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MECHANISMS FOR THE CONTROL OF BODY-WEIGHT
583
Occasional
Survey
MECHANISMS FOR THE CONTROL OF BODY-WEIGHT P. R. PAYNE
Department of Human Nutrition, London School of Hygiene and Tropical Medicine A. E. DUGDALE
Department of Child Health, University of Queensland, Brisbane, Australia Various hypotheses for the mechanism of regulation of body-weight in human adults have been proposed in the light of the magnitude of the long-term changes in weight actually observed. One of these hypotheses has been represented in the form of a computer simulation model which has been used to demonstrate that (i) it is not necessary to postulate the existence of a set-point regulatory system, and (ii) in practice, several mechanisms, including hunger and satiety, the relative constancy of habits and customs of behaviour, and the existence of cognitive thresholds combined with a relatively simple physiological negative feedback system probably constitute the simplest hypothesis for the mechanism of weight stability.
"buffer" the effects of short librium.
period disturbances of equi-
4. In man, at any rate, there is almost certainly some degree of cognitive control. People become aware of the fact that their clothes no longer fit, or that their weights are no longer consonant with efficient survival or with current social values. In response they control, or attempt to control, food intake.
Clearly these are not mutually exclusive possibilities. In reality, some aspects of these various mechanisms may all be operative. An additional feature of any acceptable hypothesis must be an ability to cope with the wide range of apparently random day to day variations in intake and expenditure, which are known to occur.2
Summary
INTRODUCTION
AT present there is no consensus on the way in which is regulated in adults. Garrow’1 has reviewed the experimental evidence and concludes that there is no basis for supporting or rejecting any of the main hypotheses which have been proposed. Current hypotheses reviewed by Garrow are:
body-weight
1. The possesses
a
set-point theory suggests that the body complete control system consisting of a sens-
ing device, which continuously monitors the weight or possibly- the volume of the body; a comparator which detects any difference between the current weight and some preferred value or set-point; and finally, a feedback, mechanism by which either appetite, metabolic rate, or work output are changed so as to bring about a restoration of the preferred weight. (This is analogous to the thermostatic control of temperature by a central-heating plant).
THE VARIABILITY OF BODY-WEIGHT
is not constant in normal adults. There fluctuations from day to day, slower cycles of about a few weeks, and long-term trends extending over years. The magnitude of these changes defines the limits within which the control system must operate. Garrowl has concluded that very short-term day-today changes have a standard deviation of about 0-3% of body-weight-i.e., that a change from one day to the next of 1 kg will occur about once in twenty weighings. Slower fluctuations about a mean value also occur, giving in one case, for example, a range of 2-4 kg over an 80-day period. Long-term changes in weight have been shown by Chinn et al. who weighed adults in communities in South Wales on two occasions 4 years apart. There were considerable fluctuations in the weight of individuals. The standard deviations of the weight change in the groups ranged from 4.8to 6.6 kg. Evidence over longer periods of time is very scanty. Forbes and Reina9 describe longitudinal observations on 6 male subjects over periods of between 10 and 30 years, and Fox5 has published recordings of his own weight collected over 20 years. All these individuals experienced slow trends and reversals of body-weight amounting to between 5 and 19 kg (7 to 21% of mean weight). Parallel changes occur in lean body-mass, but these are smaller both in absolute and percentage terms.4 There is even less information about obese subjects, but it is generally believed that they exhibit even 1 greater changes than these.
Body-weight
are
.
2. Another hypothesis is that no set-point exists but that the system exhibits dynamic equilibrium. For example, if any change in weight produces a change in metabolic rate, then for fixed levels of energy intake and work output, body-weight will tend to be self-stabilising,
FORCED CHANGES IN WEIGHT
since increased weight will increase metabolic rate, which will produce a negative energy balance and hence a subsequent decline in weight; weight reductions would similarly be automatically corrected.
