Drug dose (g) Slope (% O2/(contraction/min)) 3.6 4 4.4 4.8 5.2 5.6 6 6.4 6.8 7.2 7.6 8 8.4 6.21 6.16 6.17 6.24 6.19 6.21 6.32 6.28 6.30 6.38 6.32 6.38 6.39 Lab Instructions: Physiology Act I Mission Memo Greetings Fellow Explorer: Despite your efforts to treat Xor, she remains weak and disoriented. To make matters worse, the herd will not leave Xor to continue on its journey. If we cannot help Xor recover quickly, the other megaraffe’s 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 variables in the body that affect the reactions needed to survive? (Appendix 1) ● How should we treat Xor if one of her homeostatic systems has failed? (Appendix 2) The appendices to this mission memo will guide you in answering these questions. Once you have completed your analyses, report your conclusions via Canvas before returning to the Sanctuary. Do not underestimate the urgency of your work. Universally in your debt, The AI 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 that its blood carries sufficient resources to all cells of the body. These resources include carbohydrates and oxygen (O2), which are needed to fuel critical reactions in cells. If an organism cannot deliver enough of these resources, illness, or even death could occur. Xor’s disorientation might have resulted from a failure to regulate the concentration of O 2 [O2], or carbohydrates in her blood, or a failure to maintain a blood pressure needed for the blood to carry these resources to cells. The regulation of blood O2 concentration, blood carbohydrate concentration, and blood pressure is 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. To diagnose whether Xor’s symptoms stem from a failure to regulate the concentration of [O2], concentration of carbohydrates, or blood pressure, we must use a path model of a homeostatic system. Let’s start by making sure that we’re interpreting a path model correctly. We’ll 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 the smallest bacteria to the largest species in the universe, need to maintain a relatively constant internal environment despite a changing external environment. The process by which organisms maintain a consistent internal environment is called homeostasis. What is homeostasis? Homeostasis is the process by which organisms maintain a relatively stable internal environment in an ever-changing external environment. Like any system, homeostatic systems involve a set of components that interact to achieve a desired outcome. In this case, the outcome is the regulation of a variable within a range required to sustain life; the mean value of a regulated variable is called a set point, reflecting the idea that the organism attempts to set the value of the variable at that point. Examples of regulated variables in humans include blood O2 concentration, blood glucose concentration, blood pressure, and body temperature. How does an organism detect when the value of a variable deviates from the set point and return the variable to the set point? First, the system must have a component called a sensor, which measures the magnitude of the regulated variable. A sensor relays information about the magnitude of a variable to a component called the integrator. The integrator sums the information from all sensors and responds by activating a component that can return the regulated variable to the set point. How does the integrator cause the variable to return to the set point? Depending on the information that the integrator receives from the sensors, it sends its own signals to cells called effectors. These signals cause the effectors to function in a way that returns the variable to the set point. To summarize, a homeostatic system with a sensor, integrator, and effector detects a change in the value of a variable and counteracts that change, restoring the initial value. Because the change caused by a homeostatic system opposes the direction of the initial change, a homeostatic system is also called a negative feedback loop. Figure 1 shows a generic path model of a homeostatic system as a set of boxes and arrows. The regulated variable is represented with a dashed black box containing black text. Each component of the system is represented by a black box containing black text. These boxes state the action of the component and include the name of the component within the box – e.g., sensor, integrator, effector 1 and effector 2. In practice, the activity of each component would be measured by a specific variable; for example, a sensor’s activity might be measured by the rate of electrical impulses fired by a nerve cell. Additionally, that sensor would not be labeled as a “sensor” but rather would be labeled as the name of the cell or tissues. In this example, we would call the sensor a nerve cell. An arrow connecting one box to another indicates a relationship between two components. The direction of the arrow tells us about cause and effect; for example, the arrow pointing from the sensor’s box to the integrator’s box tells us that the activity of the sensor directly affects the activity of the integrator. When modeling this relationship, we can think of the activity of the sensor as an independent variable and the activity of the integrator as a dependent variable. Figure 1. Path model of a generic homeostatic system. The variable being regulated is represented by a dashed black box containing black text. Each variable and the physical component associated with that variable in the model is represented by a black box containing black text. There are four components in the model: a sensor, an integrator, and two effectors (effector 1 and effector 2). An arrow connecting one box to another indicates a relationship between two variables. There is an arrow pointing from the regulated variable to the activity of the sensor, from the activity of the sensor to the activity of the integrator, from the activity of the integrator to the activity of effector 1, from the activity of the integrator to the activity of effector 2, and from the activity of each effector to the regulated variable. However, Figure 1 is incomplete. Recall that in Figure 1, the activity of the sensor affects the activity of the integrator. But how? Does the activity of the integrator increase or decrease as the activity of the sensor increases? In Figure 2, you’ll notice that each arrow now has a symbol indicating whether the relationship between the variables is positive (+) or negative (-). Figure 2. Path model of a generic homeostatic system. The variable being regulated is represented by a dashed black box containing black text. Each variable and the physical component associated with that variable in the model is represented by a black box containing black text. There are four components in the model: a sensor, an integrator, and two effectors (effector 1 and effector 2). An arrow connecting one box to another indicates a relationship between two variables. A “+” or “-” symbol over each arrow indicates whether the relationship between two variables is a positive relationship or a negative relationship, respectively. There is an arrow pointing from the regulated variable to the activity of the sensor with a “+” symbol over it, from the activity of the sensor to the activity of the integrator with a “+” symbol over it, from the activity of the integrator to the activity of effector 1 with a “+” symbol over it, from the activity of the integrator to the activity of effector 2 with a “-” symbol over it, and from the activity of each effector to the regulated variable. The arrow pointing from the activity of effector 1 to the regulated variable has a “+” symbol over it. The arrow pointing from the activity of effector 2 to the regulated variable has a “-” symbol over it. For a positive relationship (“+” symbol), the activity of the dependent component increases as the activity of the independent component increases. Remember, a positive relationship also means that the activity of the dependent component decreases as the activity of the independent component decreases (Figure 3a). For a negative relationship, the activity of the dependent component decreases as the activity of the independent component increases. Remember, a negative relationship also means that the activity of the dependent component increases as the activity of the independent component decreases (Figure 3b). Figure 3. Figures 3a and 3b depict