Modeling Electrochemical Dynamics and Signaling Mechanisms in Excitable Cells with Pathological Case Studies

By Tetsuya Watanabe

Modeling Electrochemical Dynamics and Signaling Mechanisms in Excitable Cells with Pathological Case Studies covers the neuronal cell communication system in excitable cells, recognizing the most relevant mechanisms of cell communication. Along with new findings in biotechnology, medicine and pathological cases for clinicians, the book highlights electrochemical potential in living nerve and muscle cells. Written for physiological scientists, pharmaceutical scientists, medical doctors, biologists and physicists, this book an essential read for a real understanding of the signals as we see them.

• Covers neuronal cell communication systems in excitable cells
• Presents new findings in biotechnology that are being applied in medicine and pathological cases
• Covers mathematical and physical bases for readers without background in these fields

• Language: English
• Publisher: Academic Press
• Release date: Jan 18, 2022
• ISBN: 9780323972703

Tetsuya Watanabe

Dr. Tetsuya Watanabe is the President of Watanabe Institute of Mathematical Biology and Watanabe Clinic of Oral Surgery in Hamamatsu, Japan. He graduated from Kanagawa Dental College and holds a DDS degree in dental medicine. He received Postgraduate Training and Fellowship Appointments and successively Faculty Appointments of Associate and Assistant Professor at the Department of Pharmacology, Medical School, University of Pennsylvania, in Philadelphia, USA. Dr. Watanabe is the recent author of Biophysical Basis of Physiology and Calcium Signaling Mechanism in Cardiac and Smooth Muscle, published by Elsevier/Academic Press in 2018.

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Chapter 1: Introduction

Abstract

In liquid, the driving force of diffusion is the pressure produced by bumping molecules. In a high concentrated spot of certain molecules, the pressure produced by bumping between them pushes the other kind of neighbor molecules away, while some of the other kind of molecules get into the concentrated area of certain molecules, thereby causing the diffusion by mixing. The concentrated area can be made by an injection of a solute into a solvent in a container. Diffusion of ions through a leak channel and injected ions in a model axon causes oscillations, which may not be seen in sparse gaseous molecules in a large space. Physiological functions are thought to be the results of the sum of diffusion, attraction, and conformational changes of receptor proteins binding to biological molecules, i.e., ligands. Cardiac and smooth muscles are activated by conformational changes of proteins binding to a high-energy phosphate or diffusible Ca² + binding to polar receptor proteins such as ion channel protein and calmodulin. The small sinusoidal wave activity in the muscle fiber would relate to the oscillatory release of stored Ca² + from the ER or the SR and correspond to the muscle tone. In the refractory period, an impulse can not travel in the cell at all as depolarization of membrane potential cannot generate an action potential due to the inactivated voltage-gated Na+ channels. The degree of recovery of Na+ channels from inactivation can be altered by Na+ channel blocker, which causes a prolonged refractory period. Arrhythmias occur if the disorganized impulse originating in the ectopic focus interferes with normal transmission of an impulse from the SA. The cell with high Ca² + under sympathetic stimulation or in ischemic condition is considered a candidate for an ectopic focus of the premature contractions since it not only has low ion conductivity but also is excitable.

Keywords

Molecular interaction and diffusion; Conformational change of proteins; Automaticity; Oscillation of electrochemical potential; Peripheral circulation; Respiratory diseases; Cardiac arrhythmia; Ectopic depolarization

1.1: Molecular interaction and increases in entropy associated with diffusion

In the isolated system at equilibrium, the system has the maximum entropy, and then the Boltzmann distribution appears. The microstates and entropy associated with molecular interaction increase every time molecules collide, exchange kinetic energy in the space, and finally stop at the maximum when equilibrium is attained in an isolated system. The number of locations molecules probably take in a space provides the number of locations where they exchange positions and relates to the number of probable redistributions of the kinetic energy, which determines the number of microstates on molecular interaction. Huge microstates and entropy of gas are mainly as a result of the molecular interaction associated with an exchange of their kinetic energy, occurring every time they collide in an isothermal space. The collision generates pressure, and the partial pressure of gaseous molecules is proportional to the concentration. An interacting mass of gas molecules has the potential to spread spontaneously if they can obtain a sparser space (see Section 2.5). We can see this phenomenon during gas exchange in the lungs (see Chapter 9).

Liquid molecules have the microstates and entropy that are mainly associated with molecular interaction like gas molecules but are different from gas molecules in that liquid molecules fill the space and bump continuously exchanging their energy and positions. If liquid is kept in a container where molecules exchange kinetic energy randomly every time they collide, molecules exchange positions but is not able to diffuse. Molecules in a container may have about the same average kinetic energy due to continuous bumping with others under the isothermal condition. Entropy is kept the same under constant temperature. Diffusion called current will occur if we give more space to spread. Liquid is different from gas in that the space is fully occupied by molecules, and the speed of diffusion is slower than that of gas. Bumping between molecules produces pressure which drives them to diffuse. Mixing of different kinds of molecules cause diffusion (see Section 2.6).

