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In the numeral 6238, the 6 represents 6 * .

A Survey of Mathematics with Applications | 9th Edition | ISBN: 9780321759665 | Authors: Allen R. Angel, Christine D. Abbott, Dennis C. Runde ISBN: 9780321759665 194

Solution for problem 4.1.148 Chapter 4.3

A Survey of Mathematics with Applications | 9th Edition

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A Survey of Mathematics with Applications | 9th Edition | ISBN: 9780321759665 | Authors: Allen R. Angel, Christine D. Abbott, Dennis C. Runde

A Survey of Mathematics with Applications | 9th Edition

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Problem 4.1.148

In the numeral 6238, the 6 represents 6 * .

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Physiology notes: Weeks One and Two Book/Lecture/Lab Notes - Levels of organization o Chemical level o Cellular level o Tissue level o Organ level o Body system o Organism - Tissues o Cells of similar structure and specialized function combined o Four primary tissues  Muscle  smooth, cardiac, skeletal  Nervous  send signals through body  Epithelial  protection (skin), lines digestive tract  Connective  connects tissues - Organ o Body structure that integrates different tissues and carrier at a specific function - Body system o Collections of organs that perform similar functions o Combine to form the organism o 11 total body systems:  Nervous system  Muscular  Circulatory  Digestive  Endocrine  Respiratory  Reproductive  Urinary  And three others… - Homeostasis o The maintenance of a dynamic steady state in an internal environment o Each cell helps maintain the internal environment shared by cells o Factors maintained homeostatistically:  Temperature  pH (to acidic or basic, proteins die)  oxygen and carbon dioxide  nutrient concentration  colume and pressure  concentrations of water, salt, and other electrolytes (cell size)  concentration of waste products o negative feedback  a change in controlled variable triggers a response that drives the variable in the opposite direction of the initial change  example is temperature o positive feedback  amplifies the initial change  moves the system away from the set point  uncommon  example is childbirth - Major functions of cell membrane proteins o Transport  Protein pores and gated channels  Carrier proteins  Sodium Potassium ATPase enzyme proteins o Recognition  Surface glycoproteins as markers  Antigen recognition receptors on immune cells o Signal reception  Surface protein receptors for hormones, nerve transmitters and other factors: physical stimuli o Attachment  Protein junctions attach cell to cell  Adhesion proteins stick cell to surface for crawling (wbc’s) anchoring (tendon to bone) association of cells into tissues o Generation of electrical potentials  Separation of charge/ions causes a voltage to develop; especially important in explaining actions of nerve, muscle and hair-cell membranes o Membrane attached enzymes  Associated with receptor or carrier proteins or alone o Cell shape, structure  Proteins in the shapes of rods, tubes and fibers can form an elaborate framework inside the cell membrane, called the cytoskeleton that gives the cell its shape - Sodium Potassium ATPase Pump o The Sodium Potassium ATPase pump transports three sodium out of the cell for every two potassium pumped in o Cell loses more positive charge than it gains o Primary role of the pump is to actively maintain sodium and potassium concentration gradients o Only make a small direct contribution to resting membrane potential - Equilibrium potentials o Potential that would exist at equilibrium for a given ion o Two opposing factors  Concentration gradient  Electrical gradient o Potassium acting alone would establish an equilibrium potential of -90mV  Attracted to inside of cells negative charge o Sodium acting alone would establish an equilibrium potential of +60 mV  When inside reaches +60mV, Sodium gets pushed out o Equilibrium potentials are determined using the Nernst Equation - Resting Membrane Potential o RMP is 25 to 30 times more permeable to Potassium than Sodium - Excitable Cells o Neurons and muscle cells can rapidly and transiently alter their membrane permeability - Membrane Electrical States o Depolarization  Decrease in potential, membrane less negative o Repolarization  Return to resting potential; membrane more negative o Triggering event  A triggering event triggers a change in the membrane potential by altering membrane permeability  4 types of gated channels  Voltage-gated channels  open in response to membrane potential change  Chemically gated channels  open by something binding to them  Mechanically gated channels  Thermally gated channels - Permeability o If a substance can cross the membrane, the membrane is permeable to the substance o Two properties determine permeability  Lipid solubility  Particle size - Permeation through lipid bilayer o Gases can actively pass through o Steroids can pass through o Small uncharged polar molecules  slowly (water, glycerol) o Will not cross  Large uncharged polar molecules (sucrose, glucose)  Ions (sodium potassium) - Passive Transport o No energy required o Down concentration gradient o Rules of Passive Transport:  Passive transport does not require added energy (uses thermal)  The membrane must be selectively permeable to a given substance  Molecules may move in both directions (bidirectional) during passive transport  Molecules, ions, or atoms ALWAYS move from higher concentration to lower concentration  The movement of each species of particle by passive transport is considered separately.  