Mission Memo:
Physiology Act 1
Background
Despite your efforts to treat Xor, she remains weak and disoriented. To make matters worse, the herd will not leave Xor to continue their journey. If we cannot help Xor recover quickly, the other megaraffes will soon be in danger.
Having ruled out dehydration as a cause of Xor’s symptoms, three potential causes remain: (1) a low concentration of oxygen in the blood, (2) a low concentration of carbohydrates in the blood, and (3) a high blood pressure in the arteries. You must investigate the homeostatic systems that regulate these three variables in a megaraffe. Use the following questions to guide your work.
- How does a megaraffe regulate oxygen and carbohydrate concentration and blood pressure in the body needed to survive? (Appendix 1)
- How should we treat Xor if one of her homeostatic systems has failed? (Appendix 2)
Universally in your debt,
The AI
You have been asked to determine how to help Xor’s symptoms.
Appendix 1
How does a megaraffe regulate variables in the body that affect the reactions needed to survive?
To survive, an organism must regulate many variables in the body that affect the chemical reactions of life. For example, a megaraffe must ensure its blood carries sufficient resources to all cells in the body. These resources include carbohydrates and oxygen (O2), which are needed to fuel critical cell reactions. Illness or death could occur if an organism cannot deliver enough resources.
Xor’s disorientation might have resulted from her failure to regulate the concentration of O2 ([O2]) or carbohydrates in her blood or from her inability to maintain the blood pressure needed for the blood to carry these resources to cells.
The regulation of blood O2 concentration, blood carbohydrate concentration, and blood pressure are critical to the survival of a megaraffe. On Earth, systems of cells, tissues, and organs in every large, multicellular organism collaborate to maintain these variables within a narrow range needed to sustain life. The process of regulation, called homeostasis, is how organisms such as megaraffes keep their internal conditions within limits necessary for survival.
We must use a path model of a homeostatic system to diagnose whether Xor’s symptoms stem from a failure to regulate the concentration of O2 ([O2]), concentration of carbohydrates ([carbohydrates]), or blood pressure. Let’s start with practice interpreting a path model of a homeostatic system that regulates the concentration of O2 in the blood of megaraffes.
We need to complete the following step to understand how megaraffes regulate the O2 concentration in their blood.
Step 1: Interpret a path model: Interpret a path model of a homeostatic system that regulates O2 concentration in the blood of megaraffes. This step will prepare us to diagnose potential causes of Xor’s condition and determine the appropriate treatment.
Step 1: Interpret a path model
All organisms, from bacteria to complex species, must maintain a stable internal environment despite external changes—a process known as homeostasis. This stability is crucial for survival, as organisms rely on homeostatic mechanisms to regulate essential variables like blood oxygen levels, glucose concentration, blood pressure, and body temperature. Each regulated variable has a set point, representing the ideal value the organism attempts to maintain. When deviations occur, the body activates a homeostatic response to restore balance.
A homeostatic system consists of three key components: a sensor, an integrator, and one or more effectors. The sensor detects changes in the regulated variable and transmits this information to the integrator, which processes the data and determines an appropriate response. The effectors then respond, adjusting the variable to bring it back toward the set point. For example, if body temperature rises, thermoreceptors in the skin and brain detect the change and send signals to the hypothalamus, which acts as the integrator. The hypothalamus then activates effectors such as sweat glands to cool the body, restoring temperature to its optimal range.
Homeostasis operates through negative feedback loops, meaning that any deviation from the set point triggers a response that counteracts the change. Figure 1 illustrates a generic model of a homeostatic system, showing the interactions between the sensor, integrator, effectors, and the regulated variable. The sensor detects fluctuations in the variable and relays this information to the integrator, which then directs the effectors to restore stability. Each arrow in the diagram represents a cause-and-effect relationship between components.
Figure 1. This diagram represents a generic homeostatic system as a path model, illustrating how different components interact to regulate a variable. The regulated variable is shown in a dashed box, while solid boxes represent the sensor, integrator, and two effectors (Effector 1 and Effector 2). Arrows indicate cause-and-effect relationships, showing how the sensor detects changes, the integrator processes information, and the effectors adjust the variable to maintain stability.
While Figure 1 provides a basic framework, it does not indicate whether an increase in one component leads to an increase or decrease in another. Figure 2 expands upon this by introducing positive (+) and negative (-) relationships, which describe how components interact.
Figure 2. This path model of a generic homeostatic system illustrates how components interact to regulate a variable, now incorporating positive (“+”) and negative (“-“) symbols to indicate relationships. The regulated variable is shown in a dashed blue box, while the sensor (red box), integrator (green box), and two effectors (yellow boxes) are represented as solid boxes. Arrows connecting these components indicate cause-and-effect relationships, with a red “+” symbol signifying a positive relationship, where an increase in one component leads to an increase in the next (or a decrease leads to a decrease), and a blue “−” symbol indicating a negative relationship, where an increase in one component leads to a decrease in the next (or vice versa). The model shows that the regulated variable influences the sensor, which in turn affects the integrator in a positive relationship. The integrator then activates Effector 1 while simultaneously inhibiting Effector 2, leading to Effector 1 increasing the regulated variable and Effector 2 decreasing it. This expanded model clarifies how homeostatic systems regulate variables through activation and inhibition, ensuring stability in a dynamic environment.
A positive relationship (+) means that the next component’s activity also increases as one component’s activity increases—conversely, a decrease in one results in a decrease in the other. A negative relationship (-) indicates that as one component’s activity increases, the next component’s activity decreases, and vice versa. For example, in some systems, increasing the activity of an integrator may enhance the function of one effector while suppressing the activity of another.
One common misconception is that a positive (+) symbol always represents an increase in activity, but this is not necessarily the case. Instead, a positive relationship simply means a direct correlation between two components, whether that means an increase or a decrease. Similarly, a negative (-) symbol does not always indicate a decrease in activity but rather an inverse relationship between two components.
In Figure 2, the sensor positively influences the integrator, meaning that when sensor activity increases, integrator activity also increases. However, the integrator positively affects one effector while negatively affecting another, illustrating how opposing effectors help regulate a variable.
The principles of homeostasis extend beyond biological systems and can be observed in engineered systems, such as building temperature regulation. Figure 3 models a homeostatic system that controls air temperature in an Intergalactic Wildlife Sanctuary (IWS), providing an analogy to bodily homeostasis.
