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Department of Biological Sciences, University of Cincinnati, Cincinnati, OH 45221-0006
1To whom correspondence should be addressed.
| ABSTRACT |
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KEY WORDS: protein malnutrition skeletal growth organ growth rats Gompertz
| INTRODUCTION |
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Different parts of long bones respond differently to nutritional
insult. Even under extreme conditions marked by the cessation of body
weight gain, the body maintains priority for longitudinal skeletal
growth (McCance 1960
, Stewart et al. 1975
, Widdowson and McCance, 1963
). This
increase in bone length continues at the expense of having thinner,
less dense diaphyses. Yayha and Millward (1994)
report
that the epiphyseal cartilage width in the tibia of rats was more
sensitive to protein deprivation than bone length and that tibia
epiphysis length was least affected.
Although many of these studies document the effects of protein
malnutrition on the growth rate of limb bones (Stewart et al. 1975
, Yayha and Millward 1994
), none contain the
complete growth trajectories of malnourished and control individuals to
compare differences in the rates and timing of developmental events. It
is not known how protein malnutrition alters growth patterns throughout
ontogeny to produce morphological variations and whether these
differences are manifested in final size.
As part of a larger study (Miller and German 1999
), this
paper investigates the effect of protein malnutrition on limb bone
growth using longitudinal data to compare individual growth
trajectories. These data can better explain differences in final size
between malnourished and control individuals, which may result from
differences in the rate and timing of growth. These data can also show
which bones are more sensitive to protein deficiency and whether males
and females respond differently.
| MATERIALS AND METHODS |
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The data used in this study were collected as part of a larger project
(Miller and German 1999
). Rattus
norvegicus breeders were obtained from a colony of Zivic
Miller:Sprague-Dawley strain of rats at the University of Cincinnati.
The two treatments used in this study were a control diet (CT)
containing 24% protein and an isocaloric low protein diet (LPT) with
4% protein (Dyets, Bethlehem, PA). The sex of each rat was determined
at weaning and rats were randomly assigned to one of the diets yielding
four groups, i.e., male control, female control, male experimental and
female experimental. Miller and German (1999)
showed
that the LPT rats not only consume less protein at any age, but also
less protein per gram body weight than the CT rats. The males had a
significantly greater body weight than females, and body weight
continued to increase for a significantly (P < 0.01) longer period (Table 1
.).
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Data collection.
Isoflurane gas (Anaquest, Liberty Corner, NJ) at 23.5%/L
O2 was administered for 5 min through an Ohio Compact
Anesthesia Machine to lightly anesthetize the rats. Once sedated, the
rats were positioned on a film cassette for X-raying using a
Bennett Mammography Machine (Bennett X-ray, Copiague, NY) set for
0.25 s at 75 mA and 4447 kV. Both dorsoventral and lateral
radiographs were taken of each individual rat on Kodak MRM-1 diagnostic
film (Kodak, Rochester, NY). Radiograph frequency varied with
the age of the individual rat. From age 2248 d, rats were X-rayed
three times a week when growth was increasing rapidly. As growth
slowed, the frequency was reduced to two times a week (4976 d), then
to one time a week (77118 d), and finally to once every 2 wk
(119180 d). After radiography was completed, the rats awoke from
sedation within a few minutes and resumed normal activity.
Fiorello and German (1997)
have shown no adverse growth
effects resulting from radiography.
Length and width measurements of the limb bones were recorded using a
Numonics AccuGrid Digitizing tablet (Numonics, Montgomeryville, PA;
accuracy of 0.127 mm) and the program Digit (written by Dave Hertweck,
Department of Biological Sciences, University of Cincinnati). All
measurements were recorded from the right side of the body to reduce
interlimb variation. Radiographs displaying poor alignment or
resolution for a particular measurement were not included. Although
past studies indicate that measurements from radiographs are not equal
to those made with calipers on bones, the differences were not
systematically biased (unpublished data). The value of using
longitudinal data rather than cross-sectional data is one of the
reasons for the design of this study (German and Meyers 1989
, German and Stewart 2000
,
Stewart and German 1999
). A total of 35 repeatable and
homologous landmarks were digitized to give two-dimensional
distances (mm) for each long bone. Table 2
gives descriptions of the measurements recorded.
