequently it limits the flow of ions through itself. - Therefore, it is a far weaker conductor because of its lipid matrix. ### Dielectric - A dielectric is an insulator material, which prevents the movements of charges from the negative plate to the positive plate through it. - Basically, a perfect dielectric is a substance without free charges. - It reduces the intensity of the electric field between the conductors. - The dielectric constant is a main factor, which play an important role in the design of the capacitor, where the high dielectric constant enhances the capacitances. - In living cell, membrane capacitance has significant function. - Even if the conductivity of the membrane itself is very low, the membrane is so thin that the capacitance is very high, that is due to its thickness 7 nm and its dielectric constant of 3 - 10. - This represents a large dielectric strength and it acts as a dielectric, but it is not a perfect dielectric. ### Capacitance - The capacitor is a circuit element that stores electric charges. - In its simplest form it consists of two conducting plates separated by a dielectric (insulator). - Positive charges are on one side of the plate, and negative charges are on the other. - Capacitance (C) is measured in microfarads (uF.cm²). - The relation between the stored charge (Q), and the voltage across the capacitor is given by: - $C = Q/V$ - The intracellular and extracellular fluids are electrolyte solutions contain electrolyte ions act as conducting plates. - A very minute excess of cations accumulates on the outer surface of the cell membrane and equal number of anions accumulate on the inner surface. - The intracellular and extracellular electrolytes are well conductive; the cell interior is nearly completely insulated from the outside by a membrane. - The parallel plate membrane capacitor has a constant and relatively high capacitance per unit area of the membrane (µF.cm²) because the membrane is extremely thin, has relatively high dielectric constant (3-10), and the conductive fluids (outer and inner) offer relatively large surface area towards the membrane. - The parallel-plate membrane capacitor is not perfect capacitors because the membrane is not perfect dielectric and the ions can diffuse through its pores leading to dielectric loss and it needs the active membrane transport to maintain its capacitance. ## Cell Polarization (Resting State) - Cell polarization is generated by the ion pumps, which pump (drive) the ions against the electrochemical gradient. - This energy-consuming mechanism polarizes the cell so that the interior of excitable cells has a potential about - 90 mV with respect to the extracellular electrolytes. - Such a pump is a molecular device, embedded in the cell membrane, capable of generating a net electric current across the membrane. - The cell membrane is somewhat permeable to potassium ions and much less to sodium ions whereas chloride ions can readily pass through the membrane.. ## Three conditions necessary for the Establishment of Potentials across Membranes - Mobile charged ions - A concentration gradient across the membrane - The permeability of the membrane to specific species of these ions. ### Concentration gradient - In most neurons, K+ and organic anions (such as those found in proteins and amino acids) are present at higher concentrations inside the cell than outside. - In contrast, Na+ and Cl- are usually present at higher concentrations outside the cell. - This means there are stable concentration gradients across the membrane for all of the most abundant ion types. ## Types of Channels - Some channels, known as leak channels, are open in resting neurons. - Others are closed in resting neurons and only open in response to a signal. - Some ion channels are highly selective for one type of ion, but others let various kinds of ions pass through. - Ion channels that mainly allow K+ to pass are called potassium channels. - Ion channels that mainly allow Na+ to pass are called sodium channels. - The concentration gradient for K+ facilitates its movement out of the cell via K+ channels, but its electrical gradient is in the opposite direction (inward). - An equilibrium is reached in which the tendency of K+ to move out of the cell is balanced by its tendency to move into the cell, and at that equilibrium there is a slight excess of cations on the outside and anions on the inside. - The Na+-K+ pump, pumps three Na+ out of the cell for every two K+ it pumps in; thus, it also contributes a small amount to the membrane potential by itself. - Millions of such pumps in one cell membrane polarize the cell to steady state so that the cell is fully polarized and ready to be triggered. - This is the stage before the action potential and it is known as