hypothetical linear relationships between two continuous variables. In each figure, the y-axis represents a continuous, dependent variable, while the xaxis represents a continuous, independent variable. The solid line in each figure (blue and red for Figures 3a and 3b, respectively) represents a hypothetical linear model of the relationship between the independent variable and the dependent variable in each figure. (a) The blue line in this figure shows a positive relationship between the independent variable and the dependent variable. (b) The red line in this figure shows a negative relationship between the independent variable and the dependent variable. Looking back at Figure 2, the positive symbol over the arrow pointing from the sensor to the integrator in Figure 2 means that the activity of the integrator (dependent variable) increases as the activity of the sensor (independent variable) increases. Before we begin to infer the potential causes of Xor’s symptoms, we must be able to correctly interpret path models of homeostatic systems. Let’s take a closer look at an example. Example of a Homeostatic System: Air Temperature in the Intergalactic Wildlife Sanctuary You may have noticed from the dashboard on your mobile lab that the air temperature is tightly controlled throughout the Intergalactic Wildlife Sanctuary (IWS). This control depends on a homeostatic system analogous to the kind that humans have used to regulate air temperature in buildings and vehicles. The regulated variable in this system is air temperature. Sensors called thermocouples, placed throughout the sanctuary, continuously measure air temperature. My processors compare each air temperature to a set point for that region of the sanctuary. Based on this comparison, I increase or decrease the activities of heaters and coolers in the sanctuary, bringing the air temperature closer to the set point. Therefore, my computer processors are the integrator in this system. The heaters and coolers are effectors. Figure 4 shows a path model of this homeostatic system. Figure 4. Path model of a homeostatic system regulating air temperature in the Intergalactic Wildlife Sanctuary (IWS). The variable being regulated – air temperature in the IWS – is represented by a dashed black box containing black text. Each variable and the physical component associated with that variable in the model is represented by a black box containing black text. There are four components in the model: thermocouples (sensors), AI processors (integrator), coolers, and heaters (effectors). An arrow connecting one box to another indicates a relationship between two variables. A “+” or “-” symbol over each arrow indicates whether the relationship between two variables is a positive relationship or a negative relationship, respectively. There is an arrow pointing from the regulated variable – “air temperature” – to the variable “rate of signaling by the thermocouples” with a “-” symbol over it, from the variable “rate of signaling by the thermocouples” to the variable “rate of signaling by the processors” with a “+” symbol over it, from the variable “rate of signaling by the processors” to the variable “activity of coolers” with a “-” symbol over it, from the variable “rate of signaling by the processors” to the variable “activity of heaters” with a “+” symbol over it, from the variable “activity of coolers” to the variable “air temperature” with a “-” symbol over it, and from the variable “activity of heaters” to the variable “air temperature” with a “+” symbol over it. The model in Figure 4 can help us understand how components in the system interact with each other. Let’s pause for a moment to think about how each component is interacting with others to regulate air temperature. What happens when air temperature rises above the set point? ● As the air temperature increases, this causes the rate of signaling by the thermocouples to decrease – the thermocouples are sending out fewer signals per unit of time. ● As the rate of signaling by the thermocouples decreases, the processors are in effect turned off – thus their rate of signaling decreases – dropping to zero. ● As the rate of signaling by the processors essentially drops to zero, this has two effects… ○ …the activity of the heater decreases. This makes sense, as the air temperature is too high and the heaters are not needed at this moment. ○ …the activity of the coolers increases. This makes sense, as the air temperature is too high and the coolers are needed to lower the air temperature. What happens when air temperature falls below the set point? ● As the air temperature decreases, this causes the rate of signaling by the thermocouples to increase – the thermocouples are sending out more signals per unit of time. ● As the rate of signaling by the thermocouples increases, the processors are in effect turned on – thus their rate of signaling increases. ● As the rate of signaling by the processors increases, this has two effects… ○ …the activity of the heater increases. This makes sense, as the air temperature is too low and the heaters are needed to increase the air temperature. ○ …the activity of the coolers decreases. This makes sense, as the air temperature is too low and the coolers are not needed at this moment. Notice that the system modeled in Figure 4 has two effectors that oppose each other: heaters and coolers. This type of design is common among homeostatic systems, because it enables more precise control of the variable. One effector activates when the value of the variable rises above the set point, and the other effector operates when the value of the variable falls below the set point. In both cases, an effector is driving the value of the variable towards the set point. Also keep in mind that some homeostatic systems can have multiple sensors, integrators, or effectors, and that not every homeostatic system has effectors that oppose each other. Blood oxygen concentration: How does O2 get to cells? The IWS’s archives contain information about how certain variables are regulated by megaraffes. One variable that’s important for a megaraffe to maintain, like you humans, is sufficient levels of oxygen gas (O2) dissolved in blood. Oxygen enables organisms such as megaraffes to perform cellular respiration, which produces the energy needed to move, grow, and reproduce. Carbon dioxide gas (CO2) is a waste product of cellular respiration, expelled from the body. How does O2 get to the tissues of the body? How does the body expel CO2? About 21% of atmospheric air consists of O2. By breathing, a megaraffe draws air into structures called lungs. Air flows in and out of the lungs through the actions of a muscle at the base of the lungs called the diaphragm. When the diaphragm contracts, the lungs expand and air flows from the atmosphere to the lungs (breathing in). When the diaphragm relaxes, the lungs rebound back to their original size and air flows from the lungs to the atmosphere (breathing out). Figure 5 illustrates how air flows in and out of the lungs of a human. Figure 5. Diagram illustrating how humans move air into (breathing in) and out (breathing out) of the lungs. (a) Air flows into the lungs when the diaphragm contracts, causing the chest cavity to expand, which then draws air into the lungs from the atmosphere. (b) Air flows out of the lungs when the diaphragm relaxes, causing the chest cavity to compress, which then forces air out of the lungs and back into the atmosphere. When air flows into the lungs, a portion enters structures called alveoli (singular alveolus). Once in the alveoli, the O2 diffuses into very small blood vessels called capillaries, while CO2 diffuses out from these capillaries and into the alveoli. The “stale” or “used” air containing CO2 then exits the alveoli as the lungs contract and air flows out of the lungs when breathing out. See Figure 6 for a visual representation of this process. Figure 6. Diagram illustrating how oxygen gas (O2) and carbon dioxide gas (CO2) diffuse into or out of the capillaries, respectively, of humans. When breathing in, air flows into the alveoli (singular – alveolus). O2 diffuses from the air into blood vessels called capillaries. In this way, deoxygenated blood becomes oxygenated again. Conversely, CO2 diffuses from the deoxygenated blood in the capillaries and into the air in the alveoli. CO2 molecules then exit the lungs when a person breathes out. But how does O2 get to cells, tissues, and organs throughout the body? That’s where the cardiovascular system comes into play. The cardiovascular system is a series of blood vessels that transports oxygenated blood throughout the body to cells and then transports CO2 from the cells back to the lungs. Arteries – a type of blood vessel transports blood away from the heart; veins – another type of blood vessel – transports blood towards the heart. The heart is responsible for pumping blood through the cardiovascular system. The cardiovascular system can be broken down into two sections, 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 where O 2 diffuses into the tissues from the blood while CO2 diffuses from the tissues to the blood, and then back to the heart. In this way the circulatory system ensures tissues are constantly getting a fresh supply of O2 while simultaneously removing CO2 from the body. Figure 7 shows a simplified example of the cardiovascular system in humans – which is similar to the structure of the megaraffe cardiovascular system. Figure 7. 