Figure 3. This figure presents a homeostatic system regulating air temperature in the Intergalactic Wildlife Sanctuary (IWS), alongside graphical representations of positive and negative relationships between two variables. The top section contains two graphs: one illustrating a positive relationship where an increase in one variable leads to an increase in another (red line), and another showing a negative relationship where an increase in one variable leads to a decrease in another (blue line). The bottom section displays a path model of the air temperature regulation system, where thermocouples (sensors), AI processors (integrator), heaters, and coolers (effectors) interact. The regulated variable, air temperature, is represented by a dashed blue box, while solid arrows with “+” and “−” symbols indicate whether relationships are positive or negative. This model demonstrates how a homeostatic system maintains stability, adjusting heating and cooling based on real-time temperature fluctuations.
In this system, thermocouples act as sensors, continuously measuring air temperature and relaying this information to processors, which function as integrators. The processors compare the detected temperature to a set point and adjust the heaters and coolers (effectors) accordingly. If the temperature is too high, the coolers activate while the heaters deactivate. If the temperature is too low, the heaters activate while the coolers shut off. This dynamic ensures that the air temperature remains stable.
When the air temperature rises above the set point, the thermocouples detect the change and reduce their signaling. This decrease reduces processor activity, deactivating the heaters and activating the coolers. As a result, the air temperature decreases back toward the set point. When the air temperature falls below the set point, the thermocouples increase their signaling, activating the heaters and deactivating the coolers, restoring warmth.
One key takeaway from this model is that opposing effectors—heaters and coolers—work to fine-tune regulation. Many homeostatic systems function similarly, using multiple effectors to maintain a precise balance. However, not all homeostatic systems rely on opposing effectors; some use multiple sensors or integrators to achieve the same goal.
Blood oxygen concentration: How does O2 get to cells?
The archives of the Intergalactic Wildlife Sanctuary (IWS) contain important information about how megaraffes regulate key physiological variables. Like humans, one of the most critical factors for a megaraffe’s survival is maintaining sufficient oxygen (O) levels in the blood. Oxygen is essential for cellular respiration, the process that generates energy for movement, growth, and reproduction. As cells use oxygen, they produce carbon dioxide (CO2) as a waste product, which must be expelled from the body. But how does oxygen reach body tissues, and how is CO2 removed?
Oxygen makes up about 21% of the air in Earth’s atmosphere. Breathing allows organisms to take in O2 and remove CO2. The diaphragm, a muscle at the base of the lungs, controls the movement of air. When the diaphragm contracts, the lungs expand, and air flows in from the atmosphere (inhalation). When the diaphragm relaxes, the lungs return to their original size, pushing air out (exhalation). Figure 4 illustrates how air moves into and out of the human lungs.
Figure 4. This diagram illustrates how humans inhale and exhale air through changes in chest cavity volume and diaphragm movement. The left panel (Breathe In) shows air entering the lungs as the diaphragm contracts downward, expanding the chest cavity and pulling air in. The right panel (Breathe Out) shows air leaving the lungs as the diaphragm relaxes upward, compressing the chest cavity and forcing air out.
Once air enters the lungs, it reaches tiny air sacs called alveoli (singular: alveolus). These alveoli are surrounded by capillaries, the smallest blood vessels in the body, where gas exchange occurs. O2 diffuses from the alveoli into the capillaries, entering the bloodstream to be delivered to body tissues. At the same time, CO2 diffuses from the blood into the alveoli, where it is expelled from the body when exhaled. Figure 5 illustrates this critical exchange process.
Figure 5. This diagram illustrates how oxygen (O2) and carbon dioxide (CO2) are exchanged between the alveoli and capillaries in the human lungs. The upper portion shows the lungs, bronchioles, and alveolar sacs, with a magnified view of an alveolus and its surrounding capillaries. The lower portion focuses on the gas exchange process, where O2 diffuses from the alveoli into the blood, oxygenating it, while CO2 diffuses from the blood into the alveoli to be exhaled.
Once oxygen enters the blood, the cardiovascular system ensures it reaches cells, tissues, and organs while removing CO2. Blood vessels transport oxygen-rich blood to the body and return CO2-rich blood to the lungs. The heart pumps blood through these vessels, ensuring continuous circulation.
The cardiovascular system has two main circuits:
- Pulmonary Circulation: Deoxygenated blood flows from the heart to the lungs, where O2 is absorbed, and CO2 is released. The now oxygenated blood returns to the heart.
- Systemic Circulation: Oxygen-rich blood is pumped from the heart to body tissues, where O2 diffuses into cells, and CO2 diffuses into the blood. The deoxygenated blood then returns to the heart.
This continuous cycle ensures a constant supply of oxygen and removes CO2 waste. Figure 6 provides a simplified view of the human cardiovascular system, which is similar to that of a megaraffe.
Figure 6. Diagram illustrating the cardiovascular system in humans, broken down into pulmonary and systemic circulation. Deoxygenated blood in the pulmonary circuit flows from the heart, to the lungs where it is reoxygenated and where CO2 gas diffuses out of the capillaries and into the lungs, and then back to the heart. Then, this oxygenated blood in the systemic circuit flows from the heart, to tissues throughout the body (such as the liver, stomach and intestines, kidneys, and other tissues throughout the body) where O2 diffuses into the tissues from the blood while CO2 diffuses from the tissues to the blood, and then back to the heart.
Since oxygen is critical for survival, organisms must carefully regulate the amount of O2 in the arterial blood, which carries oxygen to the body’s tissues. This regulation ensures that cells receive enough oxygen for energy production while removing CO2 efficiently. The arterial blood oxygen concentration, abbreviated as [O2] in the blood, is an essential measurement for understanding respiratory and circulatory health.
Blood oxygen concentration: Interpreting a homeostatic system
To regulate blood oxygen levels, megaraffes use a homeostatic system that involves sensory, integrative, and effector components. Below is a description of how key physiological structures contribute to this regulation.
- Carotid Body: These specialized cells detect oxygen concentration (O2) in the blood. When O2 levels drop, the carotid body increases its rate of signaling. Conversely, when O2 levels rise, the carotid body reduces its signaling.
- Medulla Oblongata: This brain region receives input from the carotid body about O2 levels. When the carotid body signals more frequently, the medulla oblongata increases its own signaling output. When the carotid body signals less frequently, the medulla oblongata reduces its signaling.