In a living cell, highly concentrated Ca² + ions stored in the endoplasmic reticulum (ER) leak out through the ion channel, leading to electric potential change in the cell. If the ion conductivity of the channel is extremely low, ionic molecules may bump and travel zigzag through the narrow channel (see Section 5.9).

1.2: Functions of the cell membrane

The cell membranes are made of phospholipids, cholesterol, and proteins. The phospholipid bilayer forms the basic structure of the membrane. This self-orientation property of phospholipids leads the biological membrane into a closed spherical structure and reseals it by itself when torn out. Many of the transmembrane proteins that abut the extracellular fluid are glycoproteins. They not only give extra mechanical strength to the membrane but also make the cell capable of communicating with other cells. Some transmembrane proteins are channels and transporters. Only gases such as oxygen, carbon dioxide, and nitrogen, and small nonpolar lipid soluble molecules can diffuse freely through the phospholipid bilayer membrane along their concentration gradients. However, ions and polar molecules cannot diffuse through it, and their flux through the membrane requires channels or transporters that are made of columnar proteins firmly inserted into the phospholipid bilayer. Each kind of channels has a pore allowing the passage of only selected solute. Some channels are always open such as aquaporins (water channels) and potassium leak channels. But some channels have two states, open and closed, which can be controlled in response to the stimulus by binding a signaling molecule called a ligand to the receptor on the channel protein, or a change in membrane potential detected by means of the voltage sensor, or a mechanical force on the membrane by the pressure sensor. On the other hand, a transporter forms an intermediate complex with the solute, and a subsequent conformational change in the transporter causes translocation of the solutes to the other side of the membrane. Passive transport processes require no energy supply. They are designed for the diffusion of polar small molecules such as glucose and amino acids that are too large to go through membrane channels by themselves. Active transport processes are used for ions to diffuse across cell membranes against the electrochemical gradient by means of binding to a high-energy phosphate produced by ATP hydrolysis. Action of Na+-K+ ATPase is a good example of active transports.

The selective permeability of membrane creates osmosis, and interestingly along with the continuous actions of Na+-K+ ATPase, the membrane that is impermeable to Na+ and permeable to K+ at a resting state maintains the constant resting potential. Functions of living cells are regulated by charged or polar signaling small molecules called ligands. Some ligands can change the conformation of the ion channels in the cell membranes when they specifically bind to the receptors and open the channels for specific ions. The ion flux through the channels or transporters causes ionic current and can change the electric potential inside the cell (see Chapter 3). G protein-coupled receptors (GPCRs) are transmembrane proteins that detect ligands outside the cell and activate cellular responses via signal transduction pathways (see Section 7.3).

1.3: Oscillation of electrochemical potential in exciting living cells

We see diffusion when solids dissolve in liquid, different gases or liquids mix, solutes such as sodium ion spread in the fluid of the axon, or gases are dissolved in the blood. Diffusion is defined as the spread of solute moving from the area of higher concentration to the area of lower concentration along the concentration gradient. The concentrated area can be made by the injection of a solute into a solvent. Continuous bumping among different kinds of molecules produces pressure fluctuation that drives them down from the area of higher concentration to the area of lower concentration. The rate of diffusion depends on how much the molecules are concentrated in the certain area compared to its adjacent area, and it is inversely proportional to the resistivity of the tissue. The pressure produced by bumping between the same kind of molecule (A) drives them to push one away, while adjacent another kind of B molecule gets into the concentrated area of A molecules and replace A molecule with B molecule, thereby causing the diffusion by mixing. A higher concentration gradient suggests a higher probability of a collision between the same kind of molecules causing a replacement of one of the positions with another kind of adjacent molecule, thereby causing the diffusion by fast mixing. The speed of mixing is fast at first and gradually goes down. The diffusion by mixing will stop when its concentration becomes the same anywhere in the container, where entropy becomes maximized. Mixing makes entropy larger due to an increase in the number of probable incidences of redistribution of kinetic energy among different kinds of molecules under isothermal condition. We can see this phenomenon during gas exchange between blood and tissues (see Section 2.6.1).

