Physiology of Electrically Excitable Cells, Study notes of Physiology

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Physiology of Electrically

Excitable Cells

David McKinnon

Contents 1

Contents

Chapter 1 Cell Physiology Chapter 2 Ion Channels Chapter 3 Membrane Potential Chapter 4 Action Potentials Chapter 6 Structure and Function of Neurotransmitter Receptors Chapter 7 Synaptic Transmission Chapter 8 Functional Diversity of Voltage-Gated Channels Chapter 12 Models of Electrical Excitability Appendix 2 Numerical Methods for First Order Differential Equations This document is designed for the use of students at Stony Brook University. It contains images adapted from multiple copyrighted sources and is not to be reproduced in any form other than for the purposes of teaching.

(^1) Cell Physiology Many cells in the body have highly sophisticated electrical signaling mechanisms. These mech- anisms allow electrical impulses to travel within and between the cells of the nervous system. Elec- trical signaling translates ‘thought’ into action by triggering contractions in muscle and facilitates the control of organs within the body by triggering the release of hormones from various endocrine or- gans. The proteins that underlie these specialized electrical signaling functions are evolutionarily ancient. In most cases considerable similarity can be found between proteins used by the human brain for electrical signaling and proteins found in single cell prokaryotes. This is because cells, of all kinds, have to solve a common set of basic cell physiological problems. These problems include maintenance of salt balance, maintenance of osmotic balance, transport of useful solutes into the cell and transport of waste products out of the cell. The proteins that underlie these basic cellular func- tions have been elaborated and modified during the course of evolution to support other complex functions, including the electrical excitability of neurons and muscle cells. This elaboration of protein function by evolution has limits, however, and the molecular complexity of a neuron in a fruit fly brain and one in a human brain is similar. The much larger repertoire of behaviors seen in humans com- pared to flies is primarily a function of a more complex nervous system rather than the product of significantly more complex molecular and cellular physiology. Neural development in humans has accreted enormous complexity during the course of evolution, largely due to the evolution and elab- oration of gene regulatory function.

1. Evolution of Cellular Life

The events leading to the evolution of cellular life are very poorly understood. This ancient, apparently unique, historical event cannot be readily replicated, making it inaccessible for systematic study. Consequently, most writing on this topic remains highly speculative, if not hopelessly deluded. Even a fundamental question such as whether the pathway towards life began first with replicating nucleic acids or from a protein based origin currently remains unresolved. The evolution of the first protocells, small cells with a continuous cell membrane, was a major step in the evolution of life. Before the existence of membrane delimited structures it would have been difficult, or impossible, to define discrete individuals, whatever their biochemical basis. The cell membrane creates the basic delineation between self and non-self, creating the potential for compe- tition between individuals. From the time when individual protocells appeared it is reasonable to believe that the theory of evolution can explain all the subsequent pathways to more complex and diverse life forms. Evolution of the cell membrane represents the dividing line between life, as it is commonly understood, and non-living biochemical processes. The cell membrane’s critical role in the evolution of single cells comes about because it per- forms functions that are somewhat analogous to the property and patent laws of a capitalist economy. Like the property laws, the cell membrane distinguishes private property, what is inside the cell, from common property, everything outside the cell. This allows the cell to concentrate useful resources inside the cell (e.g. ATP, glucose) restricting them for the private use of the cell. An even more important property is that the cell membrane allows the cell to effectively pa- tent any novel innovations occurring in that cell’s genetic material by restricting the sharing of novel

proteins and metabolic products. If a cell has an advantageous mutation in its genetic material, that cell and its progeny will retain sole rights to the benefits afforded by that mutation for some time, potentially conferring a competitive advantage to cells in this lineage relative to other cells. The cell membrane can function in this way because it is an effective barrier to the transport of charged and polar molecules.

Physical Constraints on Cellular Physiology

Although the steps leading to the evolution of membrane bound, cell based life are not well understood there are several well defined physical constraints that definitely had to be resolved be- fore this could occur. Three particular problems were:

1. Transport of metabolites across the cell membrane
2. Regulation of internal calcium concentration
3. Regulation of osmotic balance/cell volume The solutions selected for these problems set the basic plan for all subsequent cellular life and reverberate to the present day. Much of the particular functionality of the neurons in your brain de- rive from the solutions selected several billion years ago to resolve these narrow apparently simple physical problems. The rest of this chapter and the next describe the basic solutions to these prob- lems.