- Diaphragm: The diaphragm controls breathing by contracting and relaxing. A higher rate of signaling from the medulla oblongata causes the diaphragm to contract more frequently, increasing breathing rate and allowing more oxygen to enter the bloodstream. A lower signaling rate leads to slower diaphragm contractions, reducing breathing rate.
Figure 7 presents a path model illustrating how these components interact to regulate O2 levels in megaraffe blood.
Figure 7. This diagram represents the homeostatic system that regulates oxygen concentration ([O2]) in the blood of megaraffes. The regulated variable, [O2] in the blood, is shown in a dashed black box. The system consists of three key components: the carotid body (sensor), the medulla oblongata (integrator), and the diaphragm (effector), each represented by a solid black box.
Arrows between the components indicate relationships, with “+” symbols representing positive relationships (increasing one variable increases the next) and “-” symbols representing negative relationships (increasing one variable decreases the next). The diagram shows how low [O2] levels increase signaling from the carotid body, which stimulates the medulla oblongata, leading to increased diaphragm contractions, ultimately raising blood oxygen levels.
Now that we have modeled the homeostatic system by which a megaraffe regulates the [O2] in its blood, you can practice interpreting this model.
Directions: Use the information above and Figure 7 to answer questions 1-10.
- Which component in this model is most likely the sensor?
- Carotid body
- Diaphragm
- Medulla oblongata
- Which statements accurately explain the function of a sensor in the context of a homeostatic system regulating O2 concentration? Select ALL that apply.
- The sensor detects changes in the concentration of O2 in the blood and relays this information to the integrator.
- The sensor directly adjusts the contraction rate of the diaphragm to regulate O2 concentration.
- The sensor is affected by changes in O2 concentration and influences the activity of the integrator based on these changes.
- The sensor independently regulates the activity of effectors without involving the integrator.
- The sensor’s activity is inversely related to O2 concentration in the blood.
- The sensor measures the regulated variable (O2 concentration) and signals to another component to address deviations from the set point.
- Which component in this model is most likely the integrator?
- Carotid body
- Diaphragm
- Medulla oblongata
- Which statements accurately describe the function of the integrator in the context of the homeostatic system regulating O2 concentration? Select ALL that apply.
- The integrator receives information from the sensor(s) and directly affects the activity of the effector(s).
- The integrator measures the magnitude of the regulated variable and relays this information to the sensor(s).
- The integrator sums the information from all sensors to coordinate an appropriate response.
- The integrator’s activity is directly influenced by changes in the activity of the sensor(s).
- The integrator directly detects changes in O2 concentration and adjusts the set point accordingly.
- The integrator directly affects the activity of the diaphragm to regulate O2 concentration.
- Which component in this model is most likely the effector?
- Carotid body
- Diaphragm
- Medulla oblongata
- Which statements accurately describe the function of the effector in the context of the homeostatic system regulating O2 concentration? Select ALL that apply.
- The effector measures the magnitude of the regulated variable and sends information to the integrator.
- The effector directly affects the magnitude of the regulated variable.
- The effector’s activity is directly influenced by changes in the activity of the integrator.
- The effector sums information from the sensor(s) and coordinates a response.
- The effector directly affects the activity of the sensor(s) in the system.
- The effector regulates the concentration of [O2] in the blood by altering its own activity.
- What independent variable(s) directly affect the dependent variable “[O2] in Megaraffe Blood”? Select ALL that apply.
- Rate of contraction by the diaphragm
- Rate of signaling by the carotid body
- Rate of signaling by the medulla oblongata
- What independent variable(s) indirectly affect the dependent variable “Rate of contraction by the diaphragm”? Select ALL that apply.
- Concentration of oxygen [O2] in the blood
- Rate of signaling by the carotid body
- Rate of signaling by the medulla oblongata
- As the rate of signaling by the medulla oblongata ____, the rate of contraction by the diaphragm ____. Select ALL that apply.
- increases, increases
- increases, decreases
- decreases, increases
- decreases, decreases
- As the concentration of O2 [O2] in the blood ____, the rate of signaling by the carotid body ____. Select ALL that apply.
- increases, increases
- increases, decreases
- decreases, increases
- decreases, decreases
Figure 8. Regulation of oxygen concentration (O₂) in Megaraffe blood and its relationship with different signaling rates. The top diagram illustrates the feedback mechanisms involving the rate of contraction by the diaphragm, signaling rates by the medulla oblongata and carotid body, and O₂ concentration in blood. Positive and negative symbols indicate stimulation or inhibition of pathways. Figures A, B, and C show scatter plots representing three different types of relationships between two continuous variables: a negative linear relationship (A), a positive linear relationship (B), and no significant relationship (C).
Directions: Use Figure 8 to answer questions 11-14. Three figures, Figures A, B, and C show a different linear relationship. The red line in each figure represents a trendline exhibited from the relationship between an independent variable and a dependent variable. For questions 11-14, select the figure that bests depicts the linear relationship between each of the following interactions:
- Independent variable = concentration of O2in the blood of megaraffes; Dependent variable = rate of signaling by the carotid body.
- Figure A
- Figure B
- Figure C
- Independent variable = rate of signaling by the carotid body; Dependent variable = rate of signaling by the medulla oblongata.
- Figure A
- Figure B
- Figure C
- Independent variable = rate of signaling by the medulla oblongata; Dependent variable = rate of contraction by the diaphragm.
- Figure A
- Figure B
- Figure C
- Independent variable = rate of contraction by the diaphragm; Dependent variable = concentration of O2 in the blood of megaraffes.
- Figure A
- Figure B
- Figure C
Appendix 2
How should we treat Xor if one of her homeostatic systems has failed?
Excellent work! Thanks to your efforts, we are ready to interpret path models of the homeostatic systems that regulate three variables in megaraffes:
- the concentration of O2 in the blood
- the concentration of carbohydrates in the blood
- the blood pressure in the arteries
With these models, we can identify potential causes of Xor’s condition and propose treatments.
Given that Xor is disorientated, sluggish, and uncoordinated—the potential causes of her symptoms have been narrowed down to three conditions:
- a low concentration of O2 in the blood,
- a low concentration of carbohydrates in the blood
- a high blood pressure in the arteries
To help Xor, we must first diagnose the cause of her symptoms. Then, we’ll need to determine how to treat Xor by calculating the appropriate dosage of any drugs to be provided.