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. Given the importance of O2, one can understand why regulating the level of O2 in the blood is crucial for many organisms. Because the blood in the arteries is what delivers O 2 to tissues, organisms regulate the amount of O2 in the arteries, not the veins. We call this the arterial blood O2. We will refer to measurements of arterial blood O2 as the concentration of O2 in the blood, abbreviated as [O2] in the blood. Blood oxygen concentration: Interpreting a homeostatic system From my digital archives, I retrieved information about the components involved in regulating the [O2] in the blood of a megaraffe. This information is described below. Carotid body: These cells send signals to other cells. When the [O2] in the blood decreases, the rate of signaling by the carotid body increases. Conversely, when the [O2] in the blood increases, the rate of signaling by the carotid body decreases. Diaphragm: This muscle, located at the base of the lungs, helps to move air in and out of the lungs – called breathing. The rate of breathing increases as the diaphragm contracts/relaxes more frequently. The diaphragm contracts more frequently when it receives signals more frequently from the brain. Conversely, the diaphragm contracts less frequently when it receives signals less frequently from the brain. Medulla oblongata: This part of the brain receives information regarding the [O2] in the blood. As the medulla oblongata receives signals more frequently, it sends out its own signals to other parts of the body more frequently. Conversely, as the medulla oblongata receives signals less frequently, it sends out its own signals to other parts of the body less frequently. Figure 8 shows a path model of the homeostatic system that a megaraffes uses to regulate the [O2] in their blood. Figure 8. Path model of the homeostatic system regulating the concentration of oxygen [O2] in the blood of megaraffes. The variable being regulated – [O2] in the blood of megaraffes – is represented by a dashed black box containing black text. Each variable and the physical component associated with that variable in the model is represented by a black box containing black text. There are three components in the model: carotid body, diaphragm, and the medulla oblongata. An arrow connecting one box to another indicates a relationship between two variables. A “+” or “-” symbol over each arrow indicates whether the relationship between two variables is a positive relationship or a negative relationship, respectively. There is an arrow pointing from the regulated variable – “[O2] in the blood of megaraffes” – to the variable “rate of signaling by the carotid body” with a “-” symbol over it, from the variable “rate of signaling by the carotid body” to the variable “rate of signaling by the medulla oblongata” with a “+” symbol over it, from the variable “rate of signaling by the medulla oblongata” to the variable “rate of contraction by the diaphragm” with a “+” symbol over it, and from the variable “rate of contraction by the diaphragm” to the regulated variable “[O2] in the blood of megaraffes” with a “+” symbol over it. 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 8 to answer questions 1-10. 1. Which component(s) in this model is/are most likely the sensor(s)? Select ALL that apply. a. Carotid body b. Diaphragm c. Medulla oblongata 2. Explain your answer to the previous question. Your explanation should minimally discuss why the structure(s) that you chose in the previous question function as sensor(s). 3. Which component(s) in this model is/are most likely the integrator(s)? Select ALL that apply. a. Carotid body b. Diaphragm c. Medulla oblongata 4. Explain your answer to the previous question. Your explanation should minimally discuss why the structure(s) that you chose in the previous question function as integrator(s). 5. Which component(s) in this model is/are most likely the effector(s)? Select ALL that apply. a. Carotid body b. Diaphragm c. Medulla oblongata 6. Explain your answer to the previous question. Your explanation should minimally discuss why the structure(s) that you chose in the previous question function as effector(s). 7. What independent variable(s) directly affect the dependent variable “Concentration of oxygen [O2] in the blood of megaraffes”? Select ALL that apply. a. Rate of contraction by the diaphragm b. Rate of signaling by the carotid body c. Rate of signaling by the medulla oblongata 8. What independent variable(s) indirectly affect the dependent variable “Rate of contraction by the diaphragm”? Select ALL that apply. a. Concentration of oxygen [O2] in the blood b. Rate of signaling by the carotid body c. Rate of signaling by the medulla oblongata 9. Fill in the blanks. As the rate of signaling by the medulla oblongata ____, the rate of contraction by the diaphragm ____. Select ALL that apply. a. increases, increases b. increases, decreases c. decreases, increases d. decreases, decreases 10. Fill in the blanks. As the concentration of O2 [O2] in the blood ____, the rate of signaling by the carotid body ____. Select ALL that apply. a. increases, increases b. increases, decreases c. decreases, increases d. decreases, decreases Directions: Use Figure 8 to answer questions 11-14. Three figures, Figures 1, 2, and 3 (below) each show a different linear relationship. The gray line in each figure represents a linear model of 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: 11. Independent variable = concentration of O2 [O2] in the blood of megaraffes; Dependent variable = rate of signaling by the carotid body. a. Figure 1 b. Figure 2 c. Figure 3 12. Independent variable = rate of signaling by the carotid body; Dependent variable = rate of signaling by the medulla oblongata. a. Figure 1 b. Figure 2 c. Figure 3 13. Independent variable = rate of signaling by the medulla oblongata; Dependent variable = rate of contraction by the diaphragm. a. Figure 1 b. Figure 2 c. Figure 3 14. Independent variable = rate of contraction by the diaphragm; Dependent variable = concentration of O2 [O2] in the blood of megaraffes. a. Figure 1 b. Figure 2 c. Figure 3 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 of and treatment for Xor’s low concentration of O2 in the blood How to use a path model of a homeostatic system to diagnose a failure to regulate a variable 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 that we’ve explored previously—the regulation of air temperature in the Intergalactic Wildlife Sanctuary (Figure 4, also shown below). Figure 4. Path model of a homeostatic system regulating air temperature in the Intergalactic Wildlife Sanctuary (IWS). The variable being regulated – air temperature in the IWS – is represented by a dashed black box containing black text. Each variable and the physical component associated with that variable in the model is represented by a black box containing black text. There are four components in the model: thermocouples (sensors), AI processors (integrator), coolers, and heaters (effectors). An arrow connecting one box to another indicates a relationship between two variables. A “+” or “-” symbol over each arrow indicates whether the relationship between two variables is a positive relationship or a negative relationship, respectively. There is