The rate of passive diffusion of a particular substance is proportional to the permeability factor and to the difference in concentrations on each side of the membrane o Three types:  Simple diffusion  Osmosis  Facilitated diffusion o Simple Diffusion  Diffusion  is the movement of molecules from high concentration to law concentration  Unassisted and passive  Uniform spreading out of molecules due to random intermingling  Occurs until equilibrium is reached o Osmosis  Similar to passive transport  How water moves - Iso-osmotic Solution o No net movement of water into or out of the cell o If a solution is iso-osmotic, the cell neither swells nor shrinks, but remains the same volume o **0.29 moles of dissolved particles/liter - Ion Channels o Ions move across the membrane through channels o Specific to the type of ion passing through o Ions move through channel  Down their concentration gradient  Down electrical gradient - Fick’s Law of Diffusion o Concentration of gradient of substance, rate of diffusion goes up o Surface area of the membrane, goes up o Lipid solubility, rate of diffusion goes up o Molecular weight of substance, rate of diffusion goes down o Distance (thickness of membrane), rate of diffusion goes down - Osmosis o Is the process of water moving passively down its own concentration gradient to an area of higher solute concentration o Water channels  aquaporins  4 types, important in kidneys o Definitions  Pure water  100% water, 0% solvent  Solute  90% water, 10% solvent  Hydrostatic pressure  Pushing pressure, opposes water  Osmolarity  Total number of solute particles per liter  Moles and osmoles o Osmole  1 mole of solute particles  1 mole glucose = 1 osm/L  1 mole NaCl = 2 osm/L - Osmotic Pressure o The pressure required to stop osmosis o “pulling pressure” - Tonicity o The effect a solution has on a cell volume o An isotonic solution has the same concentration of solute as normal body cells (300 m Osm/L) o Hypotonic  Below normal concentration of solutes (expand) o Hypertonic  Above normal concentration of solutes (shrink) - Facilitated Diffusion o Requires a carrier protein o Assisted membrane transport o The carrier moves the particle down the concentration gradient  Carriers are bidirectional, flows to where concentration is higher o Passive o Example: Glucose  Binds to carrier protein, changes conf. so binding site is exposed to lower concentration: ejected into cell - Assisted Membrane Transport o Carrier mediated transport characteristics  Specificity  Saturation  Transport maximum  Competition  Amino acids compete for carrier proteins - Active Transport o Energy is required o Area of low to high concentration o Against concentration gradient o 2 types:  Primary active transport  Requires direct use of ATP  Examples: Na+/K+ pump  Secondary Active Transport  Driven by an ion concentration gradient  Two types: o Symport  Driving ion down concentration gradient  Helps other ion o Antiport  Opposite direction  Sodium usually - Membrane potential o The plasma membranes of all cells are polarized electrically o The separation of opposite charges across the plasma membrane o When anions and cations are equal on both sides, no potential o When excess positive ions, positive potential o Electrically negative charges on both sides separate to make neutral o Magnitude of potential  More charge has more membrane potential (number of separated ions) o Nonexcitable cells and excitable cells at rest is constant  Nonexcitable ranges from -40 to -80 o Measured in millivolts (mV) o Typical resting membrane potential is -70mV o -90mV (skeletal muscle) o Influenced by the permeability of a few important ions  Sodium, potassium, large anions (negative proteins) - Na+/K+ ATPase Pump o The pump transports 3 Na+ out of the cell for every 2 K+ it pumps in o Cell loses more positive charge than it gains o Primary role of the pump is to actively maintain Na+ and K+ concentration gradients o Only makes a small direct contribution to the resting membrane potential - Equilibrium potentials o Is the potential that would exist at equilibrium for a given ion o 2 opposing factors:  Concentration gradient  Electrical gradient o K+ acting alone would establish an equilibrium potential of -90 mV  Attracted to inside the cell’s negative charge o Na+ acting alone would establish an equilibrium potential of +60 mV  When inside reaches +60mV, Na+ gets pushed out o Equilibrium potentials are determined using the Nernst Equation - Graded Potential (GP) o Flow is between the active area and adjacent inactive area o Flow is passive o The magnitude of a GP varies directly with the magnitude of a stimulus o Example  Postsynaptic potential, endplate o Die out over a short distance (decramental) o Summation  Sum together at cell body, triggers AP - Action Potential (AP) o An AP is a brief, rapid, large, change in membrane potential o Occur when an excitable cell membrane is depolarized to threshold potential o At threshold, changes in Na+/K+ permeability are initiated o During resting potential, Na+ ions enter the cell along a concentration gradient and a long electrical