Body morphology scaling

Before we determined the influence of size on muscle architecture and function, it was important to understand how the limb segments themselves responded to changes in size (Additional file 1: Table S1). We found only partial evidence for allometric scaling of body lengths in response to size. Snout-vent length (SVL) scaled less than expected 0.29 (0.27–0.32; Phylo.RMA), mostly as a result of the lower scaling of the thorax-abdomen length rather than the head-neck lengths. Hindlimb segments lengths (thigh, shank, and foot), tail length and pelvic width all scaled as expected from isometry, with an exception being pelvic height, which scaled larger than expected from isometry 0.40 (0.35–0.45).

Average muscle properties

Twenty-two hindlimb muscles were dissected from 27 individuals in 9 species of varanid lizards ranging from 7.6 to 40000 g (Fig. 2; Additional file 2: Table S2). Muscle origins and insertions were consistent with previous descriptions available for lizards [21–24] (Table 1) with two exceptions where our description may differ from existing literature: first, it was not possible to separate the multiple heads of the PIF so they were considered together as one muscle, and second, the PTIB was composed of 2 heads, one dorsal and one ventral, which join each other at one third from their origin, and share a common insertion, thus as above we considered these as one muscle (Fig. 2d). During the dissections, we observed a consistent pattern of aerobic and anaerobic (red and white) muscle fibre-type bands within a single muscle belly for the ILFIB, PTIB, and FTI (S) (Additional file 3: Figure S1). However, the functional reason for this regional arrangement of slow and fast muscle fibre types within an individual muscle remains unknown.

Fig. 2 Varanid hindlimb muscle architecture. a Dorsal superficial, b Ventral superficial, c Dorsal deep (ILTIB removed), d Ventral deep (PIT removed). Apo. – Aponeurosis; D-dorsal; S-superficial; Ten. – tendon; V-ventral Full size image

Table 1 Origin, insertion and function of major locomotor muscles of the varanid hindlimb based on Snyder, [21], Gans et al., [22], Reilly, [23] and Anzai et al., [24] Full size table

Possibly the most extensive study on muscle anatomy and architectural properties in a sprawling vertebrate is that of Allen et al. [10], and we attempt to follow a similar format to facilitate comparisons among taxa. In order to make comparisons between muscles of different sizes, muscle mass, fascicle length, tendon lengths, moment arms, and PCSA data were normalized assuming geometric similarity, that is muscle mass was scaled to body mass M1.0 (kg), fascicle length, tendon lengths, and moments arms to M0.33 (kg), and PCSA to M0.66 (kg). Species mean normalized data for 22 muscles and 9 species are displayed in Additional file 4: Table S3.

Similar to previous studies [7, 9, 10, 25–31] we observed a proximal to distal gradient in mean muscle architectural properties across all species. The heaviest muscles of the upper limb were the CFEML (1.458 ± 0.65 % of M1.0, mean ± SD), PIF (0.416 ± 0.08 %), and PIT (0.336 ± 0.13 %), whereas the heaviest muscles of the lower limb were the GAST (0.285 ± 0.16 %) and the PLONG (0.107 ± 0.02 %) (Additional file 4: Table S3).

There was a slight proximal to distal reduction in fascicle length. However, the largest muscles did not always have the longest fascicles, nor did the smallest muscles have the shortest fascicles. Average fascicle lengths were slightly longer in the upper limb (mean 3.88 ± 1.17 % of M0.33, n = 16) as compared to the lower limb (mean 3.17 ± 0.72 %, n = 6). The muscles with the longest relative fascicle lengths were all located within the upper limb: the PTIB (5.01 ± 0.29 %), PIT (5.99 ± 0.54 %), FTI (S) (4.85 ± 0.68 %), and the CFEML (4.68 ± 0.98 %) (Additional file 4: Table S3).

Six of the twenty-two muscles analysed were pennate (pennation > 3°). Most lower limb muscles were more pennate than upper limb muscles with two exceptions, the CFEML (22 ± 1.3°) and the FTIB (19 ± 3.9°). 4 of the 6 lower limb muscles were organized in a pennate arrangement: the GAST (23 ± 2.2°), PBREV (19 ± 5.1°), PLONG (14 ± 1.9°), and the TIBA (12 ± 4.9°).