We need to complete the following steps to decide how to help Xor.
Step 1: Determine the cause of and treatment for Xor’s low concentration of O2 in the blood: Use the path model of the homeostatic system of blood O2 regulation to determine potential causes of Xor’s symptoms and the best treatment to correct Xor’s potentially low blood O2 concentration.
Step 2: Determine the cause of and treatment for Xor’s low concentration of carbohydrates in the blood: Use the path model of the homeostatic system of blood carbohydrate regulation to determine potential causes of Xor’s symptoms and the best treatment to correct Xor’s potentially low blood carbohydrate concentration.
Step 3: Determine the cause of and treatment for Xor’s high blood pressure: Use the path model of the homeostatic system of blood pressure regulation to determine potential causes of Xor’s symptoms and the best treatment to correct Xor’s potentially high blood pressure.
Step 1: Determine the cause and treatment for Xor’s low concentration of O2 in the blood.
If Xor is suffering from a low concentration of O2 in her blood, we must determine the possible cause. We can use our path model to diagnose a disruption to the homeostatic system that regulates the O2 concentration in the blood. We interpreted this path model in Appendix 1, Step 1 of this mission memo (Figure 8).
The path model enables us to calculate how a change in the value of one variable directly or indirectly affects the expected value of another variable. Let’s consider an example using a system we’ve explored previously— Intergalactic Wildlife Sanctuary Temperatures.
Figure 9. Figure 9 shows how an increase of 10 signals per second in the rate of signaling by processors raises the activity of heaters by 12 kilowatts in the air temperature regulation system of the Intergalactic Wildlife Sanctuary. The path model on the left illustrates the relationships between signaling rates, heaters, coolers, and air temperature, while the right side focuses on the calculation example.
Imagine that the air temperature in a system rises above the normal level and doesn’t go back down. To figure out why this happens, we need to look at the different parts of the system that control the temperature.
First, let’s focus on the effectors, which are parts of the system that directly change the temperature. In this example, the effectors are the heater and the cooler. If the cooler stops working, it won’t be able to lower the temperature. On the other hand, if the heater keeps running without stopping, it will cause the temperature to keep rising.
Next, we need to think about what might cause the heater or cooler to malfunction. This leads us to the integrator, which is a processor that sends signals to control the heater and cooler. If the integrator sends too many signals, it could cause the cooler to work less and the heater to work more. This happens because of the different types of relationships shown in the path model: a negative relationship between the processor’s signals and the cooler’s activity, and a positive relationship between the processor’s signals and the heater’s activity.
We also need to consider the sensors in the system, called thermocouples. These sensors send signals to the integrator based on the air temperature. If the sensors send too many signals, the integrator will also send more signals to the heater and fewer to the cooler, causing the temperature to keep rising.
This example shows how we can use a path model to figure out what might go wrong in a system that is supposed to keep things at a normal level, like air temperature. By looking at how different parts of the system affect each other, we can diagnose what might be causing the problem.
We have used path models to predict how a variable would positively or negatively affect other variables, but we can also use a path model to quantify these effects. Previously, we learned how to quantify a relationship between variables with a linear model. This type of model quantifies a direct relationship between an independent variable and a dependent variable.
For example, consider the arrow pointing from the variable called rate of signaling by the thermocouple toward the variable called rate of signaling by the processors. This arrow tells us that the rate of signaling by the thermocouple is the independent variable and that the rate of signaling by the processors is the dependent variable. Finally, the positive (+) or negative (-) symbol over each arrow indicates whether the relationship between the variables is positive or negative. Recall that the linear relationship tells us how a change in the independent variable’s value will change the dependent variable’s expected value.
Importantly, the relationship between independent and dependent variables alone cannot tell us the expected value of the dependent variable; we’d also need to know an independent variable value. Assume that the relationship between the rate of signaling by the processors and the activity of the heaters is 1.2 kW/signal/sec (kiloWatts per signal/ second). How much should the activity of the heater change if the rate of signaling by the processors increases by 10.0 signals/sec? Let’s rearrange the data:
Change in Dependent Variable=Relationship ChangeIndependent Variable Values
Change in Dependent Variable=1.2kW1.0 signals/sec 10.0 signals/sec
Change in Dependent Variable=12.0 kW
In this example, the relationship change = 1.2 kW/signals/sec. If the rate of signaling by the processors increases by 10.0 signals/sec. Based on this calculation, we should expect the activity of the heater to increase by 12.0 kW if the rate of signaling by the processors increases by 10.0 signals/sec. Figure 9 illustrates this calculation.
Determining how to treat Xor for a low concentration of O2 in the blood
Now that we know how to calculate the direct effect of one variable on another variable, you’re ready to determine how to treat Xor if she has a low concentration of O2 in the blood.
According to my digital archives, the O2 concentration of blood must drop to at least 92.0% to cause the symptoms we observed in Xor. Fortunately, we have a variety of medications at the sanctuary, including a drug that can raise the O2 concentration of the blood. The drug works much like the drugs used on your planet to treat humans with asthma. At the correct dosage, the drug increases the opening of the airways that lead to the lungs. Consequently, more air flows into the lungs each time the diaphragm contracts. We’ll have to determine how much of this drug to give Xor if we discover that she suffers from a low O2 concentration.
Figure 10 (below) shows the path model for the homeostatic system that regulates the concentration of O2 in the blood of a megaraffe under normal conditions when a megaraffe is healthy (on the left). For simplicity, this figure highlights only those relationships relevant to your calculations.
Figure 10. Figure 10 shows the homeostatic system that regulates oxygen concentration in megaraffe blood. It highlights the relationships between the rate of contraction by the diaphragm, the rate of signaling by the medulla oblongata, the rate of signaling by the carotid body, and blood [O2]. A calculation example demonstrates how a change in the diaphragm’s contraction rate impacts [O2] levels, indicating that for every additional contraction per minute, blood [O2] increases by 6.3%.
Under normal conditions in the absence of the drug, Xor should be taking 15.0 breaths/minute or have 15 diaphragm contractions/minute, and the arterial blood [O2] should equal 95.0%. The relationship between the rate of contraction by the diaphragm and the [O2] in the blood of megaraffes is 6.3% O2 per 1 contraction/min, or 6.3% O2 / (contraction/min) under these conditions.