Resting Membrane Potential. ## Resting Membrane Potential - Where does the resting membrane potential come from? - The resting membrane potential is determined by the uneven distribution of ions (charged particles) between the inside and the outside of the cell, and by the different permeability of the membrane to different types of ions. - How does a neuron establish and maintains a stable voltage across its membrane - that is, a resting membrane potential? - If K+ can cross via channels, it will begin to move down its concentration gradient and out of the cell. - The movement of K+ ions down their concentration gradient creates a charge imbalance across the membrane. - The charge imbalance opposes the flow of K+ down the concentration gradient. - The electrical force driving K+ back into the cell is equal to the chemical force driving K+ out of the cell. - There is no net movement of K+ either direction, and the system is considered to be in equilibrium. - Every time one K+ leaves the cell, another K+ will enter it. - Is known as the equilibrium potential. ## Both K+ and Na+ contribute to resting potential in neurons - As it turns out, most resting neurons are permeable to Na+ and Cl- as well as K+. - Permeability to Na+, in particular, is the main reason why the resting membrane potential is different from the potassium equilibrium potential. - Because of this, the sodium equilibrium potential-the electrical potential difference across the cell membrane that exactly balances the Na+ concentration gradient-will be positive . - Na+ will try to drag the membrane potential toward its (positive) equilibrium potential. - K+ will try to drag the membrane potential toward its (negative) equilibrium potential. - You can think of this as being like a tug-of-war. - The real membrane potential will be in between the Na+ equilibrium potential and the K+ equilibrium potential. - By the activity of the sodium potassium pump Na+-K+, pumps three Na+ out of the cell for every two K+ it pumps in. - This explains why there is a slight excess of cations on the outside and anions on the inside. - However, it will be closer to the equilibrium potential of the ion type with higher permeability (the one that can more readily cross the membrane). | Concentration inside | Concentration outside | |---|---| | Na+ 15 | Na+ 150 m Mol/1 | | K+ 150 m Mol/1 | K+ 5.5 | - The Goldman equation allows for the calculation all the main ions that can diffuse across this membrane. - Goldman equation is written as such (where P is the relative permeability of the membrane to a certain ion). - $E = \frac{RT}{F} ln \frac{P_{Na+} [Na_o] + P_{K+} [K_o] + P_{Cl-} [Cl_i]}{P_{Na+} [Na_i] + P_{K+} [K_i] + P_{Cl-} [Cl_o]}$ - Where - [$Na⁺$] - Sodium ion concentration outside and inside. - [$K⁺$] - Potassium ion concentration outside and inside. - R - the ideal gas constant (joules per kelvin per mole) - T - the temperature in kelvins - F = Faraday's constant (coulombs per mole) - RT/F is approximately 26.7 mV at human body temperature (37 °C); when factoring in the change-of-base formula between the natural logarithm, In, and logarithm 61.5mV - $V_m = 61.5 log \frac{1 \times 5.5 + 0.02 \times 150 + 0.5 \times 6 }{1 \times 150 + 0.02 \times 15 + 0.5 \times 106} = -76.7mV $ - $V_m = 61.5 log \frac{1 \times 5.5 + 0.02 \times 150}{1 \times 150 + 0.02 \times 15} = -76.7mV $ - Question: Using the Goldman Equation calculate the membrane potential based on Na+ and K+ ion concentration (both inside and outside the cell) and their associated permeabilities. | Ion | Concentration (Inside) | Concentration (Outside) | Permeability | |---|---|---|---| | K+ | 145 | 5 | 60 | | Na+ | 10 | 140 | 1 | ## Stimulus ### Types of Stimuli - There are two main types of stimulus -the external stimulus and the internal stimulus - **External stimulus** - The external stimulus includes touch and pain, vision, smell, taste, sound, and balance (equilibrium). - These sensory stimuli are activated by external changes. - **Internal stimulus** - For example one of the internal stimuli is hunger which is the sign of low energy in the body. ### Stimulis and Action Potentials - When the intensity of the stimulus is increased, the size of the action potential does not become larger. Rather, the frequency or the number of action potentials increases. . - In general, the greater the intensity of a stimulus, the greater the number of action potentials. - Any stimulus that opens a gated channel produces a graded potential. - Graded potentials, or local potentials, are changes in the membrane potential that cannot spread far from the site of stimulation. - That is subjected to a mechanical stimulus that generates a sufficient graded potential will generate an action potential. ## Action Potential - The cell