an arrow pointing from the regulated variable – “air temperature” – to the variable “rate of signaling by the thermocouples” with a “-” symbol over it, from the variable “rate of signaling by the thermocouples” to the variable “rate of signaling by the processors” with a “+” symbol over it, from the variable “rate of signaling by the processors” to the variable “activity of coolers” with a “-” symbol over it, from the variable “rate of signaling by the processors” to the variable “activity of heaters” with a “+” symbol over it, from the variable “activity of coolers” to the variable “air temperature” with a “-” symbol over it, and from the variable “activity of heaters” to the variable “air temperature” with a “+” symbol over it. Imagine that air temperature rises above the set point and, for whatever reason, fails to return to the set point. What could have prevented the regulation of air temperature? First, consider the problem: high air temperature. Then, determine which components of the homeostatic system could directly or indirectly cause air temperature to remain high. Let’s start with the effectors. The actions of effectors directly impact the magnitude of the regulated variable; therefore, we should start there. Could a malfunction in either of the effectors—the heater or the cooler—cause the air temperature to be too warm? If the cooler was unable to operate, the system could not lower the air temperature. Conversely, if the heater were to operate continuously, the system would increase the air temperature more than expected. Now that we’ve considered the potential roles of the effectors, we must determine how the activity of the integrator(s) or sensor(s) could cause the effectors to malfunction as described above. In other words, what would prevent the cooler from operating or cause the heater to operate continuously? Let’s start with the integrator, a processor whose rate of signaling affects the activities of the heaters and coolers. If this processor malfunctions, sending signals at a higher rate than expected, these signals would decrease the activity of the coolers. You can infer this direct effect from the negative relationship between the rate of signaling by the processor and the activity of the coolers. At the same time, the activity of the heaters would increase, because of the positive relationship between the rate of signaling by the processors and the activity of the heaters. Finally, let’s consider the sensors, thermocouples whose rate of signaling affect the activity of the processors. If some of these sensors malfunction, sending signals at a higher rate than expected, these signals would increase the rate of signaling by the processors. You can infer this direct effect from the positive relationship between the rate of signaling by the thermocouples and rate of signaling by the processor. As a consequence, the activity of the coolers would decrease and the activity of the heaters would increase. These indirect effects result from the relationships between the rate of signaling by the processors and the activities of the coolers and heaters described in the previous paragraph. This example illustrates how one can use a path model of a homeostatic system to diagnose a failure to regulate a variable. Determining causes of a low concentration of O2 in the blood Now we can analyze a path model of a homeostatic system to determine what could have caused a low concentration of O2 in Xor’s blood. Directions: Use the path model of the homeostatic system that regulates the concentration of O2 in the blood of a megaraffe (Figure 8) to answer question 15. 15. Which scenario(s) would result in a low concentration of O2 in the blood of a megaraffe? Select ALL that apply. a. Fatigue caused the diaphragm to contract less frequently. b. Genetic mutations caused the carotid body to respond more strongly to a change in the O2 concentration of the blood. c. Neurological disorders caused the medulla oblongata to send fewer signals per unit of time. d. Traumatic injury caused the medulla oblongata to continually send more signals than normal to the diaphragm regardless of the O2 concentration of the blood. e. None of the scenarios listed above would result in a low concentration of O2 in the blood. How to use a path model of a homeostatic system to quantify a direct effect 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: y = ax + b, where y equals the dependent variable, x equals the independent variable, a equals the slope, and b equals the intercept. The slope of the relationship (a) describes how a change in the value of the independent variable affects the expected value of the dependent variable. We learned how to estimate the slope and intercept of a linear model in a previous module called Scientific Reasoning. A path model depicts a set of linear relationships between the variables in a system. Again, let’s consider the path model of the homeostatic system that regulates air temperature in the Intergalactic Wildlife Sanctuary (Figure 4, also shown above). Each variable in this system is represented by a box—a dashed box for the regulated variable and a solid box for every other variable. Each relationship between variables is represented by an arrow; the direction of the arrow indicates cause and effect. 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 slope of the relationship between the variables is positive or negative. Figures 3a and 3b illustrate how each relationship appears when plotted. We will use these relationships to quantify how a change in one variable affects the change in the expected value of another variable in a path model of a homoeostatic system. Recall that the slope of a linear relationship tells us how a change in the value of the independent variable will change the expected value of the dependent variable. For example, let’s assume that the slope of the relationship between the air temperature and the rate of signaling by thermocouples was -0.5 signals/sec/°C. This slope means that an increase in air temperature of 1.0 ℃ should cause the rate of signaling by the thermocouples to decrease by -0.5 signals/sec. Importantly, the slope alone cannot tell us the expected value of the dependent variable; we’d also need to know the intercept. However, we can use the slope to predict an expected change in the value of a dependent variable. Assume that the slope of 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, per 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: Slope = y2-y1/x2-x1= Δy/Δx where: Δ represents the change in a variable y is the dependent variable, activity of the heater in kW y2 is the value of y at point 2 y1 is the value of y at point 1 x is the independent variable, rate of signaling by the processors in signals/sec x2 is the value of x at point 2 x1 is the value of x at point 1 In this example, the slope = 1.2 kW/signals/sec. If the rate of signaling by the processors increases by 10.0 signals/sec, how much should the activity of the heater change? Slope = Δy/Δx 1.2 kW/signal/sec = Δy/10.0 signals/sec To answer this question, we need to solve for Δy. Thus, we should rearrange this equation to solve for the change in the dependent variable, activity of the heater. 1.2 kW/signal/sec ⋅ 10.0 signals/sec = Δy Δy = 1.2 kW/signal/sec ⋅ 10.0 signals/sec Δy = 12.0 kW 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. Figure 9. Example illustrating how to calculate the direct effect of a change in one variable on the change in another variable in a path model. In this case, the example illustrates the calculation one would use to determine how a 10.0 signal/sec increase in the rate of signaling by processors would change the activity of the heaters. The bottom half of this figure contains the path model highlighting two variables in the homeostatic system regulating air temperature in the Intergalactic Wildlife Sanctuary, specifically the rate of signaling by processors and the activity of heaters. Both variables and the physical component associated with each variable in the model are represented by a black box containing black text. An arrow connecting one box to another indicates a relationship between two variables. The slope of the relationship between these two variables is provided as blue text over the arrow connecting the variable “rate of signaling by the processors” to the variable “activity of heaters.” The slope of this relationship is 1.2kW/(signal/sec). The top half of the figure shows the calculation one would perform to determine how a 10.0 signal/sec increase in the rate of signaling by processors would change the activity of the heaters. Multiply 10.0 signals/sec by the slope of the relationship between the rate of signaling by the processors and the activity of the heaters, 1.2kW/(signal/sec). After canceling out appropriate units, the product is 12.0 kW, which means that a 10.0 signal/sec increase in the rate of signaling by the processors results in a 12.0 kW increase in the activity of the heaters. 