Directions: Based on the background information, select all answers to question 15. Use Figure 10 to answer questions 16-17 (below). The questions are regarding the homeostatic system that regulates the concentration of O2 in the blood of a megaraffe. For questions 16 and 17, express your answer as a decimal, rounding the value to the nearest tenth of a decimal place. For example, if you calculate a probability of 0.48, report a value of 0.5.
- Which scenario(s) would result in a low concentration of O2 in the blood of a megaraffe? Select ALL that apply.
- Fatigue caused the diaphragm to contract less frequently.
- Genetic mutations caused the carotid body to respond more strongly to a change in the O2 concentration of the blood.
- Neurological disorders caused the medulla oblongata to send fewer signals per unit of time.
- Traumatic injury caused the medulla oblongata to continually send more signals than normal to the diaphragm regardless of the O2 concentration of the blood.
- None of the scenarios listed above would result in a low concentration of O2 in the blood.
- Calculate the percent of [O2]/(contraction/minute) in Xor’s blood if she takes 15.0 breaths per minute and her blood oxygen level is 92.0%.
- How much higher or lower is the percent of [O2]/(contraction/minute) that you calculated in Question 16 compared to the healthy value of 6.3% [O2] per contraction per minute? Note: If your answer to this question is a positive value, then you are saying you want to raise the %[O2] / (contraction/min) by that value. Conversely, if your answer to this question is a negative value, you are saying you want to lower the %[O2] / (contraction/min) by that value.
Good work! Now we know how the relationship between the rate of contraction by the diaphragm and the [O2] in Xor’s blood would change if Xor’s breathing rate remained unchanged while her blood [O2] dropped to 92.0%. The oxygen concentration in the blood must drop to cause the symptoms we observed in Xor. Now, we must determine how much drug we should give to Xor if her [O2] is lower than normal.
Because the drug alters how much air flows into the lungs each time the diaphragm contracts, the drug alters the relationship between the rate of contraction by the diaphragm and the [O2] in Xor’s blood. If we’re going to determine how much drug we should give Xor, we first must model the relationship between the drug dosage and the relationship between the rate of contraction by the diaphragm and the [O2] in Xor’s blood. This will then allow us to determine how much of the drug to administer to return the relationship between the rate of contraction by the diaphragm and the [O2] in Xor’s blood back to 6.3% [O2] / (contraction/min).
Directions: For questions 18-19, use the Phys Act 1 Workbook from your Canvas assignment and refer to the sheet titled “Q18 Linear Relationship.” This sheet contains the drug dosage and the relationship between the rate of contraction by the diaphragm and the [O2] in the blood (sample size = 13). Use Excel for calculations, modeling, and graphing. For questions 19 and 20, express your answer as a decimal, rounding the value to the nearest hundredth of a decimal place. For example, if you calculate a probability of 0.448, report a value of 0.45. For question 21, express your answer as a whole number. For example, if you calculate a probability of 243.54, report a value of 244.
- Create a plot of a linear relationship between the dose of the drug and the relationship between the rate of contraction by the diaphragm and the [O2] in the blood. This plot should follow the formatting guidelines listed below.
Formatting Instructions
- Chart type: X Y (Scatter)
- Quick layout: Layout 1 – Scatter (you can delete the key/legend on the right if you want)
- Chart title: “Relationship of [O2]/(contraction/min) and Drug Dosage”, Font size = 20
- Y-axis title: “Relationship of [O2]/(contraction/min))”; Font size = 16
- Y-axis numbers: Font size = 14
- Y-axis bounds: minimum at 6.10, maximum at 6.50
- X-axis title: “Drug dose (g)”; Font size 16
- X-axis numbers: Font size = 14
- X-axis bounds: minimum at 3, maximum at 9
- Trendline: Solid or dashed line
- Add an equation for your trendline (optional: add R²)
- Calculate how much the percent of [O2]/(contraction/minute) changes for each gram of the drug. You can find this value using Excel’s trendline equation or slope function.
Thanks to your efforts, we’re ready to determine how much of the drug to administer to Xor to return the relationship between the rate of contraction by the diaphragm and the [O2] in Xor’s blood back to 6.3% O2 / (contraction/min) and thus raise Xor’s blood [O2] back to 95.0%, alleviating Xor’s symptoms should her blood [O2] levels be too low.
- According to your calculations in question 19, how much does the percent of [O2]/(contraction/minute) change for each 1 gram of the drug?
- Based on your answers to questions 17 and 20, how many grams of the drug would Xor need to reach the healthy oxygen level of 6.3% [O2] per contraction per minute? Note: Based on previous research, the drug is ineffective at dosages of 4.0 g or less, so make sure to add 4.0 g to your final answer no matter what.
Step 2: Determine the cause of and treatment for Xor’s low concentration of carbohydrates in the blood.
Excellent work! Now, we know how to treat Xor if we discover she has a low [O2] in her blood. However, if Xor has a normal [O2] of blood, we should consider another potential cause of her symptoms: a low concentration of carbohydrates in her blood.
Blood carbohydrate homeostasis in megaraffes
Like all organisms, megaraffes constantly need energy to perform the cellular processes that keep them alive. These processes range from building new molecules to repairing damage and removing waste. Everything an organism does—moving, breathing, and even eating—relies on energy. Where do organisms get this energy? Like you, megaraffes must consume food. That food contains fats, proteins, and carbohydrates (also called sugars). Organisms break all of these molecules down to produce energy; however, some cells, such as brain cells, rely primarily on carbohydrates for energy. When your blood sugar gets too low, you may feel irritable, anxious, or hungry; these symptoms are signs that your body needs food to produce energy. In between feeding, your body’s homeostatic system works to maintain a concentration of blood sugars within an acceptable range. Failure to do so could eventually cause more severe symptoms and even death.
I searched my digital archives for information about the components of the system that regulate the [carbohydrates] in the blood of a megaraffe. This information is summarized below.
Carbohydrate receptors: These receptors are activated when carbohydrates bind to them. Thus, when more carbohydrates are in the blood, the probability that these receptors will be activated increases. Conversely, when fewer carbohydrates are in the blood, the probability that these receptors will be activated decreases.
