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Glycated haemoglobin

How do red blood cells store the average values to give a 3 month average?
Here is the short version, is this what you're looking for?

Some of the glucose in your blood binds to haemoglobin (the protein that carries oxygen in your red blood cells). This combination of glucose and haemoglobin is called haemoglobin A1c (HbA1c). The amount of HbA1c formed is directly related to the average concentration of glucose in your bloodstream. Red blood cells live for 2–3 months, and because of this, the amount of HbA1c in your blood reflects the average level of glucose in your blood during the last 2-3 months.

(source: https://labtestsonline.org.uk/tests/hba1c-test)
 
Not really.

What is being implied is that red blood cells retain memory of their glucose levels over an 8-12 week period.

So glucose attaches to haemoglobin. Presumably it detached too as it is delivered to muscles for use. There must be cycle of upload and download for each red blood cell, if the cells uploaded and kept the glucose it wouldn’t be transported to muscles!? Therefore the glucose level on any red blood cell must go up and down daily (probably more frequently). So all a test will do is measure an average value on the day.
 
Not really.

What is being implied is that red blood cells retain memory of their glucose levels over an 8-12 week period.

So glucose attaches to haemoglobin. Presumably it detached too as it is delivered to muscles for use. There must be cycle of upload and download for each red blood cell, if the cells uploaded and kept the glucose it wouldn’t be transported to muscles!? Therefore the glucose level on any red blood cell must go up and down daily (probably more frequently). So all a test will do is measure an average value on the day.
No, that's not it. A glycated red blood cell has had a glucose molecule attached to it. Having had a glucose molecule attached changes the configuration of the cell, like having a bus ticket clipped.

The more glucose in the blood, the more glycated red blood cells there will be. The test can assess the number of glycated versus non-glycated RBCs, and generate a figure. This used to be expressed in percentage terms but is most often given now as millimoles per mol of blood, which is a measure of concentration.

As above, red blood cells live about 3 months tops, so the HbA1c goes back about three months, but there is a big skew towards the most recent month. If I remember right the most recent month makes up 60% of the result, the previous month 30% and the third month back about 10%. This is because some of the red blood cells that were around three or two months ago have already been replaced.

You're right that the blood glucose level will go up and down all the time. But this is for the blood as a whole, not any particular red blood cell. And if you do a fingerprick test all you will get is the current value of your capillary blood at that instant, which might not be all that informative taken in isolation. The HbA1c is better for a long-term view exactly because it can give an indication of how blood glucose levels have been over the last three months, rather than just at the instant the test was done..
 
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