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Statistical analysis.
Our previous results from studying these individual rats (Miller and German 1999
) suggested that the significant effect of
malnutrition is the variation in the growth trajectories, rather than
the endpoints of growth. Thus, models that can characterize the
trajectories are important to this analysis. Because mammalian growth
is nonlinear and characterized by a sigmoidal pattern, many workers
have used one member of the family of logistic curves, such as
logistic, Gompertz or Putter-Bertalanffy to model growth
(Cothran et al. 1985
, Eisen 1976
,
Gille et al. 1996
, Laird et al. 1965
).
Although these models differ slightly in their parameters when applied
to empirical data, their differences are usually subtle and not
biologically important (German and Meyers 1989
,
Jolicoeur and Pirlot 1988
, Laird et al. 1965
). The most overriding concern is a model whose parameters
have biological interpretations, with results that are comparable to
existing data. Thus, the Gompertz model was chosen to calculate
estimates of several parameters because the parameters are
interpretable, they have proved to be good fits in the past and the
results from this study will be comparable to others containing similar
data (German et al. 1994
, Lightfoot and German 1998
, Maunz and German 1996
, Miller and German, 1999
).
The NONLIN module of SYSTAT (Wilkonson 1997
) was used to
analyze the data obtained from two algebraically equivalent forms of
the Gompertz equation:EQUATION
![]() | (1) |
![]() | (2) |
where y represents the measurement taken and
t equals time in days. The base of the natural logarithm is
represented by e. A is the asymptote or final size of
y. It is the end product of the growth trajectory. The
remaining parameters (w, I, k,
b and Tf) are descriptions
of the growth trajectory. Parameter w is the initial size of
the measurement at t = 0, I measures the
instantaneous initial growth rate at t = 0 and
k is the rate of exponential growth decay. The parameter
b has little biological importance, describing initial
growth (Laird et al. 1965
). Values for A,
b and k were obtained from nonlinear regressions
performed in SYSTAT using Eq. (1)
, whereas values for w and
I were calculated using the following relationships:EQUATION
EQUATION
![]() | (3) |
![]() | (4) |
Growth duration, Tf, can also
be calculated from these equations. It represents the time at which
each measurement is increasing at only 5% of its maximum growth rate
(Rm) or essentially when growth stops.
Rm is calculated by taking the first
derivative of the Gompertz equation (Equation 5)
, which gives the rate
of growth over time.
![]() | (5) |
Gompertz parameters were obtained for the limb bone measurements
of all 37 rats; thus, the unit of analysis was the individual rat.
Parameters for radius and ulna width as well as all distal widths were
not obtained because of the nonsigmoidal nature of these curves. A
three-way ANOVA was then used to test for differences among these
parameters for sex, diet and litter. Interaction between sex and diet
was also tested. Litter was included to account for any differences in
growth due to litter; however, it was seldom significant. The amount of
variation explained by the model was determined by the corrected
R2 values. High
R2 values for both treatments were
essential in making growth comparisons between the diets using the same
model (Klingenberg 1998
). Groups were significantly
different if the P-value was <0.01.
Linear regressions were fit to plots of length vs. width for each
individual rat to test for allometric or scaling differences between
the diets; thus, the individual rat was once again the unit of
analysis. To test whether variation in shape differed as a result of
diet, slopes were calculated for the following measurements: humerus
length vs. proximal width; humerus length vs. deltoid tuberosity width;
humerus length vs. diaphysis width; humerus length vs. distal width;
radius length vs. diaphysis width; ulna length vs. diaphysis width;
femur length vs. proximal epiphysis width; femur length vs. proximal
width; femur length vs. diaphysis width; femur length vs. distal width;
tibia length vs. proximal width; tibia length vs. diaphysis length; and
tibia length vs. distal width. These are standard allometric
coefficients used to estimate biomechanical scaling of long bones
(McMahon 1973
and 1975
). Analysis of covariance was then
used to test for significant differences among the slopes for the four
diet-sex groups. Statistically different slopes meant that the
proportional change in length to width over time was different among
the groups being compared. No difference in slope meant that the groups
were growing identically and their bones would be similar sizes
provided the intercepts were not significantly different.