2. Water

It is difficult to ignore the central role of water in virtually every aspect of cell physiology. Water is essential for life, as we understand the term. The human body is composed primarily of water molecules, which make up about 60 % of the total body weight and 99% of the total number of molecules. Water is a polar molecule, meaning that there is an uneven distribution of charge within the water molecule. The bonds between the oxygen and two hydrogen atoms are polar covalent bonds. The polarity of the covalent bonds results from the high electronegativity of the oxygen atom rela- tive to the hydrogen atom. As a consequence, a partial charge distribution exists such that there is a local positive charge on each hydrogen atom and a partial negative charge on the oxygen atom. The uneven distribution of electrons due to the nature of the H-O bond causes the water molecule to act as a dipole , meaning that the molecule has a positive and negative pole (Figure 1 ). Figure 1 Dipole nature of water, a polar molecule. There is a partial negative charge (2-) on the oxygen atom and partial positive charges (+) on the two hydrogen atoms. Water can form hydrogen bonds between the positively charged hydrogen atoms and nega- tively charged oxygen atoms in the neighboring water molecules. Since the angle between the two covalent bonds of water is about 105°, groups of hydrogen-bonded water molecules form tetrahedral arrangements (Figure 2 ).

Distribution of Ions in the Body

The water in the body can be divided into two main compartments: intracellular and extracel- lular. These two compartments are separated by the cell membranes of individual cells. Typical val- ues for the concentration of the most common ions in these two compartments are given in Table 1. These specific values will vary among different species and between different cells in the body but the general principle is that all animal cells have a relatively high intracellular concentration of K+ ions, a low intracellular concentration of Na+^ ions and a very low intracellular concentration of Ca2+ ions. The high concentration of NaCl in the extracellular fluid is similar to sea water and reflects our origins as ocean living organisms. There is a relatively high concentration of fixed anions inside the cell. These comprise all the organic compounds synthesized or sequestered by the cell, which have a net negative charge. Table 1. Ion concentrations in the intracellular and extracellular fluids of a typical mammalian cell Ion Intracellular Concentration (mM) Extracellular Concentration (mM) K+^ 125 5 Na+^ 12 120 Cl-^ 5 125 Ca2+^ 1 x10-^4 (100 nM) 2 A-^ 108 0 A-^ = the fixed anions, sum of all the proteins, amino acids (aspartate and glutamate), inorganic ions (sulfate and phosphate), nucleotides, DNA, RNA that are located inside the cell. Maintenance of this unequal distribution of ions between the inside and outside of the cell is a primary function of the cell and dictates much of the basic cellular physiology of every cell.

4. Cell Membrane

The role of the cell membrane in distinguishing the intracellular fluid from the extracellular fluid is made possible by the fact that it is such an effective barrier to the transport of ions and polar molecules.

Lipid Bilayer Structure

Cell membranes are composed of lipids and proteins. The predominant lipids in the cell mem- brane are phospholipids. Phospholipids have two distinct regions (Figure 4 ). A polar region that is hydrophilic (water loving) that interacts with water molecules and a nonpolar region that is hydro- phobic (water hating). Molecules that have a mixed chemical nature like this are known as amphi- pathic molecules.

Figure 4 (Left panel) Structure of a phospholipid molecule. Note the charged head of the molecule and the two long hydrophobic tails. (right panel) Arrangement of phospholipids in a lipid bilayer, with the heads pointing out to the aqueous solution and the hydrophobic heads sequestered in the interior of the membrane. The lipids assemble into a lipid bilayer (Figure 4 ), which is the lowest energy arrangement for phospholipid molecules. In this arrangement the hydrophobic tails point in towards the center of the bilayer, minimizing their interaction with water molecules. The hydrophilic heads interact with the water molecules surrounding the membrane. Although the lipid bilayer is very thin, it is a very effective barrier to the diffusion of many biologically important molecules. The interior of the lipid bilayer functions like a very thin layer of oil presenting an almost impermeable barrier to the diffusion of polar or charged molecules. In con- trast, hydrophobic molecules can pass easily because they can dissolve into the hydrophobic core of the lipid bilayer. Charged molecules like ions are only stable in a highly polarizable media such as water. It is essentially impossible for a charged molecule to cross the lipid bilayer because the core of the bilayer is non-polarizable. In electrical terms, it has a low dielectric constant. If the cell membrane was composed only of a lipid bilayer only hydrophobic molecules could enter and leave the cell, which would greatly limit the function of the cell. Real cell membranes also contain proteins, and a major function of these proteins is to facilitate the movement of ions and polar molecules across the membrane.