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 that 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. As a consequence, 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. For simplicity, this figure highlights only those relationships relevant to your calculations. Figure 10. Path model of the homeostatic system regulating the concentration of oxygen [O2] in the blood of healthy megaraffes. Key components, variables, and relationships have been highlighted to help determine the appropriate dose of drug needed to help return Xor’s [O 2] in the blood back to healthy levels should her blood [O2] be too low. Two components and their variables have been highlighted – the rate of contraction by the diaphragm and the [O2] in the blood of megaraffes. The rate of contraction by the diaphragm is represented by a black box containing black text. The [O2] in the blood of megaraffes is represented by a dashed black box containing black text. An arrow points from the rate of contraction by the diaphragm to the [O2] in the blood of megaraffes. The slope of the relationship between these two variables is provided as blue text over the arrow connecting these variables. The slope of this relationship is 6.3% O2/(contraction/min). Under normal conditions in the absence of the drug, Xor should be taking 15.0 breaths/minute and the arterial blood [O2] should equal 95.0%. The slope of the relationship between the rate of contraction by the diaphragm and the [O2] in the blood of megaraffes is 6.3% O2/1.0 contraction/min, or 6.3% O2 / (contraction/min) under these conditions. According to my digital archives, the O2 concentration of blood must drop to at least 92.0% to cause the symptoms that we observed in Xor. Assuming Xor is still taking 15.0 breaths/minute, what would the slope of the relationship between the rate of contraction by the diaphragm and the [O2] in the blood of megaraffes if Xor was still taking 15.0 breaths/minute and the [O2] in her blood was 92.0%? Directions: For questions 16-17, round all calculated values to the nearest tenth of a decimal place. For example, if you calculate the value as 3.821853, round to 3.8. 16. Estimate the slope of the linear relationship ([O2] / (contraction/min)) between the rate of contraction by the diaphragm and the [O2] in the blood of Xor if she was taking 15.0 breaths/minute and the [O2] in her blood was 92.0%. Slope = 17. How much do we need to raise or lower the slope you estimated in the previous question in order to return it back to the healthy slope of 6.3% O2 / (contraction/min)? As a note, if your answer to this question is a positive value, then you are saying you want to raise the slope by that value. Conversely, if your answer to this question is a negative value, you are saying you want to lower the slope by that value. Amount to raise or lower slope = 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 [O2] concentration the blood must drop to in order to cause the symptoms we observed in Xor. Now we must determine how much drug we should give to Xor should her [O2] be lower than normal. Because the drug alters how much air flows into the lungs each time the diaphragm contracts, the drug alters the slope of 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 to Xor, we first must model the relationship between the dose of the drug and the slope of 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 slope of 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, download the Excel file, “Data: Effect of Drug on Slope,” containing the dose of the drug and the slope of 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. Round all calculated values to the nearest hundredths of a decimal place. For example, if you calculate the value as 3.821853, round to 3.82. 18. Create a single plot of a linear relationship between the dose of the drug and the slope of 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: General ● Chart type: X Y (Scatter) ● Quick layout: Layout 1 – Scatter (you can delete the key/legend on the right if you want and the chart title) ● Y-axes title: “Slope (% O2/(contraction/min))”; Font size = 18 ● Y-axis numbers: Font size = 14 ● X-axis title: “Drug dose (g)”; Font size 18 ● X-axis numbers: Font size = 14 Y-axis ● Bounds: minimum at 6.10, maximum at 6.50 X-axis ● Bounds: minimum at 3, maximum at 9 Trendline (linear model) ● Line: Solid line 19. Estimate the slope of the linear relationship (([O2] / (contraction/min)) / g) between the dose of the drug and the slope of the relationship between the rate of contraction by the diaphragm and the [O2] in the blood. Slope = Thanks to your efforts, we’re ready to determine how much of the drug to administer to Xor to return the slope of 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. Directions: Use your answers to questions 16-19 to answer questions 20-21. Pay attention to how you should round your answers for questions 20-21. 20. According to the linear relationship you modeled in questions 18-19, how much does the slope of the linear relationship ([O2] / (contraction/min)) between the rate of contraction by the diaphragm and the [O2] in the blood change for each gram of drug administered? Round your answer to the nearest hundredth of a decimal place. For example, if you calculate the value as 3.821853, round to 3.82. Slope = 21. Given your answers to the previous questions in this step, how many grams of drug would we need to administer to Xor to return the slope of the relationship between the rate of contraction by the diaphragm and the [O2] in the blood back to the healthy value of 6.3% O2 / (contraction/min)? As a 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. Round your answer to the nearest ones place. For example, if you calculate the value as 3.821853, round to 4. Dose of drug = 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 that 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, a 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 regulates 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 there are more carbohydrates in the blood, the probability that these receptors will be activated increases. Conversely, when there are fewer carbohydrates 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 body 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 decreases the rate at which it releases hormone I into the bloodstream, the concentration of hormone I in the bloodstream increases. Conversely, as the pancreas increases 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. Note there are two separate boxes for the pancreas to represent the fact that the pancreas releases two different hormones in response to changes in the signaling it receives. 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 shows a path model of the homeostatic system that regulates the [carbohydrates] in the blood of megaraffes. Figure 11. Path model of the homeostatic system regulating the concentration of carbohydrates [carbohydrates] in the blood of megaraffes. The variable being regulated – [carbohydrates] in the blood of megaraffes – is represented by a dashed black box containing black text. Each variable and the physical component associated with that variable in the model is represented by a black box containing black text. There are four components in the model: carbohydrate receptors, pancreas, hormone G, and hormone I. An arrow connecting one box to another indicates a relationship between two variables. A “+” or “-” symbol over each arrow indicates whether the relationship between two variables is a positive relationship or a negative relationship, respectively. There is an arrow pointing from the regulated variable “[carbohydrates] in the blood of megaraffes” to the variable “activity of carbohydrate receptors” with a “+” symbol over it, from the variable “activity of carbohydrate receptors” to the variable “rate at which the pancreas releases hormone I” with a “+” symbol over it, from the variable “rate at which the pancreas releases hormone I” to the variable “[hormone I] in the blood” with a “+” symbol over it, from the variable “[hormone I] in the blood” to the regulated variable “[carbohydrates] in the blood of megaraffes” with a “-” symbol over it, from the variable “activity of carbohydrate receptors” to the variable “rate at which the pancreas releases hormone G” with a “-” symbol over it, from the variable “rate at which the pancreas releases hormone G” to the variable “[hormone G] in the blood” with a “+” symbol over it, and from the variable “[hormone G] in the blood” to the regulated variable “[carbohydrates] in the blood of megaraffes” with a “+” symbol over it. 