In addition to these natural variations, it is, of course, possible to produce forced changes in weight by over or under feeding. Garrow and Stalley6have described two such experiments on a single subject, the results of which are shown in fig. 1. The shaded band encloses the range of daily weights actually observed. At point A, 1200 kcal of extra energy was taken each day, resulting in’a rapid rise in weight to a new level, which was sus-
3. A more complex system of this latter type would be one in which rapid changes in body-weight produce larger responses in metabolic rate than relatively slow changes. Such a system would also smooth out or
subject until point B, at which weight was reduced to its original value by underfeeding. A further reduction at C was followed by sustained weight-gain on a freely selected intake, until finally a stable value was attained
tained without any conscious effort
on
the part of the
584 tissue. It is a basic assumption in the model, that the same value of this ratio governs the proportions withdrawn from the compartments in order to meet negative balances, since any difference would result in continual drifts in body composition caused by the random sequence of positive and negative energy balances that
from day-to-day variability. There is sufficient data available on the composition of weight gains and losses in the same individuals to demonstrate the extent to which this is true in reality. The numerical values of the ratios used in the model are all derived from data for body composition changes during weight-loss for normal and for obese subjects. 10 11 The lean/fat tissue ratio for depositions and withdrawals from the compartments is fixed for an individual person, and characterises him as metabolically "lean" (high values of the ratio) or metabolically "fat" (low levels). "Lean individuals mobilise or deposit energy in the proportions 30% as lean tissue, 70% as fat
inevitably result not
Fig. 1--Comparison between weight-changes in the subject studied by Garrow and Stalley (shaded band) and computer model simulation.
A, B, and C indicate times of dietary changes.
by conscious control of appetite. These experiments, whilst providing some interesting information about the response time of the system, do not tell us anything conclusive about whether or not an active control system is responsible. If a set-point mechanism exists, it can clearly be re-set at least in an upward direction. If there is no set-point, how does one account for the lengthy periods of relative stability? If cognitive control is the major factor operating, as Garrow and Stalley suggest, why did it operate at the end of the 2 years but not after point A? Subjects overfed for longer periods of time gain weight at rates lower than would be expected if all of the excess energy were converted to adipose tissue, and in addition, the rates of weight-gain decline with time if the extra energy intake is continued.8 A striking feature of these experiments is the wide range of individual variability in the amount of weight-gain per unit of excess energy consumed. Thus, although it is clear that some sort of control does take place, it is difficult to interpret any of the data that we have in such a way as to support or refute any one of the hypotheses currently offered.
COMPUTER MODELS
Computer simulation studies can help in this kind of situation. First, they allow us to study the behaviour of model systems whose characteristics are defined. Second, they introduce a quantitative element into our speculations and hence suggest more stringent experimental tests, and third it is possible specifically to include and to study the effects of random variation in food intake and energy output upon different model systems. We have described9 a relatively simple model which reproduces several of the important features of the changes in body weight and composition. We shall try to demonstrate the extent to which this provides a satisfactory basis for exploring the mechanism of short and long term
weight regulation.
BEHAVIOUR OF THE MODEL
The model9 (fig. 2) is a system of four energy-storage compartments which are analogues of the fat and lean tissues of the body; the "metabolic rate" of the model is the sum of the separate rates of metabolism of the four compartments. Positive balances result in deposition in the compartments according to a fixed ratio of lean/fat
Fig 2--Compartments and transfer pathways of four compartment
computer model.
tissue, whilst in fat individuals the proportions
are
3%
lean and 97% as fat. In the model, both mean levels and coefficients of variation of daily energy intake and expenditure are specified. The actual input and output for a day are calculated from this data with the aid of a gaussian distribution of random numbers generated in the computer. For the computer runs used in this paper a coefficient of variation of ±20% was assumed for the food intake. This is a conservative estimate of the value found by Edholm et awl. The model has no set-point or preferred value for weight, but for any given mean value and range of variability of daily intake and activity there is a corresponding value for body-weight about which a dynamic equilibrium is achieved. This equilibrium weight is independent of the "starting weight" of the model man. The lean tissues are subdivided in the model into a small "fast" compartment with a high metabolic rate, as
585 and a much larger, slowly metabolising one. The small fast compartment is influenced directly by changes in energy balance, and changes in food intake therefore produce fairly rapid responses in metabolic rate. These result in a degree of smoothing out or "buffering" of the effects on body-weight of relatively transient changes in
intake.