gradient - Voltage Gated K+ Channels o Voltage gated K+ channels have one activation gate o Can exist in 2 conformations:  Closed/open - Voltage Gated Na+ Channels o Activation gate (sliding door) o Inactivation gate (ball and chain) o Can exist in three conformations:  Closed but capable of opening  Open (activated)  Closed and not capable of opening - Activation Potential Propagation o An action potential generates a new AP in the area next to it o AP’s propagate in one direction o AP’s do not diminish as they propagate (non-decremental) - Action Potentials o Very few K+ and Na+ actually cross the membrane during an AP - Refractory Periods o The Na+/K+ pump gradually restores the ions that moved during the ATP o After an AP the membrane enters its refractory period o Refractory periods endure one way propagation of AP’s - Action potentials o All or none o Variable strength of stimuli are coded by varying the frequency of action potentials, not their size - Two types of AP Propagation o Continuous conduction  In unmyelinated fibers o Salutatory conduction  Myelinated fibers - Continuous propagation o Slow conduction velocity o The AP spreads along every patch of membrane down the axon o Accomplished by local current flow - Myelin o Thick layer of lipids that cover the axon o Acts as an insulator to prevent leakage of current o Myelin farming cells are Schwann cells and digodendrocytes  Schwann Cells in PNS  Oligos in CNS o Between the myelinated regions are the nodes of Ranvier  No voltage gated channels in myelinated regions - Saltatory Conduction o Myelinated axons o 50 times faster than continuous conduction o The impulse (axon potential) “jumps” from node to node - Synapses o The junction between neurons o 2 types:  Electrical synapses  Neurons connected directly by gap junctions  Less common (5-10% in nervous systems)  Important in hippocampus of brain  Chemical synapses  Neurotransmitters (nts) are transmitted across the junctions separating neurons  More common o Chemical Synapse  A junction between the axon terminal of one neuron and the dendrites or cell body of a second neuron  First neuron is presynaptic neuron  Second neuron is postsynaptic neuron - Dendrites  electrical activity enters - Axon  electrical activity leaves o Myelinated (wrapped in myelin sheath) - All cells have sodium – potassium pumps o Sodium out (low concentration) 10x o Potassium (high concentration) 30x o Negatively charged proteins stay in cell  Anion o Sodium channels always closed - **like charges repel, opposite attract o Potassium leaves, cell gets negative - Resting potential o Due to movement of potassium (K+) ions, the only ion that can freely cross the membrane when cell is at rest - Stimulus o Something that activates sodium channels o If too many channels open, pumps have hard time  More passive transport makes cell positive - Depolarization becomes more negative - Threshold o Stimulus no longer required o Charges coming in are the stimulus o Goes from threshold to depolarization (runaway) o K+ leaves cell negative, Na+ leaves cell more positive o When Na+ becomes to high, gate closes and opens K+ channels - Conduction  instant electrical activity - Propagation  movement of action potential down a nerve o Can cause Na+ channels to open to start new action potential - Wrap of myelin leaves gaps between – leave nodes of Ranvier - Insulator – does not allow charges to cross - MS/ALS  associated with demyelination Muscles - 50% weight muscle - Muscle types o Striated muscle  Skeletal cardiac o Unstriated muscle  Smooth o Voluntary muscle  Skeletal o Involuntary muscle  Cardiac  Smooth  **autonomic nervous system - Skeletal Muscle o A single skeletal muscle cell is a muscle fiber  Large, elongated, and cylindrically shaped  Multinucleated  Fibers extend entire length of muscle  Lots of mitochondria - Myofibril o Muscle fibers composed of myofibrils o Each myofibril made of regular arrangement of  Thick filaments  myosin  Thin filaments  actin - One sarcomere is one functional unit - Z line  thick protein disk - H zone  only thick filament present - Thin  actin - Z  Z are one sarcomere - A band (thick filament length) - I band thin to thin (no thick filament present) - Myosin o Component of thick filaments o Consists of 2 identical subunits  Two tails  Two heads  Heads form cross bridges between thick and thin filaments  Actin binding site  Mosin ATPase site o Need energy o Cross bridges project from each thick filaments in 6 directions - Actin o Thin filaments consist primarily of actin o Actin interacts with the myosin cross bridges - Regular proteins o Tropomyosin  Lies alongside groove of actin spiral  Covers myosin sites blocking cross bridge binding o Troponin  Made of 3 polypeptides units  One binds to tropomyosin  One binds to actin  One binds to calcium - Sliding filament mechanism o Thin filament on each side of the sarcomere side inward over stationary thick filaments o As all sarcomeres shorten, entire fiber shortens

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Chapter 4.3, Problem 4.1.148 is Solved
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Textbook: A Survey of Mathematics with Applications
Edition: 9
Author: Allen R. Angel, Christine D. Abbott, Dennis C. Runde
ISBN: 9780321759665

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In the numeral 6238, the 6 represents 6 * .