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. Let’s start by determining what factors could cause a low concentration of carbohydrates in a megaraffe’s blood. For guidance, use Figure 11. Determining causes of a low concentration of carbohydrates in the blood Directions: Use the path model of the homeostatic system that regulates the concentration of carbohydrates in the blood of a megaraffe (Figure 11) to answer question 22. 22. Which scenario(s) would result in a low concentration of carbohydrates in the blood of a megaraffe? Select ALL that apply. a. Genetic mutations reduce how well hormone I binds to hormone I receptors. b. Tumors cause the pancreas to continually produce and release hormone I. c. Tumors cause the pancreas to continually produce and release hormone G. d. Genetic mutations reduce the sensitivity of carbohydrate receptors to high levels of carbohydrates. e. None of the scenarios listed above would result in a low concentration of carbohydrates in the blood. Determining how to treat Xor for a low concentration of carbohydrates in the blood According to my digital archives, the typical carbohydrate concentration in a healthy megaraffe is 6.00 mmol/L. The carbohydrate concentration of blood must drop to at least 4.00 mmol/L to cause the symptoms that we observed in Xor. We have a drug that can help treat low blood carbohydrate concentration in megaraffes. The drug works much like the drugs used on your planet to treat humans with a certain type of diabetes. At the correct dosage, the drug causes cells in the liver to release carbohydrates into the blood. As a consequence, more carbohydrates circulate to cells throughout the body. We’ll need to make calculations involving indirect effects rather than direct effects because of the nature of the interactions amongst the drug and key variables in Xor’s homeostatic pathway. 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 the value of one variable to indirectly affect the value of another variable? Building off the previous example involving the regulation of air temperature in the IWS (Figure 4, below), we can ask how a change in the rate of signaling by the processors should affect air temperature. To answer this question, we must focus on the paths that connect three variables: processors → heaters → air temperature. Figure 4. Path model of a homeostatic system regulating air temperature in the Intergalactic Wildlife Sanctuary (IWS). The variable being regulated – air temperature in the IWS – is represented by a dashed black box containing black text. Each variable and the physical component associated with that variable in the model is represented by a black box containing black text. There are four components in the model: thermocouples (sensors), AI processors (integrator), coolers, and heaters (effectors). An arrow connecting one box to another indicates a relationship between two variables. A “+” or “-” symbol over each arrow indicates whether the relationship between two variables is a positive relationship or a negative relationship, respectively. There is an arrow pointing from the regulated variable – “air temperature” – to the variable “rate of signaling by the thermocouples” with a “-” symbol over it, from the variable “rate of signaling by the thermocouples” to the variable “rate of signaling by the processors” with a “+” symbol over it, from the variable “rate of signaling by the processors” to the variable “activity of coolers” with a “-” symbol over it, from the variable “rate of signaling by the processors” to the variable “activity of heaters” with a “+” symbol over it, from the variable “activity of coolers” to the variable “air temperature” with a “-” symbol over it, and from the variable “activity of heaters” to the variable “air temperature” with a “+” symbol over it. Assume that the slope of the relationship between the rate of signaling by the processors and the activity of the heaters is 1.2 kW/signal/sec. The slope of the relationship between the activity of the heater and the air temperature is 0.1 °C/kW. How much would the air temperature change if the rate of signaling by the processors increased by 10.0 signals/sec? We can answer this question in either of two ways: a stepwise approach or an integrative approach. Stepwise approach Using the stepwise approach, we must sequentially calculate the expected change in the value of a dependent variable based on a given change in the value of an independent variable, repeating this calculation as many times as necessary to arrive at the expected change in the final variable of the series. In our example, where the series has three variables (processors → heaters → air temperature), we need to repeat the calculation until we arrive at the expected change in the third variable (air temperature). First, we must calculate how an increase of 10.0 signals/sec in the rate of signaling by the processors should change the activity of the heaters. We multiply the change in the rate of signaling by the processors (10.0 signals/sec) by the slope (1.2 kW/signal/sec), canceling units where appropriate. From the previous step in this appendix, we know that the answer is 12.0 kW, meaning that an increase in signaling of 10.0 signals/sec should increase the activity of the heaters by 12.0 kW. Figure 12a illustrates this calculation. Next, we must calculate how an increase of 12.0 kW in the activity of the heaters should change the air temperature. We multiply the change in the activity of the heaters (12.0 kW) by the slope (0.1 °C/kW), canceling units where appropriate. This calculation yields a value of 1.2°C, meaning that an increase of 12.0 kW in the activity of heaters should increase the air temperature by 1.2 °C. Figure 12b illustrates this calculation. Taken together, this series of calculations tells us that an increase of 10.0 signals/sec in the rate of signaling by processors directly increases the activity of heaters by 12.0 kW and indirectly increases the air temperature by 1.2 °C. Figure 12. Example illustrating how to calculate the indirect effect of a change in one variable on the change in another variable in a path model using a stepwise approach. In this case, the example illustrates the calculation one would use to determine how a 10.0 signal/sec increase in the rate of signaling by processors would change the air temperature in the Intergalactic Wildlife Sanctuary (IWS). (a) The top half of the figure shows the first step in this calculation. In this step, multiply 10.0 signals/sec by the slope of the relationship between the rate of signaling by the processors and the activity of the heaters, 1.2 kW/(signal/sec). After cancelling out appropriate units, the product is 12.0 kW, which means that a 10.0 signal/sec increase in the rate of signaling by the processors results in a 12.0 kW increase in the activity of the heaters. (b) The bottom half of the figure shows the second step in this calculation. In this step, multiply 12.0 kW by the slope of the relationship between the activity of the heaters and the air temperature in the IWS, 0.1 °C/kW. After cancelling out appropriate units, the product is 1.2 °C, which means that a 12.0 kW increase in the activity of the heaters results in a 1.2 °C increase in the air temperature in the IWS. Integrative approach Using the integrative approach, we can perform a single calculation that accounts for all variables and slopes needed to predict the change in the final variable. In this example, we compute the product of three terms: 1. the rate of signaling by the processors (10.0 signals/sec), 2. the slope of the relationship between the rate of signaling by the processors and the activity of the heaters (1.2 kW/signal/sec), and 3. the slope of the relationship between the activity of the heaters and the air temperature (0.1 °C/kW). In doing so, we arrive at the same answer that we obtained from the stepwise approach: an increase of 10.0 signals/sec in the rate of signaling by the processors should indirectly increase the air temperature by 1.2 °C. Figure 13 illustrates this calculation. Figure 13. Example illustrating how to calculate the indirect effect of a change in one variable on the change in another variable in a path model using an integrative approach. In this case, the example illustrates the calculation one would use to determine how a 10.0 signal/sec increase in the rate of signaling by processors would change the air temperature in the Intergalactic Wildlife Sanctuary (IWS). Using an integrative approach, you multiply 10.0 signals/sec by the slope of the relationship between the rate of signaling by the processors and the activity of the heaters, 1.2 kW/(signal/sec), and the slope of the relationship between the activity of the heaters and the air temperature in the IWS, 0.1 °C/kW. After cancelling out appropriate units, the product is 1.2 °C, which means that a 10.0 signals/sec increase in the rate of signaling by the processors results in a 1.2 °C increase in the air temperature in the IWS. Determining how to treat Xor for a low concentration of carbohydrates in the blood Now that we know how to calculate the indirect effect of one variable on another variable, you’re ready to determine how to treat Xor if she has a low concentration of carbohydrates in the blood. Recall that the typical carbohydrate concentration in a healthy megaraffe is 6.00 mmol/L and that the carbohydrate concentration of blood must drop to at least 4.00 mmol/L to cause the symptoms that we observed in Xor. We have a drug that can help treat low blood carbohydrate concentration in megaraffes. The drug is an agonist of receptors for hormone G, meaning that this drug activates these receptors. Figure 14 (below) shows the completed path model for the homeostatic system that regulates the [carbohydrates] in the blood of a megaraffe with the addition of (a) a box representing the dose of the drug and (b) slopes for relevant relationships. For simplicity, this figure highlights only those components relevant to your calculation. These components include the relationships among the dosage of the drug, the concentration of hormone G in the blood, and the concentration of carbohydrates in the blood. The slopes for these relationships have been provided. Figure 14. Path model of the homeostatic system regulating the concentration of carbohydrates [carbohydrates] in the blood of healthy megaraffes. Key components, variables, and relationships have been highlighted to help determine the appropriate dose of drug needed to help return Xor’s [carbohydrates] in the blood back to healthy levels should her blood [carbohydrates] be too low. Three components and their variables have been highlighted – the dose of the drug, the [hormone G] in the blood, and the [carbohydrates] in the blood of megaraffes. The dose of the drug and the [hormone G] in the blood are each represented by a black box containing black text. The [carbohydrates] in the blood of megaraffes is represented by a dashed black box containing black text. An arrow points from the dose of the drug to the [hormone G] in the blood. The slope of the relationship between these two variables is provided as blue text next to the arrow connecting these variables. The slope of this relationship is 11.96 (umol/L)/g. A second arrow points from the [hormone G] in the blood to the [carbohydrates] in the blood of megaraffes. The slope of the relationship between these two variables is provided as blue text over the arrow connecting these variables. The slope of this relationship is 0.21 (mmol/L)/(umol/L). Under normal conditions in the absence of the drug, Xor’s [carbohydrates] in her blood should be 6.00 mmol/L. The slope of the relationship between the concentration of hormone G and the concentration of carbohydrates in the blood is 0.21 (mmol carbs/L of blood) / (umol hormone G/L of blood). The question remains: What dosage of drug do we need to treat Xor if her [carbohydrates] are too low? According to my archives, (a) the drug directly affects the concentration of hormone G in the blood, (b) the drug has no effect at dosages below 0.80 g and has a linear effect thereafter, using the following slope: the slope of this relationship at dosages above 0.80 g is 11.96 (umol hormone G/L of blood) / g of drug, and (c) the drug must increase the concentration of hormone G to a point that raises the concentration of carbohydrates in blood by 2.00 mmol/L. The key to remember here is that the goal is to determine the appropriate drug dose that raises the concentration of carbohydrates in blood by 2 mmol/L. We’ll work backwards from this goal to determine the correct dose. Directions: Use the path model and slopes in Figure 14 to answer questions 23-24. Round all calculated values to the nearest tenth of a decimal place. For example, if you calculate the value as 3.821853, round to 3.8. 23. How much does the concentration of hormone G (umol hormone G/L) need to increase or decrease by in order to raise the concentration of carbohydrates in the blood by 2.00 mmol/L? As a note, if your answer to this question is a positive value, then you are saying you want to increase the concentration of hormone G by that value. Conversely, if your answer to this question is a negative value, you are saying you want to decrease the concentration of hormone G by that value. Amount to increase or decrease the concentration of hormone G (umol hormone G/L) = 24. What dosage of the drug (g) needs to be administered to change the concentration of hormone G (umol hormone G/L) by the amount you indicated in the previous question? As a 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. Dosage of drug (g) = 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 need to prepare for the possibility that Xor may have high blood pressure. Blood pressure homeostasis in megaraffes Blood is a solution of cells and proteins that travels through the heart and vessels of a circulatory system (Figure 7). Blood carries nutrients to cells throughout the body, while also carrying wastes away from these cells. Being a fluid, blood exerts pressure against the walls of the heart and vessels (Figure 15), a force that we call blood pressure. Figure 15. Diagram illustrating blood pressure in the systemic arteries. Two arteries – a type of blood vessel – are shown side by side. Both arteries are the same size and have the same wall thickness. Arrows inside each artery indicate the amount of force exerted by blood against the walls of the arteries – also known as blood pressure. The thicker the arrow →the greater the force exerted against the walls of the arteries → the greater the blood pressure. The arrows in the artery on the left are thinner than the arrows in the artery on the right. This means that there is more force being exerted against the walls of the artery on the right as compared to the artery on the left. The blood pressure in the artery on the left is within the typical or expected ranges, while the blood pressure in the artery on the right is higher than expected. To survive, an organism must keep its blood pressure within a certain range. Therefore, any species that uses blood for circulation has evolved a homeostatic system to regulate its blood pressure. I searched my digital archives for information about the components of the system that regulates blood pressure in a megaraffe. This information is summarized below. Blood vessels: Blood flows through vessels to cells throughout the body. Certain vessels contain muscular tissue. As the muscular tissue contracts, a vessel constricts and the resistance to flow increases. Conversely, when the muscular tissue relaxes, the vessel expands and the resistance to flow decreases. The contraction or relaxation of blood vessels depends on signals from the megaraffe’s brain (a part of its brain analogous to the medulla oblongata of your brain). Vessels contract when receiving signals from the brain less frequently; this contraction increases the