A recent paper published in the British Journal of Nutrition by Roux(Reference Roux1) describes the use of theoretical efficiencies of protein and fat synthesis to calculate the energy requirements for growth in pigs. Not only is this an important topic for animal science, but the issues highlighted by Roux have significant implications for mathematical modelling of human weight gain – a fact that becomes especially clear when considering the consequences of a small mathematical error in the paper.
Roux erroneously asserts that the energy intake devoted to maintenance, IM, must either equal the intercept of the Kielanowski regression equation(Reference Kielanowski and Blaxter2), INT, or the intercept plus the full cost of protein resynthesis: INT+PB/6, where PB is the protein breakdown rate in MJ/d. However, this is a false choice since there are actually an infinite number of alternatives for IM given by: IM = INT+xPB, where x is an arbitrary fraction. This implies that the energy intake devoted to protein retention (IPR) is given by:
where PR is the protein retention rate in MJ/d.
The two choices proposed by Roux are equivalent to x = 0 or 1/6. The infinity of possible choices for x demonstrates that the energy cost for protein turnover can be distributed arbitrarily between the maintenance energy requirement and the efficiency of protein deposition which is often represented by the dimensionless parameter k P. Thus, it is not surprising that the value of k P calculated via linear regression depends sensitively on the functional form of the maintenance energy expenditure since different expressions for IM will account for different proportions of the protein turnover cost(Reference Birkett and de Lange3, Reference Whittemore, Green and Knap4). Furthermore, a particular value for k P can therefore only be applied in conjunction with the particular expression for IM determined in the same linear regression procedure. Otherwise, the energy cost of protein turnover will be inappropriately partitioned and incorrectly accounted. Nevertheless, several mathematical models of human weight gain have used regression values for k P derived from rats(Reference Pullar and Webster5), pigs(Reference Noblet, Karege and Dubois6) and infants(Reference Roberts and Young7) and have erroneously combined these values with equations for IM modelled for human adults(Reference Payne and Dugdale8, Reference Christiansen, Garby and Sorensen9) and adolescents(Reference Butte, Christiansen and Sorensen10).
How can this problem be avoided for modelling human energy expenditure? I have previously proposed modelling tissue deposition costs using the theoretical biochemical efficiencies for protein and fat synthesis in combination with an explicit model of protein and fat breakdown rates and their dependence on diet and body composition(Reference Hall11). This approach avoids the arbitrary partitioning problem and Roux also follows this path by advocating the choice x = 1/6 with the corresponding theoretical value of k P = 6/7, thereby allocating all of the protein turnover cost to the maintenance energy requirement. Thus, the main conclusions of Roux's paper are unaffected by his small mathematical error and he correctly points out that the theoretical biochemical efficiency of protein synthesis is a constant and can be applied across different genetic backgrounds and probably also across species.
I am supported by the Intramural Research Program of the National Institutes of Health National Institute of Diabetes and Digestive and Kidney Diseases (NIH/NIDDK).
I declare no conflict of interest.