Cell Membrane Structure

Current ideas about how the cell membrane functions originate with the fluid mosaic model of Singer and Nicolson. In their model a class of proteins, known as integral membrane proteins , are sequestered within the lipid bilayer, something like icebergs floating in a lipid sea (Figure 5 ). These proteins have amphipathic properties, meaning that they have both nonpolar portions, which are buried in the hydrocarbon core of the bilayer, and polar or charged portions, which protrude from the bilayer to form a hydrophilic surface that interacts with the aqueous phase. Typically, charged residues in the protein are only found in regions that contact the aqueous solution.

voltage-gated channels the amino terminus of the protein is located intracellularly and the first mem- brane spanning domain functions as a start-transfer signal, causing the translocon to mediate the translocation of the peptide trailing this transmembrane sequence through the translocon pore. This displaces the intralumenal plug that normally gates the translocon channel. Transfer of the peptide continues until the translocon encounters a stop-transfer signal (typically the second membrane spanning domain) causing the translocon to stop transferring the peptide across the membrane, thereby allowing the peptide to accumulate on the cytoplasmic side. In general, alternating start and stop-transfer signals in the protein’s peptide sequence will combine to allow the channel to assemble with the correct membrane topology. This topology signaling can include cues from regions of the polypeptide outside the transmembrane domain of the protein and more complex schemes may be required to ensure that proteins with non-canonical transmembrane domains, such as voltage sen- sors and channel pores, can achieve the correct topology. In addition to having a trans-membrane pore for movement of the peptide across the mem- brane, the translocator complex is hinged and can open to allow the hydrophobic membrane span- ning domains of the ion channel-forming protein to partition into the hydrophobic core of the mem- brane ( Figure 7 ). By this means, the channel-forming protein is integrated into the lipid bilayer of the membrane. Translocation of the growing peptide occurs co-translationally, meaning that the transfer of the protein into the ER lumen and membrane occurs at the same time as the protein is being synthe- sized. In general, the pore-forming subunit will first undergo further maturation, aided by proteins associated with the translocon complex such as oligosaccharyl transferase as well as by ER resident Figure 7 Most integral membrane proteins have hydrophobic transmembrane (TM) domains of 20 – 25 residues in length that form membrane spanning α-helices in the fully assembled protein (marked with red and green in the figure). The first of these TM domains acts as a targeting se- quence to target the nascent peptide to the translocon in the ER membrane. This sequence is rec- ognized by the signal recognition particle (SRP), which targets the entire complex to the ER mem- brane by binding to the SRP receptor. The ribosome and nascent peptide then attach directly to the translocon. The first TM domain is recognized as a start-transfer sequence by the translocon. This initiates movement of the downstream peptide through the translocon pore into the ER lu- men. During subsequent translation of the protein the TM domains each signal to the translocon to start or stop transfer of the peptide across the ER membrane. The translocon has a lateral gate that can open to allow lateral transfer of each of the hydrophobic TM domains into the lipid bi- layer.

membrane chaperones (such as calnexin). Glycosylation of the channel peptide by oligosaccharyl transferase also occurs cotranslationally and can contribute to establishing the correct topology.

Diffusion of Hydrophobic Molecules through the Lipid Bilayer

There are several ways in which a solute can either enter or leave the cell. If the solute is hydrophobic (lipophilic) and can dissolve into the lipid membrane, it can cross the cell membrane by diffusion since the lipid bilayer does not present a diffusion barrier. Many key molecules can act like this: oxygen, carbon dioxide, fatty acids and steroid hormones are all examples of nonpolar molecules that diffuse rapidly through the lipid portions of membranes. The majority of molecules in the cell cannot diffuse through the membrane, or diffuse only poorly. For example, most of the molecules that make up the intermediate stages of the various met- abolic pathways are ionized or polar molecules that cannot cross the cell membrane. There is a good reason for this, it is inefficient for the cell to expend energy producing metabolic intermediates that can then simply diffuse out of the cell in an uncontrolled manner. For the typical polar and charged molecules found inside the cell the lipid bilayer represents an almost complete barrier to passive diffusion.