single points plotted in fig. 1 are the result of a run simulating Garrow and Stalley’s feeding experiments.67This is partly to demonstrate that the
The model
transient response characteristics of the model are close to observed values even to the reproduction of the small "overshoot" of weight at A. Mainly, however, it is a means of assessing the changes in habitual energy intake which are likely to have occurred during the experiment. Garrow and Stalley did not measure food intakes, but the model predicts that the initial weight of 74.7 kg would require an average intake of 3250 kcal/day for maintenance. After A, the higher weight of 79.8kg would need 3400 kcal. The return to a stable weight after reduction at B is well simulated by an intake of 3300 kcal, and that after C by a level of 3400 kcal/day. This means that the most likely explanation for the whole sequence of events apart from the short periods of forced over and under feeding is that the various levels of relatively stable body-weight were the result of changes in habitual average intake of less than 5%.
SHORT-TERM DYNAMIC
SIMULATION OF LONG-TERM WEIGHT CHANGES
A food intake of 3020 kcal/day with a coefficient of variation of 20%, and an energy output of 400 kcal/day produce dynamic stability about a weight of 65 kg in the computer "model man". Fig. 3 shows the weightchanges which are predicted by the model as a result of feeding 5% above and below this level. Runs were made for the equivalent of 8 years using both "fat" and "lean" types of individual. This shows clearly that if
average intake is changed, then average body-weight will change, albeit slowly-i.e., half a small chocolate bar which is about 150 kcal extra a day will ultimately increase body-weight by 5 or 6 kg, but takes 3 years to do so-and the rate of change declines with time. As
EQUILIBRIUM
Fig. 1 shows that for the periods when average intake is fixed, body-weight also on average remains constant but exhibits short-term fluctuations. The changes from day to day are caused by the random components of intake and activity. However, there are also somewhat longer period fluctuations (of the order of weeks) due to a "random walk" phenomenon. Weight swings above and below the mean value in a way which resembles active control about a preferred value but is in fact a dynamic equilibrium in which departures from the mean value due to random drifts are counteracted over a subsequent period by changes in metabolic rate.
Fig 4-Weight-changes predicted by model throughout 10-yr programme of food intakes.
would be expected intuitively, a predisposition towards storing energy as fat does lead to a greater gain in weight for the same level of intake as well as producing a higher body-fat content, but with underfeeding, there is little difference between the body-weights of lean and fat individuals. The model therefore describes the following features of weight regulation:
(1) Provided
the mean values of intake and expendiremain constant, the effects on body-weight of short-term fluctuations are smoothed out, and a state of dynamic equilibrium is maintained. Small cyclic variations occur about a mean value, with magnitudes of about + 1 kg over time periods of a few weeks. (2) The mean value of body-weight about which equilibrium is established does depend upon the average levels of energy intake and expenditure. Thus if sustained sufficiently long, changes of mean intake do result in changes in weight. However, the rate of change declines over time, and a new equilibrium value eventually results. (3) Differing propensities towards storing energy as fat result in individual differences in the extent of weightgain caused by overfeeding.
ture
Fig 3-Long-term weight-changes predicted by model for excess or deficit
of energy intake of S%.
An
objection
at
this
point might
be that in order
to
586
weight constant over long periods, the model requires that mean intake and expenditure should be maintain
We have therefore devised a 10-year programme of daily activities and food intakes in which there is the variation that might realistically be expected in a suburban man. The 10-year programme includes:altered levels of intake and expenditure at weekends as opposed to week days, a 6-month seasonal cycle of intake (±5%), a randomised incidence of illness (10 days in each year) sufficiently serious to cause loss of appetite. There is a major surgical operation once during the 10 years (at B), and two sustained changes of +5% such as might result from a change of domestic life or of job location (at A and C). All of these changes are in addition to the normal random day to day variation of ±20%. Fig. 4 shows examples of runs made, with this programme, again with both lean and fat versions of the model. Because of the large element of randomness introduced, repeated runs vary considerably, even though the starting weight is the same. The average range of weight changes found for three runs was 9.5kg for lean and 12.8kg for fat versions of the model; very similar, in fact, to the changes found in real-life situations. constant.