Concentration of hormone G: Hormone G is a peptide hormone. This hormone binds to receptors on liver cells. When bound to its receptors, it activates these receptors and causes liver cells to release stored carbohydrates into the bloodstream, effectively adding carbohydrates to the bloodstream. As the pancreas increases the rate at which it releases hormone G into the bloodstream, the concentration of hormone G in the bloodstream increases. Conversely, as the pancreas decreases the rate at which it releases hormone G into the bloodstream, the concentration of hormone G in the bloodstream decreases.
Concentration of hormone I: Hormone I is a peptide hormone. This hormone binds to receptors on cells throughout the body, including liver cells. When bound to its receptors, it activates these receptors and causes these cells to take up and use or store carbohydrates, effectively removing carbohydrates from the bloodstream. As the pancreas increases the rate at which it releases hormone I into the bloodstream, the concentration of hormone I in the bloodstream increases. Conversely, as the pancreas decreases the rate at which it releases hormone I into the bloodstream, the concentration of hormone I in the bloodstream decreases.
Pancreas: This organ receives signals regarding the [carbohydrates] in the blood. This organ can release two different hormones, hormone I and hormone G.
Hormone I: As the pancreas receives more signals, it increases the rate at which it releases hormone I into the bloodstream. Conversely, as the pancreas receives fewer signals, it decreases the rate at which it releases hormone I into the bloodstream.
Hormone G: As the pancreas receives more signals, it decreases the rate at which it releases hormone G into the bloodstream. Conversely, as the pancreas receives fewer signals, it increases the rate at which it releases hormone G into the bloodstream.
Figure 11. This figure shows a path model of the homeostatic system that regulates carbohydrate concentration ([carbohydrates]) in the blood of megaraffes. The regulated variable, [carbohydrates], is represented by a dashed box. Solid boxes represent other components: carbohydrate receptors, the pancreas, hormone G, and hormone I. Arrows between these boxes show relationships, with plus (+) or minus (-) symbols indicating whether these relationships are positive or negative. For example, hormone I has a negative effect on carbohydrate levels, while hormone G has a positive effect.
Figure 11 shows a path model of the homeostatic system that regulates the [carbohydrates] in the blood of megaraffes. With this information, we can analyze a path model of a homeostatic system to determine what could have caused a low concentration of carbohydrates in Xor’s blood.
How to use a path model of a homeostatic system to quantify an indirect effect
Previously, we learned how to quantify a relationship between variables with a linear model. This type of model quantifies a direct relationship between an independent variable and a dependent variable. However, path models also enable one to consider indirect effects in a system, as well as direct effects. How should we expect a change in one variable’s value to indirectly affect another variable?
Path models help us understand how changes in one variable can indirectly affect another in a series of connected variables. In this example, we’ll see how changes in the rate of signaling by processors can influence air temperature in the Intergalactic Wildlife Sanctuary (IWS) by affecting the activity of heaters first. To do this, we’ll use two methods: the stepwise approach and the integrative approach.
Figure 12. This figure shows a path model of the homeostatic system that regulates air temperature in the Intergalactic Wildlife Sanctuary (IWS) and illustrates how to calculate the indirect effect of changes in one variable on another using a stepwise approach. The regulated variable, air temperature, is shown in a dashed box, while other components like thermocouples (sensors), AI processors (integrator), coolers, and heaters (effectors) are in solid boxes.
Arrows between these components indicate relationships, with “+” or “−” symbols showing if these relationships are positive or negative. In the top part of the figure, Step 1 demonstrates how a 10 signals/second increase in the rate of signaling by processors leads to a 12 kW rise in heater activity. Step 2 shows that this 12 kW increase raises air temperature by 1.2 °C. This example highlights how changes in signaling rates can influence air temperature through linked components.
Stepwise approach
The stepwise approach involves breaking down the problem into smaller steps and solving each step one at a time. In this example, we want to know how a change in the rate of signaling by processors affects air temperature. The path we’ll follow is: Processors → Heaters → Air Temperature
We start by calculating how an increase of 10 signals per second in the rate of signaling by processors affects the activity of heaters. According to the path model, the relationship between these variables is given as 1.2 kW per signal per second. This means that for every additional signal per second, heater activity increases by 1.2 kW.
Processors → Heaters
Change in Heaters=Relationship ChangeProcessors Value
Change in Heaters=1.2kW1.0 signals/sec 10.0 signals/sec
Change in Heaters=12.0 kW
This means the activity of the heaters increases by 12 kW when the rate of signaling increases by 10 signals per second.
Now that we know heater activity increases by 12 kW, we calculate how this change affects air temperature. The path model shows that for every kilowatt increase in heater activity, air temperature rises by 0.1 °C per kW.
Heaters → Air Temperature
Change in Air Temperature=Relationship ChangeChange in Heaters Value
Change in Air Temperature=0.1°C1.0kW 12.0 kW
Change in Air Temperature=1.2 °C
So, a 12 kW increase in heater activity results in a 1.2 °C rise in air temperature.
The stepwise approach simplifies the process of understanding how changes in one part of a homeostatic system affect another by breaking the calculation into smaller, manageable steps. In this example, a 10 signals per second increase in the rate of signaling by processors first leads to a 12 kW rise in heater activity. This is determined by multiplying the change in signaling rate by the relationship between signaling and heater activity, ensuring that units are canceled appropriately. Next, the 12 kW increase in heater activity is used to calculate the resulting change in air temperature by multiplying it by the relationship between heater activity and air temperature. This second step shows that the 12 kW rise in heater activity leads to a 1.2 °C increase in air temperature. By following each step in sequence and focusing on one relationship at a time, the stepwise approach makes it easier to track how an initial change propagates through a system.
Integrative approach
The integrative approach simplifies the process of calculating the effect of a change in one variable on another by combining all steps into a single calculation. To find the indirect effect of a 10 signals per second increase in the rate of signaling by processors on air temperature, we multiply three parts directly.
First, we use the rate of signaling by processors, which is 10 signals per second. Next, we multiply this by the relationship between the rate of signaling by processors and heater activity, which is 1.2 kW per signal per second. This step gives us 12 kW as the increase in heater activity. Then, we take the 12 kW result and multiply it by the relationship between heater activity and air temperature, which is 0.1 °C per kW. This final step provides the change in air temperature. Processors → Air Temperature
Change in Air Temperature=Multiple Conversions between RelationshipsProcessors Value
Change in Air Temperature=0.1°C1.0kW1.2kW1.0 signals/sec 10.0 signals/sec
Change in Air Temperature=0.1°C1.0kW1.2kW1.0 signals/sec 10.0 signals/sec
Change in Air Temperature=1.2 °C
By multiplying these parts directly, the integrative approach quickly determines that an increase of 10 signals per second in processor signaling would indirectly cause a 1.2 °C rise in air temperature, providing the same result as the stepwise approach but in a more streamlined manner.