5. Membrane Transport

A diverse set of proteins facilitate the movement of polar and charged molecules in various ways across the cell membrane. These proteins fall into three major classes: Table 2. Classes of integral membrane proteins involved in transport of ions and polar molecules Pumps require energy in the form of ATP to move ions up their concentration gradients Transporters do not directly use energy in the form of ATP, are often linked to ion gradients that indirectly provide energy Ion channels facilitate diffusion of ions by creating pores across the cell mem-brane

6. Membrane Transport – Pumps

Most of the solutes distributed across the cell membrane are not in equilibrium. In particular, the major inorganic ions have steep distribution gradients across the cell membrane (Table 1). As a consequence, energy must be expended in order to maintain those transmembrane concentration gradients. Typically, the source of energy is chemical energy in the form of ATP. If the cell is poisoned so that ATP is no longer produced, then the transmembrane gradients dissipate and the cell dies. The proteins that actively transport solutes against their concentration gradients are known as membrane pumps. Four pumps have been identified, each is an ATPase and each is involved in transporting one or more of the following ions: Na+, K+, H+^ or Ca2+. Table 3. Membrane pumps Na,K-ATPase maintains the Na+, K+ ion gradients across the cell membrane Ca-ATPase maintains the very low intracellular Ca2+^ ion concentration H-ATPase maintains intracellular pH (H+^ ion concentration) H,K-ATPase acid secretion in stomach and kidneys

shape. The kinase function of the pump is used to phosphorylate the pump protein, which then in- duces the first conformational change (Figure 9 ). Dephosphorylation of the pump, to remove the co- valently linked phosphate group, results in the reversion of the pump to its original conformation. Figure 9 Cycle of Na+^ and K+^ binding and movement during one cycle of the Na,K-ATPase pump. The detailed structure of the Ca-ATPase pump has been solved. It is a large protein and has ten membrane spanning domains (Figure 10 ). There are two binding sites for Ca2+^ ions within the membrane and it has a very large intracellular domain, which contains the ATPase enzyme that hy- drolyzes ATP. The pump undergoes large rearrangements upon phosphorylation and dephosphory- lation of the ATPase site (Figure 10 ). This results in the rearrangement of the alpha helices in the membrane so that the Ca2+^ binding sites are moved from facing the intracellular region of the mem- brane to facing the extracellular region and also causes a reduction of the affinity for Ca2+^ ion binding so that the ions are released into the extracellular fluid or the interior of membrane bound organelles. Figure 10 Conformational changes of the Ca-ATPase before and after phosphorylation.

This requirement for a large conformational change limits the rate at which ion pumps can move ions across the membrane. In general, the pumps are continuously active in order to keep up with the flux of ions through the membrane’s ion channels, which allow ions to move very rapidly down their ion concentration gradients. In most cells the ion channels turn on for only brief periods of time in order to limit the amount of work required of the pumps. An exception to this is found in cardiac myocytes, where the Ca2+^ pumps have to return Ca2+^ ions back to the lumen of the sarcoplas- mic reticulum after it has escaped through Ca2+^ channels that remain open for the duration of the cardiac contraction. In this case, very high concentrations of the Ca-ATPase pump are required in the SR membrane in order to keep up with the calcium release and this protein makes up a large fraction of the total membrane protein in cardiac cells. This is one reason why we are so vulnerable to ische- mia during a heart attack. When blood flow stops even for a short period of time there can be signif- icant damage to the cardiac muscle because it fails to meet the energy demands of the Ca-ATPase pump.

Ion Gradients as Sources of Cellular Energy

The generation of ion gradients by pumps is one way in which the cell can convert chemical energy, stored in the form of ATP, into another form of chemical energy, in this case a concentration gradient of ions. The gradient of ions acts as a source of chemical energy that can be used for other cellular functions such as secondary active transport. The generation of ion gradients can also function to convert chemical energy into electrical energy. The ion gradients created by the pumps allow the generation of an electrical potential across the cell membrane, known as the membrane potential.