DISCUSSION
Body-weight in adults is not by day, month by month, and
constant, but varies day year by year. Also, it is known that food intake and energy expenditure vary widely from day to day. Although weight, intake, and
expenditure must have some broad limits to variability set by physiological and psychological factors, the magnitude of long-term trends in body-weight actually observed are small enough to suggest that there must, in addition, be some sort of control system in operation. The problem is to suggest which kind of control system would explain the known facts whilst needing the fewest and the most plausible assumptions about any physiological mechanisms involved. Of all the hypotheses which have been considered up to now, the most complex is the set-point theory of weight control which implies the existence of physiological mechanisms for representing a set-point or preferred value for weight; for comparing actual weight with that preferred value; and for controlling intake or expendiany errors. None of these mechanisms has been shown to exist. An alternative hypothesis is the one which we have described as the dynamic equilibrium hypothesis. The operation of this is shown in fig. 5. Any imbalance between intake and the sum of the energy outputs results in a change in body-weight. This in turn alters the tissue metabolic energy (maintenance energy) in a direction which will tend subsequently to counter the original imbalance-i.e., there is a built-in negative feedback. This results in a slow change of body-weight in response to any moderate and sustained change in energy balance, with a new equilibrium value of bodyweight always being ultimately attained. The computer model based on this system, satisfactorily imitates the changes in weight, composition, and metabolic rate durexperiments of ing the 36 weeks of et the Keys al.,10 weight-changes during overfeeding of diets by Miller and Mumford,8 and the high protein ture so as to correct
starvation/refeeding
Fig.
5-Flow
diagram illustrating
the
dynamic equilibrium
hypothesis for body-weight regulation.
weight and body-composition changes in dieted obese subjects described by Passmore et al." The dynamic equilibrium hypothesis implies that for any individual there is a mean body-weight which corresponds to any given fixed mean values of energy intake and activity expenditure. The question that arises then is whether in normal people average levels of expenditure and intake are sufficiently well-regulated, because of habitual patterns of behaviour and eating, together perhaps with some broad limits imposed through feelings of hunger and satiety, to result in the magnitude of long-term weight-changes we know to occur. The computer model demonstrates that the kinds of changes of circumstance and habits which we might reasonably expect during 10 years of urban working life would in fact be accompanied by very plausible changes in weight, and we believe therefore that there is certainly no basis for suggesting the existence of any more complex regulation such as a set-point device. Whilst in most people simple habit, together perhaps with some quite rough limits imposed by appetite, would seem quite sufficient; there will of course be some for whom the resulting trends in body-weight will prove unacceptable for cosmetic or health reasons, and who will then deliberately alter their intake or activity. The dynamic equilibrium mechanism is therefore best seen as providing the basic degree of physiological stability which may be supplemented in some people from time to time by a psychological cognitive control. REFERENCES 1. Garrow, J. S. Energy Balance and Obesity in Man. Amsterdam, 1974. 2. Edholm, O. G., Adam, J. M., Healy, M. J. R., Wolff, H. S., Goldsmith, R., Best, T. W. Br. J. Nutr. 1970, 24, 1091. 3. Chinn, S., Garrow, J. S., Miall, W. B. Unpublished. Cited by Garrow.1 4. Forbes, G. B., Reina, J. C. Metabolism, 1970, 19, 653. 5. Fox, F. W. Lancet, 1973, ii, 1487. 6. Garrow, J. S., Stalley, S. F. Proc. Nutr. Soc. 1975, 34, 84A. 7. Garrow, J. S., Stalley, S. F. ibid. (in the press). 8. Miller, D. S., Mumford, P. Am. J. clin. Nutr. 1967, 20, 1212. 9. Payne, P. R., Dugdale, A. E. Ann hum. Biol. (in the press). 10. Keys, A., Brozek, J., Henscel, A., Mickelsen, O., Taylor, H. L. The Biology of Human Starvation, vols I and IL Minneapolis, 1950. 11. Passmore, R., Strong, J. A., Ritchie, F. J. Br J. Nutr. 1958, 12, 113.