membrane is polarized at rest, with positive charges lined up along the outside of the membrane and negative charges along the inside. - When a surface of a single axon or section of a cell membrane (nerve or muscle) is excited effectively and if excitation exceeded firing level (threshold value usually around-55mV). - By some form of external energy (Stimulus) (chemical, thermal, mechanical, electrical...etc.), changing in membrane characteristics (properties) starts; - resistance decreases (Na+ channels in the membrane open) and sodium ions enter the cell. - This influx of sodium ions makes the membrane potential increase very rapidly, going all the way up to about +40 mV. and the cell is depolarized. - Once the action potential reaches +40 mV, the membrane closes the Na+ channels. - In addition, the direction of the electrical gradient for Na+ is reversed during the overshoot because the membrane potential is reversed, and this limits Na+ influx. - The membrane permits some of the potassium ions to leave the cell, thus the outflow of potassium constitutes an outward current, where the polarity is abolished for a brief period and actually reverses (from positive to negative) and falls rapidly toward the resting level. - The cell is said to be repolarized and assumes its resting potential when full repolarization has occurred. - The excess sodium ions are actively pumped out of the cell whereas the excess potassium is actively pumped into the cell. - This is by the sodium-potassium pump which constantly brings potassium in and pump sodium out of the cell. ## Standard Waveform of A.P - In the normal resting state, the potential across the nerve fiber is about - 90mV. - Standard waveform is graphical recording of an action potential of a single nerve fiber, which initiate at the resting potential depolarization, and return to the resting potential after full repolarized state as shown in Figure (7). - Action potential is a beginning depolarization of the membrane. - After the rate of depolarization increases. - The point at which this change in rate occurs is called the firing level or sometimes the threshold. - The ascending phase on the action potential, called the depolarization phase, is produced by the inward current of sodium ions whereas the descending phase called the repolarization phase is produced by the outward current of potassium ions, which represent the reduction of potential from spike potential to resting state (-90mV). ## Refractory Period - This refractory period is divided into: - Absolute refractory period - Corresponding to the period from the firing level until the end 2/3 of the repolarized phase. - Relative refractory period - Starts from the end of 2/3 of the repolarization phase, until the beginning of the new action potential. - Absolute refractory period: membrane can not respond to any stimulus. - Relative refractory period: membrane can respond to intense stimulus. ### Refractory Period Explanation - Absolute refractory period - The time following an action potential during which a stimulus cannot elicit a second action potential - Overlaps the depolarization and around 2/3 of repolarization phase. - A new action potential cannot be generated during depolarization because all the voltage-gated sodium channels are already opened - Relative refractory period - The period when the generation of a new action potential is possible, but only upon a suprathreshold stimulus. - This period overlaps the final 1/3 of repolarization. ## Latent Period - The stimulus artifact is followed by an interval (latent period) that ends with the start of the action potential and corresponds to the time it takes the impulse to travel along the axon from the site of stimulation to the recording electrodes. ## Local Response - The local response can be defined as the event formed in the interval between resting state and the threshold (firing level). - Normally channels have closed gates. A gate can be opened by a voltage change. - The voltage gated is the voltage across the cell membrane that determines whether channel is opened or remains closed. - A polarized cell may suddenly become depolarized according to the stimulus and threshold intensity, where threshold intensity varies with the duration; with weak stimuli it is long, and with strong stimuli it is short. - The action potential fails to occur if the stimulus is lower than threshold intensity (around -50mV) and such event is known as local response as shown in Figure (8). - Action potential occurs with constant amplitude and form regardless of the strength of the stimulus if the stimulus is at or above threshold intensity. - The local response can be defined as the event formed in the interval between resting state and the threshold (firing level).