7. Membrane Transport - Transporters

Pumps and ion channels only move ions across the cell membrane. All cells, however, have to transport a large number of solutes in addition to ions. These solutes belong to a diverse set of bio- chemical molecules that are useful to the cell, including amino acids and glucose. In general, the dif- ferent chemical natures of these solutes requires that there are specialized transport systems for each type, or at least class, of molecule that is transported. There are two types of transport systems, those that facilitate the movement of solutes down their concentration gradients and those that actively transport the solute up a concentration gradient (Figure 11 ). As mentioned earlier, hydrophobic mol- ecules can move freely cross the membrane without the requirement of a specific transport system. It would be self-defeating to actively transport these molecules since their movement is not limited by the cell membrane and they could easily diffuse back across the membrane.

than directly use ATP. They are active transporters, like pumps, in that they move solutes up a con- centration gradient. An important example of a secondary active transporter is the Na+/glucose transporter (Figure 13 ). In addition to having a binding site for glucose the glucose transporter has an additional binding site for a Na+^ ion. The binding of the Na+^ ion to the transporter alters the affinity of the binding site for glucose. The change is brought about through allosteric modification of the protein’s confor- mation as a result of ion binding. One glucose molecule is translocated up its concentration gradient at the cost of one Na+^ ion moving down its concentration gradient. The Na+/glucose transporter is used to actively transport glucose out of the intestines and into the blood stream and also out of the kidney tubules and back into the blood. Figure 13 Na+/glucose transporter. During secondary active transport a solute can be transported either into the cell ( cotran- sport ) or out of the cell ( countertransport ). In both cases, however, Na+^ ions move into the cell, down their concentration gradient (Figure 14 ). Figure 14 Cotransport and countertransport. Another important secondary active transporter is the Na-Ca countertransporter, or Na-Ca exchanger. This uses downhill movement of sodium ions into the cell to move calcium ions out of the cell by secondary active transport. Other transporters linked to the sodium ion gradient move amino

acids. Amino acids can be actively transported out of the kidney tubules and into the blood by so- dium-driven transporters. Related transporters mediate the reuptake of some neurotransmitters from the synaptic cleft in the nervous system.

Structure of Secondary Active Transporters

The LacY transporter is the prototype for transporter proteins. The LacY transporter mediates the coupled cotransport of lactose and protons (H+) down a proton gradient in prokaryotyes. It has a roughly symmetrical clamshell-like structure with twelve membrane spanning domains (Figure 15 ). Figure 15 Structure of lactose permease (LacY). Note the two different conformations of the trans- porter Relatively large movements of the protein are required to produce the translocation of the solute binding site. Like pumps, active transporters move solutes slowly compared to the movement of ions through ion channels.

8. Membrane Transport - Ion channels

The function of ion channel proteins is captured almost perfectly by their name, they are chan- nels through which ions can pass across the membrane. Ion channels are integral membrane proteins and they shield the charged ions from the hydrophobic lipid bilayer as the ions cross the cell mem- brane (Figure 16 ). One key feature of ion channels is that they show ion selectivity. There are chan- nels that only let K+^ ions to pass and channels that only let Na+^ ions to pass. Figure 16 A K+^ selective ion channel and a Na+^ selective ion channel in the cell membrane. At rest, in a typical cell, only a small number of channels are open and available to pass ions at any one time. Collectively, the channels open in a resting cell are known as the leak channels and these leak channels are predominantly K+^ selective with few or no Na+^ channels open. As a conse- quence, at rest, the cell membrane is predominantly permeable to K+^ ions. Ion channels are found in the cell membrane of all cells in the human body and in the cell membranes of almost all living organisms, and many viruses. Ion channels are of particular interest in electrically excitable cells because of their key role in generating electrical excitation. The other two types of transporters are also ubiquitous and create the basic cellular environment necessary to

remove the ions from the intracellular fluid. The buffers limit the duration and extent of the change in free Ca2+^ ion concentration within the cell. Figure 18 Summary of the various systems for handling Ca2+^ ions within the cell.

