Optimal Line of protein to carbohydrate ratio and the implications for nutrition.
Stan Bleszynski (C) 1-July-2003 (Resume)
Original preliminary version was posted at: http://boards.health.msn.com/message.asp?message_id=4288028 ; current version has been changed and amended. Updated 3-June-2004
Abstract & summary
Many nutritionists are recommending consumption
of proteins with carbohydrates in order to ensure proper digestion and
metabolism.
For example [1] recommends about P = 1g
+ 0.4*C (per 1kg body per day), where C=carbohydrates per weight per 1kg
per day, P=proteins per weight per 1kg per day. Other nutritionists recommend
a substantial ratio of proteins to carbs as well, for example some recommend
between P/C = 0.3 - 1 , green vegetables contain typically P/C = 0.3 -1
(but not root vegetables and grains!). Author [2] recommends P/C
to be 0.75. These assumption can be combined with the constraints
of total caloric intake and lead to relation between the optimal carbohydrate
and fat contents in a diet. The optimal line proportions
are:
XF = 85.0% - 1.341*XC [percentage of calories]
And the total caloric intake (in model II) is protein dependent and equal to:
T = E/(1 - XP) = 23/(1 - XP) [kcal/per 1kg body/day]
Interesting conclusions are that the above constraints are close to certain high carbohydrate diets, for example Sears' Zone:
XP:XF:XC = 30:30:40% (by calories)
as well as some high fat diets, for example Kwasniewski's Optimal Diet, for example:
XP:XF:XC = 14:80:6% (by calories)
In addition, high carbohydrate diets require
more total calories than high fat diets, by about 20%, for example:
about 32 kcal/kg
body/day for Zone, versus about 28 kcal/kg body/day for Optimal
Diet
Important conclusion of this article is that certain very high carbohydrate diets such as those advocated by American Health Association or US and other government endorsed "food pyramids", which contain greater or equal than 60% carbohydrates (by calories) must by design be defficient in proteins or fats or both.
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Assumptions, model I:
1) body needs 0.4 parts of proteins to generate enzymes per every one part of carbohydrates, in order to maintain a proper metabolism
2) In addition to above, we need about 1g of proteins per 1kg body weight to regenerate/repair body tissues
3,a) Body requires about E=35kcal total per every one kg of body weight per day. Note this model assumes that caloric intake is independent on the protein intake, even though the proteins are not normally used for supplying energy but are used for metabolising carbohydrates and body tissue repare and regeneration.
Derrivation:
Assumptions 1 and 2 can be combined in the following equation:
P = 1 + 0.4*C [g per kg/day] (I)
And assumption 3 turns into:
4*P + 9*F + 4*C = E = 35 [kcal/1kg/day] (ii)
- where P is amount of proteins in grams consumed per 1kg of body weight per day
F = fat in g/kg/day
C = carbs in g/kg/day
P from (i) can be substituted into (ii) and 9*F expressed as:
9*F = E – 4 + 5.6*C
if we denote XF as a percentage of caloric contents of fat in total, and XC as fractional caloric contents of carbs, in total and XF=9*F/35, XC=4*C/E then we obtain:
XF = 1-4/E
– 5.6/4*XC
XF =
0.886 - 1.40*XC
(iiia)
XC =
0.633 - 0.714*XF
More complex model II - assumptions:
1) body needs 0.4 parts of proteins to generate enzymes per every one part of carbohydrates, in order to maintain a proper metabolism
2) In addition to above, we need about 1g of proteins per 1kg body weight to regenerate/repair body tissues
Note: above assumptions are identical to model I, however the one below is different:
3,b) Body requires about
E=23kcal per every one kg of body weight per day, not counting proteins.
Note this model assumes that caloric intake includes carbohydrates and
fat but not proteins, since the proteins are normally used only for metabolising
carbohydrates and body tissue repaire and regeneration. However this assumption
may be incorrect in case of excessive proteins, when the proteins beyond
the amount specified by 1 may be metabolised for energy or excreted.
Derrivations for model II:
Assumptions 1 and 2 can be combined in the following equation:
P = 1 + 0.4*C [g per kg/day] (i)
And assumption 3b turns into:
9*F + 4*C = E = 23 [kcal/1kg/day] (ii)
T = 4*P + E
- where P is amount of proteins in grams consumed per 1kg of body weight per day, F = fat in g/kg/day , C = carbs in g/kg/day, and T is the total number of calories per 1kg body per day, including proteins.
P can be substituted into (ii) and 9*F expressed as:
9*F = T - 4 - 5.6*C
if we denote XF as a percentage
caloric contents of fat in total, and XC as fractional caloric contents
of carbs, and XF=9*F/T, XC=4*C/T then we obtain:
XP +
XF + XC = 1
T = E/(1 -
XP ) = E/(XF + XC)
XF =
E/(E+4) – (1.4*E+4)/(E+4)*XC
In spite of different assumption as to the total caloric requirements, model II leads to a surprisingly simliar results compared to model I, in percentages:
XF = 0.850
- 1.341*XC
(iiib)
XC =
0.634 - 0.746*XF
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Table 1. Various
food groups ratios that fulfill Optimal Line (model II).
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Fig.1. Graphic overview of various diets in relation to____________________________________________________________
Optimal Line, as per model II.
( Here is a high resolution picture 210KB )
References:
1) Jan Kwasniewski, Marek
Chylinski "Homo Optimus", WGP, 1996
2) Barry Sears, "Enter
the Zone", Harper Collins / Regan Books, 1995