To effectively use path models for understanding homeostatic systems, it is essential to identify the path, use units to guide calculations, and choose an appropriate approach for solving the problem. Identifying the path involves determining the series of variables that connect the starting point to the end point of interest. Paying attention to units is also crucial; ensuring that units cancel out properly at each step helps verify that calculations are done correctly and that the final result is meaningful. Additionally, selecting the right approach is important. The stepwise approach is useful for breaking down complex paths into simpler, manageable steps, making it easier to follow the impact of each variable. On the other hand, the integrative approach is helpful for those who are comfortable handling the entire path at once, as it allows for quickly calculating the final outcome. By following these guidelines, one can confidently determine how changes in one part of a homeostatic system influence another.
Determining how to treat Xor for a low concentration of carbohydrates in the blood
To determine the appropriate drug dosage to treat Xor’s low blood carbohydrate concentration, we need to understand how the drug affects hormone G and, in turn, how hormone G influences carbohydrate levels in the blood. According to the data, the typical carbohydrate concentration in a healthy megaraffe is 6.00 mmol/L, and symptoms appear if this level drops to 4.00 mmol/L. The drug works by activating receptors for hormone G, causing liver cells to release stored carbohydrates into the bloodstream. This process involves calculating indirect effects because the drug influences hormone G first, which then affects carbohydrate levels.
Figure 13 shows how drug dosage affects the concentration of hormone G in the blood, which then influences the carbohydrate concentration. The arrows in the figure indicate the direction of these relationships, while the blue numbers next to the arrows show how much one variable changes in response to changes in another. For example, the arrow from drug dosage to hormone G has a label of 11.96 µmol/L per gram. This means that for every gram of drug administered, the concentration of hormone G in the blood increases by 11.96 µmol/L. Similarly, the arrow from hormone G to carbohydrate concentration shows that for every 1 µmol/L increase in hormone G, the carbohydrate concentration increases by 0.21 mmol/L. An important detail to remember is that the drug does not work at dosages below 0.80 g, so if our calculation suggests a dosage below this amount, we need to add 0.80 g to make sure the drug is effective.
Drug Dosage → Hormone G → [Carbohydrates] in Blood
The path from drug dosage to hormone G to carbohydrates in the blood can also be reversed to determine the required drug dosage based on a target increase in carbohydrate concentration. By working backward through the path model, students can first find out how much hormone G is needed to raise the carbohydrate concentration by a specific amount. Then, using the relationship between drug dosage and hormone G levels, they can calculate the necessary dose of the drug. It is essential to carefully follow the units at each step of this process, as the units help confirm that the calculations are set up correctly. By ensuring that the units cancel appropriately and match the desired outcome, students can stay on track and avoid mistakes in their calculations.
Figure 13. This figure shows a path model of the homeostatic system that regulates the concentration of carbohydrates ([carbohydrates]) in the blood of healthy megaraffes. It highlights key components and relationships to help determine the appropriate drug dosage if Xor’s carbohydrate levels are too low.
The model includes three main components: drug dosage, the concentration of hormone G in the blood, and the concentration of carbohydrates in the blood. Solid boxes represent drug dosage and hormone G, while a dashed box represents carbohydrates.
Arrows indicate relationships between these variables, with blue text showing how much one variable changes in response to changes in another. For example, increasing the drug dosage raises hormone G levels by 11.96 micromoles per liter per gram of drug. In turn, higher hormone G levels raise carbohydrate levels by 0.21 millimoles per liter per micromole per liter of hormone G.
Directions: Based on the background information, select all answers to question 22. Use Figure 14 to answer questions 23-24 (below). The questions are regarding the homeostatic system that regulates the concentration of carbohydrates in the blood of a megaraffe. For questions 23 and 24, express your answer as a decimal, rounding the value to the nearest tenth of a decimal place. For example, if you calculate a probability of 0.48, report a value of 0.5.
- Which scenario(s) would result in a low concentration of carbohydrates in the blood of a megaraffe? Select ALL that apply.
- Genetic mutations reduce how well hormone I binds to hormone I receptors
- Tumors cause the pancreas to produce and release hormone I continually
- Tumors cause the pancreas to produce and release hormone G continually
- Genetic mutations reduce the sensitivity of carbohydrate receptors to high levels of carbohydrates
- None of the scenarios listed above would result in a low concentration of carbohydrates in the blood.
- How much higher or lower does the concentration of Hormone G (μmol/L) need to be in order to raise the [carbohydrate] in the blood by 2.00 mmol/L? Note: If your answer to this question is a positive value, then you are saying you want to raise the concentration of Hormone G (μmol/L) by that value. Conversely, if your answer to this question is a negative value, you are saying you want to lower the concentration of Hormone G (μmol/L) by that value.
- Calculate the drug dosage (g) that would raise or lower the concentration of Hormone G (μmol/L) by the amount you indicated in question 24.
Note: Based on previous research, the drug is ineffective at dosages of 0.8 g or less, so make sure to add 0.8 g to your final answer no matter what.
Step 3: Determine the cause of and treatment for Xor’s high blood pressure.
Xor’s symptoms could also be explained by high blood pressure. As such, we must prepare for the possibility that Xor may have high blood pressure.
Blood pressure is the force exerted by blood against the walls of arteries as it circulates. To maintain proper blood flow and nutrient delivery, blood pressure must stay within a specific range. In megaraffes, a homeostatic system regulates blood pressure through a series of sensors, integrators, and effectors.
Figure 14. This diagram compares typical blood pressure and high blood pressure in systemic arteries. The left side shows an artery with normal wall thickness, a normal interior diameter, and free-flowing blood cells, indicating typical blood pressure. The right side shows an artery with increased wall thickness, a narrower interior diameter, and congested blood cells, indicating high blood pressure.
Arrows inside the arteries represent the force of blood against the walls, with thicker arrows indicating greater force and higher blood pressure. The artery on the right has thicker arrows than the one on the left, suggesting higher pressure exerted on its walls. The descriptions emphasize how changes in wall thickness, interior diameter, and blood cell congestion can influence blood pressure.