The organ data were analyzed with a complete three-way,
fixed-factor ANOVA using sex, diet, and litter as crossed, fixed
factors. Litter was not a significant factor for these data. Data on
muscle and organ size were scaled by dividing by final body weight.
Previous work (Miller and German 1999
, Stewart and German 1999
) suggested that there are significant
differences between males and females, as well as small but significant
differences in final size between rats fed the CT and those fed the
LPT. We were interested in testing whether diet effect on organ and
muscle size went beyond its effect on body size. The only variable
analyzed separately for each sex was gonad weight. Growth and function
of the gonads is not equivalent in the same sense as the other organs
included in this study.
| RESULTS |
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The Gompertz model gave an accurate growth estimate for the limb bone
data (Fig. 1
). For all measurements, the mean corrected
R2 was 0.928. The minimum corrected
R2 was 0.803 for proximal tibia width,
whereas the maximum corrected R2 was
0.982 for femur length.
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Dietary effects.
Longitudinal limb bone data collected for the CT rats produced
sigmoidal growth trajectories for all 13 skeletal measurements, whereas
the longitudinal limb bone data for the LPT rats produced more linear
growth trajectories (Fig. 2
). Therefore, it was more difficult to obtain a good empirical fit using
the Gompertz model for the LPT group. The mean corrected R2
was slightly lower for the LPT curves (R2 = 0.915) compared with the CT (R2 =
0.942). The initial size, w, should not be significantly
different between the two groups because the rats were selected
randomly for the two diets after weaning. Nevertheless, the LPT rats
had larger initial sizes in half of the measurements recorded.
Statistical tests of the actual initial sizes showed no difference
between the dietary groups (P > 0.01). These two
results suggest that the Gompertz model was not estimating the initial
size accurately due to the linear nature of the LPT curves.
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In contrast to the final size estimates obtained from the Gompertz
equation, significant differences (P < 0.01) occurred
in all of the actual final measurements between CT and LPT males
(Table 4
). For the 13 skeletal measurements, the CT male rats had significantly
(P < 0.01) greater final lengths. These differences
were on average 5.7%, ranging from 0.0320.108. The differences in
width were greater in size averaging 12.7% and ranging from
0.0760.158. When comparing actual final size differences between the
CT and LPT females, the number of significant differences decreases to
8 of the 13 measurements. The LPT females ultimately reached final
sizes similar to those of the CT females for five measurements, four of
which were length measurements. The average difference in length
between the CT females and the LPT females was 1.7%, ranging from
0.0020.034. Like the males, the average difference in bone width for
females increased to 7.5% with a range of 0.0470.134.
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There were few instances in which the males and females reacted differently to the low levels of dietary protein. Therefore, variation in growth can be explained by two factors, sex and diet, implying that the growth response to the low protein diet was the same for males and females. The parameter with the most interactions was Tf, with a significant difference in humerus diaphysis width and femur diaphysis width. For humerus diaphysis width and femur diaphysis width, the effect of low dietary protein on growth duration resulted in a higher degree of sexual dimorphism between the LPT males and females.
Allometry and scaling.
During ontogeny, some scaling differences could arise between the two diets and sexes due to variations in the growth parameters. Only two scaling differences were observed between the sexes, whereas several differences occurred between diets. The males had a significantly faster slope for tibia length vs. tibia diaphysis width and a marginally steeper slope for radius length vs. radius width. When comparing differences between the diets, the CT rats had significantly greater slopes than the LPT rats for 6 of the 13 scaling measurements, meaning that for any increase in width, the CT increased in length at a faster rate. Therefore, the LPT rats had shorter but proportionately wider bones. For all of the remaining measurements except radius width, there were no significant scaling differences in slopes between the diets, meaning that the LPT and CT rats grew proportionately larger at the same rate. For radius length vs. radius width, the LPT rats grew longer at a significantly faster rate than the CT rats. There was only one interaction between sex and diet for proximal femur width, indicating that the majority of scaling differences were attributable to differences in sex or diet.
Muscles and organs.
Although the weight of muscles in males was larger absolutely than that
of females for both dietary groups (Table 5
), there were no significant differences due to sex, diet, or
interaction between sex and diet, in the weights of muscles relative to
body weight (P > 0.10) and only one marginal
difference due to diet in the masseter muscle (P = 0.07,
= 0.01). Thus, all differences in muscle size were a
function of differences in body weight.
