Friday, April 21, 2017

Erythropoietin and Feedback Loops

In Chapter 10 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss feedback loops. We included two new problems about feedback loops in the 5th edition of IPMB, but as Russ says "you can never have too many examples." So, here is another.

The number of red blood cells is controlled by a feedback loop involving the hormone erythropoietin. The higher the erythropoietin concentration, the more red blood cells are produced and therefore the higher the hematocrit. However, the kidney adjusts the production of erythropoietin in response to hypoxia (caused in part by too few red blood cells). The lower the hematocrit the more erythropoietin produced. This new homework problem illustrates the feedback loop. It reinforces concepts from Chapter 10 on feedback and from Chapter 2 on the exponential function, and requires the student to analyze data (albeit made-up data) rather than merely manipulating equations. Warning: the physiological details of this feedback loop are more complicated than discussed in this idealized example.
Section 10.3

Problem 17 ½. Consider a negative feedback loop relating the concentration of red blood cells (the hematocrit, or HCT) to the concentration of the hormone erythropoietin (EPO). In an initial experiment, we infuse blood or plasma intravenously as needed to maintain a constant hematocrit, and measure the EPO concentration. The resulting data are

HCT EPO
(%) (mU/ml)
20 200
30   60.1
40   18.1
50     5.45
60     1.64

In a healthy person, the kidney adjusts the concentration of EPO in response to the oxygen concentration (controlled primarily by the hematocrit). In a second experiment, we suppress the kidney’s ability to produce EPO, control the concentration of EPO by infusing the drug intravenously, and measure the resulting hematocrit. We find

EPO HCT
(mU/ml) (%)
  1 35.0
  2 36.0
  5 39.1
10 45.0
20 59.5

(a) Plot these results on semilog paper and determine an exponential equation describing each set of data.
(b) Draw a block diagram of the feedback loop, including accurate plots of the two relationships.
(c) Determine the set point (you may have to do this numerically).
(d) Calculate the open loop gain.
Biochemist Eugene Goldwasser first reported purification of erythropoietin when working at the University of Chicago in 1977. In his essay Erythropoietin: A Somewhat Personal History he writes about his ultimately successful attempt to isolate erythropoietin from urine samples.
“Unfortunately the amounts of active urine concentrates available to us from the NIH source or our own collection were still too small to make significant progress, and it seemed as if purification and characterization of human epo might never be accomplished—that it might remain merely an intriguing biological curiosity. The prospect brightened considerably when Drs. M. Kawakita and T. Miyake instituted a very large-scale collection of urine from patients with aplastic anemia in Kumamato City, Japan. After some lengthy correspondence, Dr. Miyake arrived in Chicago on Christmas Day of 1975, carrying a package representing 2550 liters of urine [!] which he had concentrated using our first-step procedure. He and Charles Kung and I then proceeded systematically to work out a reliable purification method…we eventually obtained about 8 mg of pure human urinary epo .”
You can learn more about Goldwasser and his career in his many obituaries, for instance here  and here. A more wide-ranging history of erythropoietin can be found here.

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