302_HW_8_solutions

BIOE 302: Modeling Human Physiology Fall 2023 Bioengineering, University of Illinois at Urbana-Champaign 1 BIOE 302: Modeling Human Physiology Fall 2023 Bioengineering, University of Illinois at Urbana-Champaign 1 Problem Set 8, Due: November 3 by 10am, online. Respiratory System Problems: 1. What is: A. hypoxia? B. hypercapnia 2. Do problem 11 in Problem Set 6.2, page 684. Note: Problem 2C is just asking for a conversion from ml plasma to ml blood – directly related to hematocrit. 3. Oxygen binding to hemoglobin is positively cooperative. What does that term mean? Looking at the Hill equation in Equation 6.4.2, plot the saturation ratio of hemoglobin (hemoglobin with oxygen, [HbO2] to total possible oxygen bound to hemoglobin [HbO2] max ), as a function of the partial pressure of oxygen across a physiologically reasonable range. Note that we are replacing the [O 2 ] in this equation with P aO2 . Use K = 4500 mmHg (units raised to power of h, i.e. mmHg h ) and Hill coefficients, h, of 0.5, 1, and 2.4. Which Hill coefficient makes a plot similar to the way oxygen and hemoglobin in blood behave? 4. We have had strange weather this fall, with some days being into the 80 ’ s and others starting at the 30 ’ s. On one of the 80-degree days, you are running across the quad, describe how changes in three physiological parameters lead to meeting the increased oxygen demand of running. (Hint: think about oxyhemoglobin dissociation curve shifts.) 5. List three general classes of receptors that enable the body to monitor respiration. What physiological parameters are measured by each receptor. Where is the information from these receptors utilized to control respiration? Which receptor is sensitive to the partial pressure of oxygen? 6. Describe the different mechanisms by which carbon dioxide is transported in the blood. How does this relate to pH of the blood - use the Henderson-Hasselbalch equation in your answer. Muscular System Problems: 7. What is tetanus? Why would it be referred to as temporal summation? Why is the force generated by a twitch so much smaller than that generated during tetany? 8. What is an eccentric contraction? What is a concentric contraction? What is an isometric contraction? Which one produces the greatest force? 9. Describe differences between fast-twitch and slow-twitch muscle fibers. Generally fast-twitch motor units (or muscles) are larger in diameter than slow-twitch motor units (or muscles). Why would this make fast-twitch motor units generally stronger than slow twitch motor units? 10. Draw a sarcomere and label the following: Z-line, H-zone, M-line, A-band, I-band. Which region has thin filaments but no thick filaments? Which region contains all the thick filaments? 11. Describe the steps of the actin-myosin crossbridge cycle. Include the role of ATP and how force is generated. 5 Completion 14 7 6 6 8 6 8 8 5 8 2 pts each part: 1) setup, 1) answer 3) Plots, 2) Code 2) which Hill coefficient 2 for each of three parameters: 1) parameter 1) how it changes (which direction curve shifts) 2 for each of three receptors: 1) receptor name 1) what it measures 2 pt each mechanism of transport (bicarbonate, carbaminoHb, dissolved), 2 for acid/base Carbonic acid, with HH equation 2 pts for each of three questions 2 pts for each of four questions 6) 3 differences, 2 each: myosin type, glycolytic/oxidative, fatigue. 2) more in parallel, forces in parallel add Completion 2 points for each step. Sequential, but can start anywhere in cycle. Completion Completion

BIOE 302: Modeling Human Physiology Fall 2023 Bioengineering, University of Illinois at Urbana-Champaign 2

BIOE 302: Modeling Human Physiology Fall 2023 Bioengineering, University of Illinois at Urbana-Champaign 4 3. Positive cooperative binding refers to the increasing affinity between hemoglobin and oxygen as more oxygen binds, up to the 4 atoms of oxygen that bind to each atom of hemoglobin. Binding of each O 2 makes the affinity higher to bind the next O 2 . A hill coefficient of h=2.4 matches well the observed oxyhemoglobin dissociation curve.

BIOE 302: Modeling Human Physiology Fall 2023 Bioengineering, University of Illinois at Urbana-Champaign 5 IN ADDITION:

BIOE 302: Modeling Human Physiology Fall 2023 Bioengineering, University of Illinois at Urbana-Champaign 7 𝑝𝐻 = 𝑝𝐾 𝑎 + log ( 𝐻𝐶𝑂 3 − 𝐻 2 𝐶𝑂 3 )

BIOE 302: Modeling Human Physiology Fall 2023 Bioengineering, University of Illinois at Urbana-Champaign 8 7.

BIOE 302: Modeling Human Physiology Fall 2023 Bioengineering, University of Illinois at Urbana-Champaign 10 Region with only thin filaments and no thick filaments is the I-band. Region with only thick filaments and no thin filaments is the H-zone. The thick filaments are fully contained in the A band.