Occasional
Survey
MECHANISMS FOR THE CONTROL OF BODY-WEIGHT P. R. PAYNE
Department of Human Nutrition, London School of Hygiene and Tropical Medicine A. E. DUGDALE
Department of Child Health, University of Queensland, Brisbane, Australia Various hypotheses for the mechanism of regulation of body-weight in human adults have been proposed in the light of the magnitude of the long-term changes in weight actually observed. One of these hypotheses has been represented in the form of a computer simulation model which has been used to demonstrate that (i) it is not necessary to postulate the existence of a set-point regulatory system, and (ii) in practice, several mechanisms, including hunger and satiety, the relative constancy of habits and customs of behaviour, and the existence of cognitive thresholds combined with a relatively simple physiological negative feedback system probably constitute the simplest hypothesis for the mechanism of weight stability.
"buffer" the effects of short librium.
period disturbances of equi-
4. In man, at any rate, there is almost certainly some degree of cognitive control. People become aware of the fact that their clothes no longer fit, or that their weights are no longer consonant with efficient survival or with current social values. In response they control, or attempt to control, food intake.
Clearly these are not mutually exclusive possibilities. In reality, some aspects of these various mechanisms may all be operative. An additional feature of any acceptable hypothesis must be an ability to cope with the wide range of apparently random day to day variations in intake and expenditure, which are known to occur.2
Summary
INTRODUCTION
AT present there is no consensus on the way in which is regulated in adults. Garrow’1 has reviewed the experimental evidence and concludes that there is no basis for supporting or rejecting any of the main hypotheses which have been proposed. Current hypotheses reviewed by Garrow are:
body-weight
1. The possesses
a
set-point theory suggests that the body complete control system consisting of a sens-
ing device, which continuously monitors the weight or possibly- the volume of the body; a comparator which detects any difference between the current weight and some preferred value or set-point; and finally, a feedback, mechanism by which either appetite, metabolic rate, or work output are changed so as to bring about a restoration of the preferred weight. (This is analogous to the thermostatic control of temperature by a central-heating plant).
THE VARIABILITY OF BODY-WEIGHT
is not constant in normal adults. There fluctuations from day to day, slower cycles of about a few weeks, and long-term trends extending over years. The magnitude of these changes defines the limits within which the control system must operate. Garrowl has concluded that very short-term day-today changes have a standard deviation of about 0-3% of body-weight-i.e., that a change from one day to the next of 1 kg will occur about once in twenty weighings. Slower fluctuations about a mean value also occur, giving in one case, for example, a range of 2-4 kg over an 80-day period. Long-term changes in weight have been shown by Chinn et al. who weighed adults in communities in South Wales on two occasions 4 years apart. There were considerable fluctuations in the weight of individuals. The standard deviations of the weight change in the groups ranged from 4.8to 6.6 kg. Evidence over longer periods of time is very scanty. Forbes and Reina9 describe longitudinal observations on 6 male subjects over periods of between 10 and 30 years, and Fox5 has published recordings of his own weight collected over 20 years. All these individuals experienced slow trends and reversals of body-weight amounting to between 5 and 19 kg (7 to 21% of mean weight). Parallel changes occur in lean body-mass, but these are smaller both in absolute and percentage terms.4 There is even less information about obese subjects, but it is generally believed that they exhibit even 1 greater changes than these.
Body-weight
are
.
2. Another hypothesis is that no set-point exists but that the system exhibits dynamic equilibrium. For example, if any change in weight produces a change in metabolic rate, then for fixed levels of energy intake and work output, body-weight will tend to be self-stabilising,
FORCED CHANGES IN WEIGHT
since increased weight will increase metabolic rate, which will produce a negative energy balance and hence a subsequent decline in weight; weight reductions would similarly be automatically corrected.