Ca2+^ Ions as Second Messengers

Perhaps oddly, given the effort that cells expend in keeping internal Ca2+^ ion concentrations low, Ca2+^ ions have an important role as intracellular signaling molecules. Although an apparently unlikely candidate, given the simple nature of these molecules, Ca2+^ ions modulate the function of a myriad of proteins and a wide variety of cellular functions are sensitive to changes in intracellular Ca2+^ ion concentrations. Typically, increases in Ca2+^ ion concentrations are triggered by the opening of Ca2+^ channels, either in the cell membrane or in the membranes of the organelles that sequester Ca2+^ ions. These calcium fluxes produce a transient increase in the free calcium ion concentration in the cell that trig- gers downstream cell signaling pathways. This signaling system is used by all cells but is particularly important for electrically excitable cells because it provides a means of converting an electrical signal into a biochemical one. Examples of important cellular functions dependent on Ca2+^ signaling include synaptic transmission and muscle contraction.

Internal Ca2+^ Concentration and Cell Death

Maintenance of a low intracellular Ca2+^ ion concentration is critical for normal cell function. In most cells, a prolonged increase in intracellular Ca2+^ ion concentrations rapidly leads to cell death. Blockade of blood flow (and thus oxygen) in the brain or the heart quickly leads to ischemic tissue damage in these organs. The brain and the heart are very metabolically active tissues and as a consequence use up their local energy supplies very quickly. This makes them particularly vulner- able to ischemic tissue damage because the maintenance of low Ca2+^ ion concentrations inside the cell is strongly dependent on maintained cellular energy levels. The decrease in local oxygen tension during ischemia results in a rapid fall in ATP levels inside the cell, which leads to a rise in calcium levels. The rise in intracellular calcium levels can trigger cellular processes that lead to the destruc- tion of the cell.

11. Maintenance of Cell Volume

The most abundant molecules both inside the cell and in the extracellular solution are water molecules, which make the major contribution to the volume of the intracellular and extracellular solutions. As a consequence, the flow of water into or out of the cell across the cell membrane is the primary determinant of changes in cell volume.

Water Channels

The cell membrane is highly permeant to water molecules. For much of the history of cellular physiolgy the high permeability of the cell membrane to water was something of a mystery because H 2 O is a highly polar molecule that cannot easily cross the lipid bilayer. It was ultimately determined that there are specialized membrane transport proteins for water molecules known as water chan- nels (or aquaporins ). Water channels are integral membrane proteins, analogous to ion channels, that provide a low resistance pathway for the movement of water molecules across the cell membrane.

Osmolarity

Osmolarity is a measure of the concentration of osmotically active particles in a solution, typ- ically expressed as osmoles of solute per liter of solution. For molecules such as glucose, sucrose and urea that do not dissociate, a solution containing 1 mole of dissolved molecules in 1 liter of water is a 1 osmole/liter solution. For salts or acids dissolved in solution the situation is slightly more complex because these compounds dissociate into two or more ions in solution. For NaCl, which dissociates into two dissolved particles, the Na+^ and Cl-^ ions, a 1M NaCl solution is a 2 osmole/l solution. For CaCl 2 , which dissociates into three ions, a 1M CaCl 2 solution is a 3 osmole/l solution.

Regulation of Cell Volume

Maintaining a balance between the osmolarity inside the cell versus the osmolarity of the ex- tracellular solution is critical to maintain the integrity of the cell membrane. To limit potential dam- age to the cell membrane, the osmolarity of extracellular solution is kept within relatively tight limits, in the range 275 - 295 mosmole/l in mammals. To understand the effect of changes in intracellular or extracellular osmolarity on cell volume it is important to recognize that water has a concentration (number of molecules per unit volume) just like the solutes dissolved in a solution. The concentration of H 2 O molecules in pure water is ap- proximately 55.5M. If sugar molecules are dissolved into water the volume of the resulting solution increases because the sugar molecules take up some volume in the solution. Assuming that each so- lute molecule takes up the space of one water molecule, for a 1 M glucose solution, the water concen- tration falls to approximately 54.5M, significantly less that the 55.5M value for pure water. As a con- sequence, the concentration of water molecules in a sugar solution is lower than it is in pure water. Water can flow down its concentration gradient across the cell membrane, just like membrane permeable solutes. If the concentration of water outside of a cell is higher than it is inside the cell, water will flow into the cell across the cell membrane until the concentration of water is equal on each side of the membrane. An extreme example of this is if a cell is placed in distilled water (water containing no ions or other solvents). In this case the cell rapidly expands and dies, because the os- molarity inside the cell is much higher than outside and water flows rapidly into the cell, down its concentration gradient.