Average PCSAs were almost twice as large in the upper limb (mean 0.0084 ± 0.01 % of M0.66) compared to the lower limb (mean 0.0044 ± 0.003 %). In the upper limb, PCSA was greatest in the CFEML (0.039 ± 0.011 %), PIF (0.011 ± 0.003 %), and CFEMB (0.010 ± 0.003 %), whereas in the lower limb PCSA was greatest in the GAST (0.011 ± 0.003 %).

Where present, we measured tendon lengths at both the proximal and distal regions of the muscle. 16 of the 22 muscles analysed had substantial external tendons. External tendons were more prevalent in the distal limb muscles as compared to the proximal limb. Similar to Alligators there were no strong proximal to distal patterns of tendon length [10]. The longest tendon belonged to the primary insertion of the CFEML onto the femoral trochanter (2.67 ± 1.08 % of M0.33) and the FDL (1.37 ± 0.23 % of M0.33) and GAST (1.46 ± 0.07 %) displayed substantial distal tendons. The FTE (1.47 ± 0.07 %) and ILTIB (1.36 ± 0.09 %) displayed substantial proximal tendons. The ILTIB originates from 2 observable tendons which arise from the lateral surface of the ilium. ILTIB tendon length was computed as the average of these anterior and posterior tendons.

Scaling regression analysis

The slopes and 95 % confidence intervals of the RMA lines for log transformed muscle properties versus body mass are shown in Fig. 3 and Additional file 5: Table S4. Scaling was determined to be statistically different from the expected exponent if the expected exponent fell outside these confidence intervals.

Fig. 3 Scaling exponents for muscle properties versus body mass. The boxes represent the slopes and 95 % confidence intervals of the species mean RMA lines for log transformed muscle properties: muscle mass, PCSA, and fascicle length. Horizontal lines show predictions based on geometric scaling at M0.33 (length), M0.66 (area), M1.0 (mass) Full size image

Muscle mass

The scaling of muscle mass with body mass was found to be highly correlated with R 2 values above 0.9 for all muscles, even when phylogenetically informed statistics were used. Of the 22 muscles included in our analysis, 4 muscles showed significantly greater scaling of muscle mass than expected from geometry using phylogenetically informed statistics. Muscle mass scaled with exponents >1 in the AFEM (slope: 1.049–1.385), the ILFEM (slope: 1.040–1.379) and 2 of the knee flexors, the ILFIB (slope: 1.001–1.269) and the PIT (slope: 1.019–1.244). A further 4 muscles showed significantly higher scaling at the individual level, although the CI’s increased when phylogenetically informed species means were used. These included the EDL (slope individuals: 1.006–1.156; slope species: 0.944–1.363), FDL (slope individuals: 1.082–1.88; slope species: 0.84–2.229), ILTIB (slope individuals: 1.028–1.140; slope species: 0.984–1.235) and the PTIB (slope individuals: 1.019–1.288; slope species: 0.993–1.233) (Fig. 3).

Fascicle length

Fascicle length scaled differently than geometric expectations in only one of the 22 muscles; the ILFEM showed greater than expected scaling of fascicle length (slope: 0.351–0.420) indicating greater range of motion with increased body mass. Two muscles showed lower than expected scaling of fascicle length though not with universal agreement. The AMB (V) showed significantly lower scaling at the species level (slope: 0.208–0.348), though this was not supported for individuals (slope: 0.249–0.350), while the EDL showed significantly lower scaling at the individual level (slope: 0.261–0.322) but not at the species level (slope: 0.156–0.357) (Fig. 3).

Pennation angle

We expected pennation angle to scale with M0 however 4 muscles scaled with positive allometry. The ankle plantarflexors GAST and PLONG scaled as 0.024–0.104 and 0.038–0.140, respectively, the femur retractor CFEML scaled as 0.014–0.075 while the knee extensor FTIB scaled as 0.039–0.278, though this latter case showed large CI’s.

PCSA

Three muscles showed greater than the expected geometric scaling of M0.66 for PCSA, but did not differ from the predicted elastic similarity scaling exponent of M0.75. The femur abductor ILFEM scaled as 0.684–0.967, while the knee flexor, ILFIB scaled as 0.665–0.968, and the ankle plantarflexor GAST scaled as 0.702–0.939. Two other knee flexors also showed weak evidence of greater than geometric scaling. The FTI (S) scaled significantly greater than expected for individuals (slope: 0.693–0.953), but this was not supported among species (slope: 0.635–0.996). Similarly the PTIB scaled significantly higher than 0.66 among individuals (slope: 0.714–0.984), but not among species (slope: 0.639–0.928) (Fig. 3).