In addition to these natural variations, it is, of course, possible to produce forced changes in weight by over or under feeding. Garrow and Stalley6have described two such experiments on a single subject, the results of which are shown in fig. 1. The shaded band encloses the range of daily weights actually observed. At point A, 1200 kcal of extra energy was taken each day, resulting in’a rapid rise in weight to a new level, which was sus-
3. A more complex system of this latter type would be one in which rapid changes in body-weight produce larger responses in metabolic rate than relatively slow changes. Such a system would also smooth out or
subject until point B, at which weight was reduced to its original value by underfeeding. A further reduction at C was followed by sustained weight-gain on a freely selected intake, until finally a stable value was attained
tained without any conscious effort
on
the part of the
584 tissue. It is a basic assumption in the model, that the same value of this ratio governs the proportions withdrawn from the compartments in order to meet negative balances, since any difference would result in continual drifts in body composition caused by the random sequence of positive and negative energy balances that
from day-to-day variability. There is sufficient data available on the composition of weight gains and losses in the same individuals to demonstrate the extent to which this is true in reality. The numerical values of the ratios used in the model are all derived from data for body composition changes during weight-loss for normal and for obese subjects. 10 11 The lean/fat tissue ratio for depositions and withdrawals from the compartments is fixed for an individual person, and characterises him as metabolically "lean" (high values of the ratio) or metabolically "fat" (low levels). "Lean individuals mobilise or deposit energy in the proportions 30% as lean tissue, 70% as fat
inevitably result not
Fig. 1--Comparison between weight-changes in the subject studied by Garrow and Stalley (shaded band) and computer model simulation.
A, B, and C indicate times of dietary changes.
by conscious control of appetite. These experiments, whilst providing some interesting information about the response time of the system, do not tell us anything conclusive about whether or not an active control system is responsible. If a set-point mechanism exists, it can clearly be re-set at least in an upward direction. If there is no set-point, how does one account for the lengthy periods of relative stability? If cognitive control is the major factor operating, as Garrow and Stalley suggest, why did it operate at the end of the 2 years but not after point A? Subjects overfed for longer periods of time gain weight at rates lower than would be expected if all of the excess energy were converted to adipose tissue, and in addition, the rates of weight-gain decline with time if the extra energy intake is continued.8 A striking feature of these experiments is the wide range of individual variability in the amount of weight-gain per unit of excess energy consumed. Thus, although it is clear that some sort of control does take place, it is difficult to interpret any of the data that we have in such a way as to support or refute any one of the hypotheses currently offered.
COMPUTER MODELS
Computer simulation studies can help in this kind of situation. First, they allow us to study the behaviour of model systems whose characteristics are defined. Second, they introduce a quantitative element into our speculations and hence suggest more stringent experimental tests, and third it is possible specifically to include and to study the effects of random variation in food intake and energy output upon different model systems. We have described9 a relatively simple model which reproduces several of the important features of the changes in body weight and composition. We shall try to demonstrate the extent to which this provides a satisfactory basis for exploring the mechanism of short and long term
weight regulation.
BEHAVIOUR OF THE MODEL
The model9 (fig. 2) is a system of four energy-storage compartments which are analogues of the fat and lean tissues of the body; the "metabolic rate" of the model is the sum of the separate rates of metabolism of the four compartments. Positive balances result in deposition in the compartments according to a fixed ratio of lean/fat
Fig 2--Compartments and transfer pathways of four compartment
computer model.
tissue, whilst in fat individuals the proportions
are
3%
lean and 97% as fat. In the model, both mean levels and coefficients of variation of daily energy intake and expenditure are specified. The actual input and output for a day are calculated from this data with the aid of a gaussian distribution of random numbers generated in the computer. For the computer runs used in this paper a coefficient of variation of ±20% was assumed for the food intake. This is a conservative estimate of the value found by Edholm et awl. The model has no set-point or preferred value for weight, but for any given mean value and range of variability of daily intake and activity there is a corresponding value for body-weight about which a dynamic equilibrium is achieved. This equilibrium weight is independent of the "starting weight" of the model man. The lean tissues are subdivided in the model into a small "fast" compartment with a high metabolic rate, as
585 and a much larger, slowly metabolising one. The small fast compartment is influenced directly by changes in energy balance, and changes in food intake therefore produce fairly rapid responses in metabolic rate. These result in a degree of smoothing out or "buffering" of the effects on body-weight of relatively transient changes in
intake.