resistance to flow, which increases blood pressure in the arteries. Conversely, vessels relax when receiving signals from the brain more frequently; this relaxation decreases the resistance to flow and decreases blood pressure. Heart: This muscular organ pumps blood through two circuits of vessels: a circuit that involves the lungs (pulmonary circuit) and a circuit that involves the rest of the body (systemic circuit). Both the frequency of and the strength of the heart’s contraction determine the rate at which blood flows through these circuits. The heart contracts more frequently and more strongly when receiving fewer signals from the medulla oblongata, increasing blood flow. Conversely, the heart contracts less frequently and less strongly when receiving more signals from the brain, decreasing blood flow. As the rate of blood flows into a vessel increases, blood pressure increases. Medulla oblongata: The medulla oblongata receives information about the blood pressure in the arteries from nerves cells. As the medulla oblongata receives signals from nerve cells more frequently, it sends its own signals to other parts of the body more frequently. Conversely, as the medulla oblongata receives signals from the nerve cells less frequently, it sends its own signals less frequently. Nerve cells with baroreceptors: These cells send signals to the brain according to the pressure of the blood. When blood pressure increases, these nerve cells send signals more frequently. Conversely, when blood pressure decreases, these nerve cells send signals less frequently. Figure 16 shows a path model of the homeostatic system that regulates blood pressure in megaraffes. Figure 16. Path model of the homeostatic system regulating the blood pressure of megaraffes. The variable being regulated – blood pressure in megaraffes – is represented by a dashed black box containing black text. Each variable and the physical component associated with that variable in the model is represented by a black box containing black text. There are four components in the model: the blood vessels, the heart, the medulla oblongata, and nerve cells with baroreceptors. An arrow connecting one box to another indicates a relationship between two variables. A “+” or “-” symbol over each arrow indicates whether the relationship between two variables is a positive relationship or a negative relationship, respectively. There is an arrow pointing from the regulated variable – “Blood pressure in megaraffes” – to the variable “Rate of signaling by nerve cells with baroreceptors” with a “+” symbol over it, from the variable “Rate of signaling by nerve cells with baroreceptors” to the variable “Rate of signaling by the medulla oblongata” with a “+” symbol over it, from the variable “Rate of signaling by the medulla oblongata” to the variable “Rate of blood flow from the heart” with a “-” symbol over it, from the variable “Rate of signaling by the medulla oblongata” to the variable “Resistance of blood vessels” with a “-” symbol over it, from the variable “Rate of blood flow from the heart” to the regulated variable “Blood pressure in megaraffes” with a “+” symbol over it, and from the variable “Resistance of blood vessels” to the regulated variable “Blood pressure in megaraffes” with a “+” symbol over it. With this information, we can analyze a path model of a homeostatic system to determine what could have caused high blood pressure in Xor. Let’s start by determining what factors could cause high blood pressure in a megaraffe. For guidance, use Figure 16. Determining causes of high blood pressure Directions: Use the path model of the homeostatic system that regulates blood pressure of a megaraffe (Figure 16) to answer question 25. 25. Which scenario(s) would result in a megaraffe having high blood pressure? Select ALL that apply. a. Tumors cause nerve cells with baroreceptors have a continually high rate of signaling. b. Gene mutations weaken the muscles of the heart reducing the strength of each heart beat. c. Exposure to chemicals causes blood vessels to narrow, increasing resistance to blood flow. d. Brain trauma severed the connection between the medulla oblongata and the heart. e. None of the scenarios listed above would result in high blood pressure. Determining how to treat high blood pressure According to my digital archives, the typical blood pressure in a healthy megaraffe is 850 mmHg. Blood pressure must rise to at least 975 mmHg to cause the symptoms that we observed in Xor. We have a drug that can help treat high blood pressure in a megaraffes. The drug works much like the drugs used on your planet to treat humans with high blood pressure. At the correct dosage, the drug causes blood vessels to dilate, reducing the resistance to flow. I’ll need your help to determine how much of this drug to give Xor if we discover that she suffers from high blood pressure. Figure 17 (below) shows the completed path model for the homeostatic system that regulates the blood pressure of a megaraffe with the addition of (a) a box representing the dose of drug and (b) slopes for relevant relationships. For simplicity, this figure highlights only those components relevant to your calculation. These components include the relationships among the dosage of the drug, the resistance of blood vessels, and blood pressure. The slopes for these relationships have been provided. Figure 17. Path model of the homeostatic system regulating the blood pressure of healthy megaraffes. Key components, variables, and relationships have been highlighted to help determine the appropriate dose of drug needed to help return Xor’s blood pressure back to healthy levels should her blood pressure be too high. Three components and their variables have been highlighted – the dose of the drug, the resistance of blood vessels to blood flow, and the blood pressure in megaraffes. The dose of the drug and the resistance of blood vessels to blood flow are each represented by a black box containing black text. The blood pressure in megaraffes is represented by a dashed black box containing black text. An arrow points from the dose of the drug to the resistance of blood vessels to blood flow. The slope of the relationship between these two variables is provided as red text next to the arrow connecting these variables. The slope of this relationship is -2.29 (mmHg*min)/g. A second arrow points from the resistance of blood vessels to the blood pressure in megaraffes. The slope of the relationship between these two variables is provided as blue text over the arrow connecting these variables. The slope of this relationship is 1.0 mmHg/(mmHg*min). Under normal conditions in the absence of the drug, Xor’s blood pressure should be 850 mmHg. The slope of the relationship between the resistance of blood vessels and the blood pressure in megaraffes is 1.0 mmHg/(mmHg*min). The question remains: What dosage of drug do we need to treat Xor if her blood pressure is high? According to my archives, (a) the drug directly affects the resistance of blood vessels, (b) the drug has no effect at dosages below 24 g and has a linear effect thereafter, using the following slope: the slope of this relationship at dosages above 24 g is 2.29 (mmHg*min) / g of drug, and (c) the drug must decrease resistance of blood vessels enough to cause a decrease in blood pressure of -125 mmHg. 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: Use the path model and slopes in Figure 17 to answer questions 26-27. Round all calculated values to the nearest ones of a decimal place. For example, if you calculate the value as 3.821853, round to 4. 26. How much does the resistance of the blood vessels to blood flow (mmHg*min) need to increase or decrease by in order to reduce the blood pressure by -125 mmHg? As a note, if your answer to this question is a positive value, then you are saying you want to increase the resistance of the blood vessels to 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 the blood vessels to blood flow by that value. Amount to increase or decrease the resistance of the blood vessels to blood flow (mmHg*min) = 27. What dosage of the drug (g) needs to be administered to change the resistance of the blood vessels (mmHg*min) by the amount you indicated in the previous question? As a 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. Dosage of drug (g) =
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