If the solute is an ion or polar molecule, the speed of diffusion depends on the ion conductivity of the tissue and charges of the solute. Ions and polar molecules cannot pass through the phospholipid bilayer of the cell membrane and the scar tissue that have extremely low ion conductivity. They need channels and transporters to be able to pass through the membrane. If the ion resistivity of the channel is extremely high, the concentrated ionic molecules may bump and travel zigzag through it, which can make them oscillate. Diffusion of ions through a leak channel and injected ions in a model axon causes oscillations (see Sections 5.9 and 6.9), which may not be seen in sparse gaseous molecules in a large space. The oscillation of concentrated ions will cause the oscillation of electrical potential in living nerve and muscle fibers in an exciting state. By solving the cable equation, we found the membrane potential in the excited model axon shows a damped oscillation and withers over time and the distance that measures how far away from the origin of the current injection. This phenomenon is called diffusion and is evaluated mathematically. As the internal axoplasmic resistance is small, the oscillation damps fast. High friction is a prerequisite for consistent oscillation. Interestingly, similar damped oscillation occurs in the oscillatory release of stored Ca² + in the sarcoplasmic reticulum (SR) through RyR2 channels (see Section 5.9). The cyclic release of stored Ca² + from the SR or the endoplasmic reticulum (ER) was thought to be the basic source of the inherent automaticity. The RyR2 channels in the heart and IP3-gated Ca² + channels in the intestine provide the places where oscillatory Ca² + currents occur.

1.4: Physiological functions regulated by diffusion, attraction, and binding of ligands to their receptors

Physiological functions are thought to be results of the sum of diffusion, attraction, and binding of biological molecules in the cells. Different kinds of atoms have different abilities to attract electrons toward themselves, and the resultant bond has a partial ionic character. Electrostatic force attracts small polar molecules [1] and changes conformation of polar proteins. Cardiac and smooth muscles are activated by conformational change of proteins binding to a high-energy phosphate or to diffusible messengers, called ligands when binding to the polar site of a target proteins. A ligand is usually a small molecule which produces a signal by binding specifically to the site called a receptor on a target protein. Ligands may be hormones such epinephrin (EPI), or neurotransmitters such as GABA, glutamate, acetylcholine (Ach), and norepinephrine (NE), or substrates of enzyme, or second messengers such as cAMP, Ca²+, inositol triphosphate (IP3), and diacylglycerol (DG). Binding between a ligand and its receptor results from intermolecular forces such as electrostatic forces, which cause the conformational change of the target protein. The binding typically changes the three-dimensional shape of the target protein, which switch on various physiological effects depending on the target protein. The target protein may be (1) enzymes, (2) ligand-gated ion channels, or (3) G protein-coupled transmembrane proteins that bind selectively to hormones or the neurotransmitters. Neurons communicate one another by the neurotransmitter at the specialized small gap called a synapse. The neurotransmitter released from the terminals of presynaptic neuron diffuses across the synaptic cleft and activates the ligand-gated ion channels in the dendrites or cell body of the postsynaptic neuron to open, causing ion influxes to generate small localized-potentials called graded potentials in the dendrites and cell body. Graded potentials are either less negative than the resting membrane potential (>−70 mV), which makes the cell more excitable, or more negative compared to the resting potential (−70mV), which makes the cell not to excite. Influxes of positive ions such as Na+, Ca²+ cause the excitatory graded potentials in the cell body. Efflux of positive ion like K+ and influx of negative ion like Cl− cause the inhibitory graded potentials in the cell body. Once formed, the graded potentials are decaying over distance. Graded potentials vary in size which are the results of summation of the excitatory and inhibitory postsynaptic potentials. When the sum of the postsynaptic potentials reaches the threshold (−55 mV) at axon hillock, it opens voltage-gated sodium channel in the axon. The sudden Na+ influx initiates an action potential (see Chapter 6). G protein-coupled receptors detect ligands outside the cell and activate cellular responses by means of signal transduction pathways. The binding of the ligands to the receptors relays signals down to the interior of cardiac and smooth muscle cells and operates cellular metabolic responses via changing activities of the enzymes which catalyze production of second messengers such as cyclic AMP in cardiac and smooth muscles, and IP3 and diacylglycerol in smooth muscles (see Section 4.4).

1.5: Basic mechanism of automaticity and its modulation

The cyclic release of stored Ca² + from the SR produces the tone of the muscle and was thought to be the basic source of rhythmic cardiac automaticity. Pale oval P cells are located centrally in the SA and AV nodes and so named as they are pale, primitive, and pacemaker cells. These cells are oval or rounded in contrast to the elongated shape of other myocardial cells. They are low-conductive cells with a shorter refractory period and have slower depolarization rate. The P cells in the SA node initiate rhythmical impulses automatically at a regular speed, that is, 60–80 beats per minute. Additionally, the P cells in the AV node are called latent pacemakers, which take over rhythmic impulse activities at the slightly slower pace, i.e., 40–60 beats per minute if the SA node stops initiating