single points plotted in fig. 1 are the result of a run simulating Garrow and Stalley’s feeding experiments.67This is partly to demonstrate that the
The model
transient response characteristics of the model are close to observed values even to the reproduction of the small "overshoot" of weight at A. Mainly, however, it is a means of assessing the changes in habitual energy intake which are likely to have occurred during the experiment. Garrow and Stalley did not measure food intakes, but the model predicts that the initial weight of 74.7 kg would require an average intake of 3250 kcal/day for maintenance. After A, the higher weight of 79.8kg would need 3400 kcal. The return to a stable weight after reduction at B is well simulated by an intake of 3300 kcal, and that after C by a level of 3400 kcal/day. This means that the most likely explanation for the whole sequence of events apart from the short periods of forced over and under feeding is that the various levels of relatively stable body-weight were the result of changes in habitual average intake of less than 5%.
SHORT-TERM DYNAMIC
SIMULATION OF LONG-TERM WEIGHT CHANGES
A food intake of 3020 kcal/day with a coefficient of variation of 20%, and an energy output of 400 kcal/day produce dynamic stability about a weight of 65 kg in the computer "model man". Fig. 3 shows the weightchanges which are predicted by the model as a result of feeding 5% above and below this level. Runs were made for the equivalent of 8 years using both "fat" and "lean" types of individual. This shows clearly that if
average intake is changed, then average body-weight will change, albeit slowly-i.e., half a small chocolate bar which is about 150 kcal extra a day will ultimately increase body-weight by 5 or 6 kg, but takes 3 years to do so-and the rate of change declines with time. As
EQUILIBRIUM
Fig. 1 shows that for the periods when average intake is fixed, body-weight also on average remains constant but exhibits short-term fluctuations. The changes from day to day are caused by the random components of intake and activity. However, there are also somewhat longer period fluctuations (of the order of weeks) due to a "random walk" phenomenon. Weight swings above and below the mean value in a way which resembles active control about a preferred value but is in fact a dynamic equilibrium in which departures from the mean value due to random drifts are counteracted over a subsequent period by changes in metabolic rate.
Fig 4-Weight-changes predicted by model throughout 10-yr programme of food intakes.
would be expected intuitively, a predisposition towards storing energy as fat does lead to a greater gain in weight for the same level of intake as well as producing a higher body-fat content, but with underfeeding, there is little difference between the body-weights of lean and fat individuals. The model therefore describes the following features of weight regulation:
(1) Provided
the mean values of intake and expendiremain constant, the effects on body-weight of short-term fluctuations are smoothed out, and a state of dynamic equilibrium is maintained. Small cyclic variations occur about a mean value, with magnitudes of about + 1 kg over time periods of a few weeks. (2) The mean value of body-weight about which equilibrium is established does depend upon the average levels of energy intake and expenditure. Thus if sustained sufficiently long, changes of mean intake do result in changes in weight. However, the rate of change declines over time, and a new equilibrium value eventually results. (3) Differing propensities towards storing energy as fat result in individual differences in the extent of weightgain caused by overfeeding.
ture
Fig 3-Long-term weight-changes predicted by model for excess or deficit
of energy intake of S%.
An
objection
at
this
point might
be that in order
to
586
weight constant over long periods, the model requires that mean intake and expenditure should be maintain
We have therefore devised a 10-year programme of daily activities and food intakes in which there is the variation that might realistically be expected in a suburban man. The 10-year programme includes:altered levels of intake and expenditure at weekends as opposed to week days, a 6-month seasonal cycle of intake (±5%), a randomised incidence of illness (10 days in each year) sufficiently serious to cause loss of appetite. There is a major surgical operation once during the 10 years (at B), and two sustained changes of +5% such as might result from a change of domestic life or of job location (at A and C). All of these changes are in addition to the normal random day to day variation of ±20%. Fig. 4 shows examples of runs made, with this programme, again with both lean and fat versions of the model. Because of the large element of randomness introduced, repeated runs vary considerably, even though the starting weight is the same. The average range of weight changes found for three runs was 9.5kg for lean and 12.8kg for fat versions of the model; very similar, in fact, to the changes found in real-life situations. constant.