Moment arms

Moment arms did not convincingly scale different to the expectations of geometric similarity for any muscles measured. Distal moment arms were measured for 17 muscles, with the highest exponents observed for the AMB (D) (slope: 0.320–0.619), the FTE (slope: 0.324–0.594), FTI (D) (slope: 0.319–0.496) and the ILFIB slope: (0.324–0.514). Proximal moment arms were measured for 6 muscles. Of these only the EDL scaled differently than geometric expectations, though this was only significant at the individual level (slope: 0.341–0.493), and was not supported when using phylogenetically informed slopes with species means (slope: 0.316–0.432).

Posture

To determine the influence of posture on muscle properties we used residual size-corrected muscle characteristics in relation to kinematic data (Table 2) available for varanids from previously published values in Clemente et al. [17, 18, 32].

Table 2 Supported correlations of muscle properties with posture variables. The sign indicates whether the relationship between kinematic and muscle properties was positive or negative Full size table

Muscle mass

None of the muscles which insert onto the femur (referred to below as femur muscles) showed a consistent relationship between muscle mass and kinematic variables. Of the knee extensors, the ILTIB showed the strongest response to changes in kinematics. There was a positive relationship between muscle mass and femur adduction meaning larger muscles were associated with a more upright stance (r = 0.78, P = 0.020). This was also supported by a positive association with size-corrected hip height (r = 0.86, P = 0.012). A weaker, and negative relationship was suggested for this muscle between muscle mass and knee angle at midstance (r = −0.73, P = 0.061). Of the other knee extensors, the only noteworthy association was for the FTIB which similarly had a weak association with knee angle at midstance (r = −0.88, P = 0.046).

Among the knee flexors, there was a strong negative association between muscle mass and femur retraction at midstance. The PIT, ILFIB, and FTI (S) all showed significant associations (r = −0.92, P = 0.003; r = −0.80, P = 0.016; r = −0.97, P = 0.030 respectively) with the FTI (D) showing the weakest association (r = −0.94, P = 0.051). Three of these muscles FTI (D), FTI (S) and the PIT also showed a negative association with the knee angle at midstance (r = −0.96, P = 0.036; r = −0.99, P = 0.008; r = −0.85, P = 0.015 respectively). There was also evidence for an association with these muscles and femur rotation; the FTI (S) showed a positive association with femur rotation at midstance (r = 0.95, P = 0.044), whereas both the ILFIB and the PTIB showed a negative relationship with the change in femur rotation during the stance phase (r = −0.84, P = 0.015; r = −0.96, 0.035 respectively).

The ankle muscles show less association with kinematics. The ankle plantarflexor PLONG had a positive correlation with femur adduction (r = 0.99, P = 0.028) whereas the ankle dorsiflexor EDL showed a negative relationship between muscle mass with knee angle and femur retraction at midstance (r = −0.87, P = 0.010; r = −0.86, P = 0.012).

Fascicle length

Among the femur retractor muscles the PIF showed relatively longer fascicles which are linked with relatively higher hip heights at midstance (r = 0.93, P = 0.022). The CFEML showed a negative association of fascicle length with the change in femur retraction (r = −0.97, P = 0.025). In contrast, longer fascicles of the femur abductor ILFEM were associated with greater angular changes in the abduction/adduction axis of the femur (r = 0.97, P = 0.026).

Among knee extensors only the FTIB showed a strong response with kinematics. Longer fascicles were associated with greater femur adduction (upright posture) for this muscle (r = 0.91, P = 0.032). Similarly, fascicle length of the knee flexors show little association with kinematics, with the exception of the FTI (S) which displayed evidence for a negative relationship between the change in femur retraction and fascicle length (r = −0.92, P = 0.03).