I searched my digital archives for information about the components of the system that regulate blood pressure in a megaraffe. This information is summarized below.
Sensors: Nerve Cells with Baroreceptors
Nerve cells with baroreceptors detect blood pressure in the arteries and send signals to the brain accordingly. When blood pressure rises, these cells increase the frequency of their signals. Conversely, when blood pressure drops, they send signals less frequently.
Integrator: Medulla Oblongata
The medulla oblongata acts as the integrator by receiving signals from nerve cells with baroreceptors about blood pressure levels. In response, it adjusts the frequency of signals it sends to other parts of the body. When it receives signals more frequently, it also sends signals more frequently, and vice versa.
Effectors: Heart and Blood Vessels
- Heart: This muscular organ pumps blood through the pulmonary and systemic circuits. The frequency and strength of its contractions determine the rate of blood flow and, consequently, blood pressure. The heart contracts more frequently and strongly when it receives fewer signals from the medulla oblongata, increasing blood flow and blood pressure. When it receives more signals, it contracts less frequently and less strongly, reducing blood flow and blood pressure.
- Blood Vessels: Vessels contain muscular tissue that contracts or relaxes based on signals from the medulla oblongata. When vessels receive fewer signals, they constrict, increasing resistance to blood flow and raising blood pressure. When they receive more signals, they relax, reducing resistance and lowering blood pressure.
Figure 15. Path model of the homeostatic system regulating blood pressure in megaraffes. The variable being regulated—blood pressure—is represented by a dashed box with black text, while other components such as blood vessels, the heart, the medulla oblongata, and nerve cells with baroreceptors are represented by solid boxes with black text.
Arrows between these components indicate relationships, with “+” or “−” symbols showing if these relationships are positive or negative. An arrow points from blood pressure to the rate of signaling by nerve cells with baroreceptors, marked with a “+” symbol. Arrows also point from these nerve cells to the medulla oblongata with a “+” symbol, from the medulla oblongata to the rate of blood flow from the heart with a “−” symbol, and to the resistance of blood vessels with a “−” symbol. Additionally, arrows point from the rate of blood flow and the resistance of blood vessels to blood pressure, marked with “+” symbols.
The right side of the figure highlights the drug’s effect on blood pressure. The drug dose and resistance of blood vessels are represented by solid boxes, while blood pressure is shown in a dashed box. An arrow from the drug dose to the resistance of blood vessels is labeled with a relationship of −2.29 (mmHgmin)/ 1g, indicating a negative relationship. Another arrow from the resistance of blood vessels to blood pressure is labeled with a relationship of 1.0 mmHg/(mmHgmin), indicating a positive relationship. These elements collectively show how drug dosage affects blood vessel resistance and, subsequently, blood pressure.
With this information, we can analyze a path model of a homeostatic system to determine what could have caused high blood pressure in Xor.
Determining how to treat high blood pressure
High blood pressure in megaraffes can result from several factors. One potential cause is increased resistance in blood vessels. When blood vessels become narrower, they create more resistance to blood flow, which raises blood pressure. Another factor is increased heart activity. If the heart contracts more frequently or with greater force, it pumps more blood through the vessels at a faster rate, leading to higher blood pressure. Disrupted signaling within the homeostatic system can also contribute to high blood pressure. Abnormal rates of signaling from baroreceptors or the medulla oblongata can cause imbalances in how the heart and blood vessels respond, potentially resulting in higher blood pressure.
Drug Dosage → Resistance of Blood Vessels → Blood Pressure in Megaraffe
If Xor’s blood pressure is confirmed to be high, we need to determine how much of a specific drug to administer to help reduce it. According to Figure 15, the typical blood pressure for a healthy megaraffe is 850 mmHg, while symptoms appear if blood pressure rises to at least 975 mmHg. The drug available for treatment works by dilating blood vessels, which reduces resistance to blood flow. The relationship between the drug dose and the resistance of blood vessels is represented by a value of -2.29 mmHg·min per gram of drug. This means that for each gram of the drug administered, the resistance decreases by 2.29 mmHg·min. Additionally, the model shows that blood pressure changes by 1 mmHg for every mmHg·min change in vessel resistance. To find the appropriate drug dose, we must first calculate the required change in vessel resistance to lower blood pressure by -125 mmHg. Then, using the value provided, we can determine how much drug is needed to achieve this change. It is important to remember that the drug is ineffective at doses below 24 grams, so any calculated dosage must have at least 24 grams added to it.
The key to remember here is that the goal is to determine the appropriate drug dose that reduces the blood pressure by -125 mmHg. We’ll work backwards from this goal to determine the correct dose.
Directions: Based on the background information, select all answers to question 25. Use Figure 15 to answer questions 26-27 (below). The questions are regarding the homeostatic system that regulates the blood pressure of a megaraffe. For questions 26 and 27, express your answer as a whole number. For example, if you calculate a probability of 243.54, report a value of 244.
- Which scenario(s) would result in a megaraffe having high blood pressure? Select ALL that apply.
- Tumors cause nerve cells with baroreceptors have a continually high rate of signaling
- Gene mutations weaken the muscles of the heart reducing the strength of each heart beat
- Exposure to chemicals causes blood vessels to narrow, increasing resistance to blood flow
- Brain trauma severed the connection between the medulla oblongata and the heart
- None of the scenarios listed above would result in high blood pressure
- How much higher or lower does the blood flow (mmHg • min) need to be in order to reduce the blood pressure by -125 mmHg? Note: If your answer to this question is a positive value, then you are saying you want to increase the resistance of blood flow by that value. Conversely, if your answer to this question is a negative value, you are saying you want to decrease the resistance of blood flow by that value.
- Calculate the drug dosage (g) that would increase or decrease resistance of blood flow (mmHg • min) by the amount you calculated in question 27.
Note: Based on previous research, the drug is ineffective at dosages of 24 g or less, so make sure to add 24 g to your final answer no matter what.
- Which ONE monitoring approach best assesses whether an intervention to restore Xor’s oxygen homeostasis is working?
- Track diaphragm contraction rate and expect it to fall if [O₂] is low
- Measure blood [O₂] and look for values rising back toward 95%
- Monitor blood glucose ([carbohydrates]) and look for it to drop into the normal range
- Record mean arterial pressure and expect it to increase if O₂ is restored