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The results for eye and brain weight are more complex. In both cases, females had proportionately larger eyes (P < 0.01) and brains (P < 0.01) than males. There was also a significant diet effect for both eyes (P < 0.01) and brain (P < 0.01) when they were scaled to body size. The significant diet effect showed that the LPT rats were proportionately larger than the CT rats for both eyes and brain relative to body size. Using the raw data, i.e., without scaling for body size, the diet effect was not significant for either organ (P = 0.20 brain; P = 0.28 eyes). Thus for each sex, the eyes and brain were absolutely the same size, but the LPT rats were slightly smaller in body weight.
| DISCUSSION |
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The differences we measured in the growth of lengths between LPT rats
and CT rats were not the same as those in the growth of widths. For
final size in both sexes, the lengths were closer between the two
treatments than were the widths. However, looking at the allometric
results for scaling over time, the relative length to width slope, the
CT rats had larger scaling coefficients, indicating for a given
increase in width, the length of the bones of the CT rats increased
faster than those of the LPT rats. Because the two treatments end up at
approximately the same length and the rates of growth for both widths
and lengths were significantly lower in the LPT rats, the duration of
growth for the lengths of bones must have been relatively longer than
for the widths (Table 3)
.
These results on length vs. width suggest a hypothesis for the dietary
effect of the specifics of limb bone growth. After the primary center
of ossification forms in the diaphysis of the long bone, the
perichondral template is ossified and becomes the periostium of the
long bone. Ossification forms a girdle of bone around the diaphysis,
and lengthening of the bone occurs at the diaphyseal-epiphyseal
junctions at the ends of the bones. Thus the width of the bone is
determined earlier (although remodeling can occur) than the length,
which continues to exhibit primary growth until epiphyseal fusion
occurs (Larsen 1997
). It is possible that a longer
duration of growth in LPT rats is due to a developmental delay in
epiphyseal fusion that is not possible in the earlier diaphyseal
ossification.
The pattern of size differences among organs is also a function of the
timing of growth. The lack of differences between LPT and CT rats for
muscles per body size likely reflects the fact that muscles continue
growing even after final ossification of the limb bones. Structures
that could continue to grow, either skeletal or muscular, did so.
Significant size differences due to diet in the eyes and brains, with
the LPT rats being relatively larger than the CT rats, are probably
subject to different timing and growth considerations. We propose two,
not mutually exclusive explanations. First, the LPT rats were not
nutritionally compromised until after weaning, and much of the growth
of these structures occurs prenatally. Eyes, as is true of the brain,
are characterized by "excessive early enlargement" (Marsh and Vannier 1985
) and attainment of adult size far in advance
of most other adult structures. Second, it is likely that the brain and
eyes have developmental priority (Larsen 1997
) and that
if the body had limited resources, it would devote more to the brain.
Thus, even during growth of rats fed the low protein diet, the brains
and eyes would be less affected than other organs.
Given the data in this paper, it is difficult to sort out the relative
importance of these two explanations. However, we have some preliminary
data to support the second hypothesis (Reichling 2000
).
Offspring of malnourished dams, a second generation of LPT rats, were
killed at weaning and their organs weighed. These pups, subjected to
the effect of malnutrition through early development, had patterns of
brain scaling when corrected for body weight similar to the data
described here. The LPT pups had relatively larger brains per gram body
than the CT pups
The overall conclusion, given the different systems we have examined,
is that structures that grow or have the potential for extended growth
are less affected by the nutritional insult, thus lengths of bone
relative to widths, and the cranial widths. In general, structures with
less flexibility in the duration of growth, e.g., bone widths or
various aspects of the mandible will end up smaller in the malnourished
animals (Miller and German 1999
). The exceptions to this
latter conclusion appear to be the elements of the neural system we
examined, which seem to maintain developmental priority. Although rats
fed the low protein diet grew more slowly, cessation of growth was
sufficiently delayed for them to achieve near adult size for several
different physiological systems.
| ACKNOWLEDGMENTS |
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Manuscript received January 10, 2000. Initial review completed February 28, 2000. Revision accepted April 7, 2000.
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