The ankle plantarflexor PLONG showed multiple associations with kinematic variables. Longer fascicles were associated with greater femur rotation (r = 0.95, P = 0.012) and greater femur adduction at midstance (r = 0.97, P = 0.030), but were negatively correlated to femur retraction at midstance (r = −0.92, P = 0.027). This could be related to the weak negative association of fascicle length with knee angle (r = −0.87, P = 0.054) or the weak positive association with the change in femur depression (r = 0.88, P = 0.045) this same muscle exhibited. The antagonist to this muscle the ankle dorsiflexor EDL also showed some association with kinematics. Fascicle lengths for this muscle were positively associated with femur adduction (r = 0.92, P = 0.028) similar to the PLONG, and negatively associated with the change in knee angle over the stance phase (r = −0.90, P = 0.035).

Pennation angle

Of the 6 muscles which showed pennation angles >3°, only two showed any strong association with kinematics. The knee extensor FTIB showed a significant positive association with the change in knee angle during the stance phase (r = 0.97, P = 0.045). The ankle plantarflexor PLONG displayed a positive relationship between the change in femur retraction and pennation among species (r = 0.90, P = 0.037).

PCSA

When considering PCSA, the largest muscle of the hindlimb, the femur retractor muscle CFEML showed several associations with kinematics. PCSA was positively associated with femur rotation at midstance (r = 0.94, P = 0.013) suggesting greater muscle force produced by the CFEML results in an increased clockwise rotation of the femur at midstance. Further, both femur retraction at midstance (r = −0.95, P = 0.011) and knee angle at midstance (r = −0.97, P = 0.025) were negatively associated with PCSA. This suggests that an increase in femur protraction and decrease in knee angle (i.e. crouched, anteriorly outstretched hindlimb at midstance) is associated with an increase in the force-generating capacity of the CFEML.

None of the knee extensors showed convincing associations between PCSA and kinematics, though a few of the knee flexors did. Further, in these cases a similar pattern emerges. The PTIB showed negative associations with ankle angle at midstance (r = −0.95, P = 0.046). Similarly there was evidence for a weak negative association between knee angle at midstance with PCSA for the FTI (S) (r = −0.95, P = 0.048). In each case, this suggests that a more crouched posture, as displayed through smaller joint angles, is associated with larger PCSAs.

This trend continues among the ankle plantarflexors and ankle dorsiflexors. The GAST shows a negative association between PCSA and knee angle at midstance (r = −0.89, P = 0.039), along with a negative association with femur retraction at midstance (r = −0.91, P = 0.032), though the association of this latter variable with posture remains unclear. The change in knee angle over the stance phase was negatively associated with PCSA for both the ankle plantarflexor PLONG (r = −0.95, P = 0.044) and the ankle dorsiflexor EDL (r = −0.89, P = 0.041). Perhaps most curious is the positive association between the GAST and PLONG and femur adduction (r = 0.95, P = 0.044; r = 0.94, P = 0.056) which is also weakly present in the EDL (r = 0.81, P = 0.095). These results may suggest a transition towards an increased functional importance for the distal muscles during the propulsion phase with a more upright posture.

Moment arms

Of the 17 muscles for which we were able to measure a distal moment arm, only 6 showed a significant correlation with posture. None of the femur muscles showed an association of moment arm with posture, but the knee extensor ILTIB did show a significant positive relationship with knee angle at midstance (r = 0.92, P = 0.028), though this result was not supported by independent contrasts (IC) (r = 0.90, P = 0.095). The knee flexors FTI (D) and FTI (S) both show a similar positive relationship with the change in ankle angle throughout the stance (r = 0.96, P = 0.039; r = 0.98, P = 0.012) as did the ankle plantarflexor GAST (r = 0.96, P = 0.041). Another knee flexor the PTIB showed a negative relationship of distal moment arm with the change in knee angle throughout stance (r = −0.93, P = 0.021), though support was weaker using IC (r = −0.94, P = 0.054). Finally the ankle plantarflexor PLONG showed a positive association with femur adduction (r = 0.98, P = 0.016).

Among the 5 muscles for which we recorded proximal moment arms, only two significant interactions with posture were evident, both among ankle plantarflexors. The GAST showed a positive association with ankle angle change throughout the stance (r = 0.95, P = 0.023) similar to results for the distal moment arm above, though these results were weaker when using IC (r = 0.93, P = 0.065). Another ankle plantarflexor PLONG showed a positive relationship between proximal moment arm and the change in femur depression (r = 0.97, P = 0.028).

Tendon lengths

None of the 16 muscles for which we measured substantial external tendons showed a significant relationship with body mass among the species measured. This may reflect the difficulty in accurately determining the boundary between aponeurosis and external tendon.