DISCUSSION
Body-weight in adults is not by day, month by month, and
constant, but varies day year by year. Also, it is known that food intake and energy expenditure vary widely from day to day. Although weight, intake, and
expenditure must have some broad limits to variability set by physiological and psychological factors, the magnitude of long-term trends in body-weight actually observed are small enough to suggest that there must, in addition, be some sort of control system in operation. The problem is to suggest which kind of control system would explain the known facts whilst needing the fewest and the most plausible assumptions about any physiological mechanisms involved. Of all the hypotheses which have been considered up to now, the most complex is the set-point theory of weight control which implies the existence of physiological mechanisms for representing a set-point or preferred value for weight; for comparing actual weight with that preferred value; and for controlling intake or expendiany errors. None of these mechanisms has been shown to exist. An alternative hypothesis is the one which we have described as the dynamic equilibrium hypothesis. The operation of this is shown in fig. 5. Any imbalance between intake and the sum of the energy outputs results in a change in body-weight. This in turn alters the tissue metabolic energy (maintenance energy) in a direction which will tend subsequently to counter the original imbalance-i.e., there is a built-in negative feedback. This results in a slow change of body-weight in response to any moderate and sustained change in energy balance, with a new equilibrium value of bodyweight always being ultimately attained. The computer model based on this system, satisfactorily imitates the changes in weight, composition, and metabolic rate durexperiments of ing the 36 weeks of et the Keys al.,10 weight-changes during overfeeding of diets by Miller and Mumford,8 and the high protein ture so as to correct
starvation/refeeding
Fig.
5-Flow
diagram illustrating
the
dynamic equilibrium
hypothesis for body-weight regulation.
weight and body-composition changes in dieted obese subjects described by Passmore et al." The dynamic equilibrium hypothesis implies that for any individual there is a mean body-weight which corresponds to any given fixed mean values of energy intake and activity expenditure. The question that arises then is whether in normal people average levels of expenditure and intake are sufficiently well-regulated, because of habitual patterns of behaviour and eating, together perhaps with some broad limits imposed through feelings of hunger and satiety, to result in the magnitude of long-term weight-changes we know to occur. The computer model demonstrates that the kinds of changes of circumstance and habits which we might reasonably expect during 10 years of urban working life would in fact be accompanied by very plausible changes in weight, and we believe therefore that there is certainly no basis for suggesting the existence of any more complex regulation such as a set-point device. Whilst in most people simple habit, together perhaps with some quite rough limits imposed by appetite, would seem quite sufficient; there will of course be some for whom the resulting trends in body-weight will prove unacceptable for cosmetic or health reasons, and who will then deliberately alter their intake or activity. The dynamic equilibrium mechanism is therefore best seen as providing the basic degree of physiological stability which may be supplemented in some people from time to time by a psychological cognitive control. REFERENCES 1. Garrow, J. S. Energy Balance and Obesity in Man. Amsterdam, 1974. 2. Edholm, O. G., Adam, J. M., Healy, M. J. R., Wolff, H. S., Goldsmith, R., Best, T. W. Br. J. Nutr. 1970, 24, 1091. 3. Chinn, S., Garrow, J. S., Miall, W. B. Unpublished. Cited by Garrow.1 4. Forbes, G. B., Reina, J. C. Metabolism, 1970, 19, 653. 5. Fox, F. W. Lancet, 1973, ii, 1487. 6. Garrow, J. S., Stalley, S. F. Proc. Nutr. Soc. 1975, 34, 84A. 7. Garrow, J. S., Stalley, S. F. ibid. (in the press). 8. Miller, D. S., Mumford, P. Am. J. clin. Nutr. 1967, 20, 1212. 9. Payne, P. R., Dugdale, A. E. Ann hum. Biol. (in the press). 10. Keys, A., Brozek, J., Henscel, A., Mickelsen, O., Taylor, H. L. The Biology of Human Starvation, vols I and IL Minneapolis, 1950. 11. Passmore, R., Strong, J. A., Ritchie, F. J. Br J. Nutr. 1958, 12, 113.