Problem 7 - Animal Physiology: From Genes to Organisms

Question

If the plasma concentration of substance \(X\) is \(200 \mathrm{mg} / 100 \mathrm{~mL}\) and the GFR is \(125 \mathrm{~mL} / \mathrm{min}\), what is the filtered load of this substance? If the \(T_{\mathrm{m}}\) for substance \(\mathrm{X}\) is \(200 \mathrm{mg} / \mathrm{min}\), how much of the substance will be reabsorbed at a plasma concentration of \(200 \mathrm{mg} / 100 \mathrm{~mL}\) and a GFR of \(125 \mathrm{~mL} / \mathrm{min}\) ? How much of substance \(X\) will be excreted?

Step-by-Step Solution

Answer

Filtered load is 250 mg/min, reabsorbed load is 200 mg/min, and excreted load is 50 mg/min.

Step 1 - Calculate the Filtered Load

The filtered load of a substance is calculated using the formula: \[ \text{Filtered Load} = \text{Plasma Concentration} \times \text{GFR} \] Substitute the given values: \[ \text{Plasma Concentration} = 200 \text{ mg/100 mL} = 2 \text{ mg/mL} \] \[ \text{GFR} = 125 \text{ mL/min} \] Therefore, \[ \text{Filtered Load} = 2 \text{ mg/mL} \times 125 \text{ mL/min} = 250 \text{ mg/min} \]

Step 2 - Determine the Amount Reabsorbed

Given that the \(T_{m}\) (maximum reabsorptive capacity) for substance \(X\) is 200 mg/min, it can reabsorb up to 200 mg/min. Since the filtered load is 250 mg/min, the amount reabsorbed will be the maximum value of 200 mg/min.

Step 3 - Calculate the Amount Excreted

The amount excreted is given by the formula: \[ \text{Excreted Load} = \text{Filtered Load} - \text{Reabsorbed Load} \] Substitute the known values: \[ \text{Filtered Load} = 250 \text{ mg/min} \] \[ \text{Reabsorbed Load} = 200 \text{ mg/min} \] Therefore, \[ \text{Excreted Load} = 250 \text{ mg/min} - 200 \text{ mg/min} = 50 \text{ mg/min} \]

Key Concepts

Filtered Load

The filtered load of a substance is a crucial concept in renal physiology. It represents the total amount of a substance filtered into the Bowman's capsule of the nephron per unit time. Essentially, it tells us how much of a substance is initially taken out of the blood by the kidneys.

To calculate the filtered load, you can use the formula: \[ \text{Filtered Load} = \text{Plasma Concentration} \times \text{GFR} \] In our example, the plasma concentration of substance X is given as 200 mg/100 mL (which converts to 2 mg/mL). The GFR, or glomerular filtration rate, is 125 mL/min. Thus, \[ \text{Filtered Load} = 2 \text{ mg/mL} \times 125 \text{ mL/min} = 250 \text{ mg/min} \] This means the kidneys filter 250 mg of substance X per minute from the blood.

Glomerular Filtration Rate (GFR)

The glomerular filtration rate (GFR) is a measurement of how well the kidneys are filtering blood. It indicates the volume of filtrate the kidneys produce each minute. GFR is a critical indicator of kidney function, and it's used to diagnose and stage kidney disease.

GFR can be influenced by various factors, including blood pressure and blood flow to the kidneys. In the context of our exercise, we use GFR to calculate the initial amount of substance X that is filtered from the blood. With a GFR of 125 mL/min, for every minute, 125 milliliters of blood plasma are filtered by the kidneys.

Reabsorption

Reabsorption plays a significant role in kidney function. After the filtration process, substances like glucose, amino acids, and ions are reabsorbed back into the bloodstream from the renal tubules. The reabsorptive capacity of a substance is often given by its tubular maximum (Tm).

For substance X in our exercise, the Tm is 200 mg/min. This means the kidneys can reabsorb up to 200 mg of substance X from the filtrate back into the blood per minute. Given a filtered load of 250 mg/min, the kidneys will reabsorb only up to the maximum capacity of 200 mg/min.

Excretion

Excretion is the final step in the process, where waste substances and excess ions are eliminated from the body through urine. The amount of a substance excreted is what remains after reabsorption.

The excreted load can be found using the formula: \[ \text{Excreted Load} = \text{Filtered Load} - \text{Reabsorbed Load} \] From our example, the filtered load is 250 mg/min, and the reabsorbed load is 200 mg/min. Therefore, the excreted load is \[ 250 \text{ mg/min} - 200 \text{ mg/min} = 50 \text{ mg/min} \] Thus, 50 mg of substance X is excreted per minute in the urine.

Tubular Maximum (Tm)

Tubular maximum (Tm) is the maximum rate at which a substance can be reabsorbed by the renal tubules. Once the reabsorption rate reaches its Tm, any excess amount of the substance will be excreted in the urine.

In the provided exercise, the Tm for substance X is 200 mg/min. Despite the filtered load being 250 mg/min, only 200 mg/min can be reabsorbed. This limitation ensures that excess amounts of the substance do not accumulate in the blood, maintaining homeostasis.

Understanding Tm helps in grasping how the kidneys handle substances that are filtered in large amounts, such as glucose in cases of diabetes, where high blood sugar levels can exceed the Tm for glucose reabsorption, leading to its presence in urine.