Results of the modelling

__Time
dependence of temperature changes__

The time-courses of the temperature changes for three different rates of pH fall in pig carcasses chosen to simulate those in a normal carcass (0.01 units/min), a marginal case of PSE (0.02 units/min) and a very rapidly glycolysing muscle (0.1 units/min) are shown in Fig. 1. For the normal rate of pH fall, the heat liberated from the conversion of glycogen to lactic acid is produced over a relatively long time and the two phases of temperature fall, pre- and postrigor, are not readily distinguishable. At the higher rates of pH fall, rigor onset is more rapid and the metabolic heat is produced sufficiently rapidly that the two phases are more apparent. At very high rates (>0.067 pH units/min) the temperature initilly rises before falling. The time-course for a higher rate of pH fall must inevitably cross over that for a lower rate, since the total metabolic heat is the same whether glycolysis is fast or slow and, if the rate is slow, most of it will be liberated at later times.

For beef, glycolysis is sufficiently slow that the biphasic nature of the temperature fall would not be readily discernible and the temperature difference between carcasses with different rates of pH fall would be small.

__Time
dependence of the rate of denaturation of myosin__

Figure 2
shows the time-course of the rate of constant of denturation for rates
of glycolysis that simulate the range likely to be experienced by pig carcasses.
The five rates of pH fall chosen span the range from 0.01 to 0.1 units/min.
The initial rate of denaturation is finite but low because, although, the
temperature is high (39^{o}C), the pH is also
high (pH 7). For all rates of pH fall shown, the rate constant increases
throughout the pre-rigor period, reaching its maximum value at rigor. At
the very high rates of pH fall, the rise in the rate of denaturation with
time is very steep, and at a rate of 0.1 units/min, the rate constant increases
110-fold from immediately post-mortem to rigor onset. At these high rates
of pH fall, the temperature does not much alter during the pre-rigor period,
whereas the pH is rapidely falling. So as a first approximation the rate
constant is proportional to 10^{-1.3pH} and
hence to 10^{1.3yt}. A plot of log
*k* against time is therefore approximately a stright line (not shown).
At rigor onset, the combination of the myosin heads with actin is assumed
to pretect them completely from denaturation and the rate constant falls
instanteously to zero. The higher the rate of pH fall, the higher is the
maximum rate constant immediately before rigor and the sooner is this maximum
achieved. The cooling of the carcass pre-rigor is the cause of the lower
rate of the lower rate of denaturation at rigor for the lower-rates of
pH fall.

Fig 3a and 3b show the time-courses of the rate constant of denaturation for lower rates of pH fall including that typical of beef carcasses (0.001 units/min). The half-cooling time for the calculations in Fig 3a was 180 min so that the time-cooling could be compared directly with those in Fig 2. Such a condition resembles that typical for beef flank. Under these conditions, the rate constant first falls, because the temperature is decreasing, and then increases, because of the fall in pH. At the lower rates of pH fall, the rate constant is highest immediately before rigor.

A larger value (700 min) for half-cooling time, more appropriate for the slower cooling regions of a beef carcass, was used for the calculations shown in Fig. 3b. For a rate of pH fall of 0.001 units/min, the rate of constant still falls from its initial value, albeit more slowly, and increases only slightly towards the end of the pre-rigor period. At a rate of 0.002 units/min the rate constant initially decreases only slightly and then increases, while at 0.004 units/min the rate constant increases rapidly from the beginning.

__Time-course
of myosin denaturation__

The time-course of myosin denaturation for conditions resembling those in a pig carcass are shown in Fig. 4. As before, the range of rates of pH fall considered span from 0.01 to 0.1 units/min. As would be expected from Fig. 2, for all these rates the amount of myosin denatured increases relatively slowely at first but accelerates until at rigor a plateau is reached. Somewhat more of the denaturation in these models of pig carcasses therefore occures in the second half of the pre-rigor period than the first half. At the lowest rate of pH fall shown (0.01 units/min), the fraction of myosin denatures at rigor, the plateau value, is about 0.1 for a half-cooling time of 180 min. At higher rates of pH fall, the plateau is higher, but at still higher rates (>0.04 units/min), the plateau decreases again.

Plots of the time-courses of myosin deanturation for lower rates of pH fall, including those that might be experienced in a beef carcass, are shown in Fig. 5a and 5b. In Fig. 5a a half-cooling time of 180 min, appropriate for beef flank, has been chosen. As would be expected from Fig. 3a, for a rate of pH fall of 0.001 units/min, the greatest rate of incrrease in the fraction denatured occures initially and most of the denaturation occures in the first 100 min. However, the total fraction of myosin denatured at rigor (~0.01) is very small with this chilling regime, and presumably its contribution to drip loss would be negliglible.

With a longer half-cooling time (700 min), appropriate for beef leg, the amount of myosin denatured was much greater (Fig. 5b). The time-course of denaturation for a rate of pH fall of 0.001 units/min, characteristic for beef, showed an initial fast rise but denaturation continued slowely troughout the pre-rigor period. The fraction denatured at rigor under these conditions is about 0.1.

__Effect
of rate of glycolysis on the fraction of myosin denaturated__

Figure 6 shows in more detail how
the fraction of myosin denatured at rigor depends on the rate of pH fall
for a range of rates of pH fall from the rate that occures typically in
beef carcasses (0.001 units/min) to the fastest rate that have been observed
in pork (0.1 units/min). Plots for six widely different cooling rates,
including those typical for beef and pork, are compared with an extreme
case in which the meat is thermally insulated and unchilled. For the chilled
carcasses, the fraction of myosin denatured at rigor increases steeply
as the rate of pH fall increases, then reaches a maximum, declining more
gradually with further increase in the rate. As would be expected, the
faster the rate of cooling, the smaller the fraction of myosin denatured
at rigor. At the faster rates of cooling, the maximum amount of denaturation
occures at a relatively haigh rate of pH fall. For example, with a half-cooling
time of 100 min, the maximum occures at a rate of pH fall of 0.056 pH units/min,
whereas with a half-cooling time of 200 min, it occures at a rate of pH
fall of 0.028 pH units/min, woth a half-cooling time 0f 500 min at a rate
of 0.001 pH units/min, with a half-cooling time of 700 min at 0.0080 units/min.
The uppermost curve in Fig. 6 shows what would be
expected for a thermally insulated carcass. In this case the temperature
increases up to rigor onset due to the generation of metabolic heat raising
the temperature by 3^{o}C but then reamins
constant. For this special case, essentially all the myosin is denatured
for the slowest rates of glycolysis but the amount denatured actually falls
as the rate of pH fall increases.

The data of Fig. 6 have been replotted in Fig.
7 with pH_{45} as the abscissa. It can
be seen that as the pH_{45 }value decreases
below 7, the fraction of myosin denatured at rigor increases steeply, reaches
a maximum and then, for the slower cooling rates with still lower pH_{45}.
However, at the two faster cooling rates, this latter decline in denaturation
with fall in pH_{45 }is not seen because,
if rigor is reached in a time less than 45 min, faster rates of glycolysis
are not reflected in a lower pH_{45}. With
a half-cooling time of 200 min, the denaturation increases rather steeply
with decline in the pH_{45 }value from 7,
but reaches a plateau below 6.1. With a half-cooling time of 100 min the
fraction of myosin denatured increases monotonically with a decline in
pH_{45 }value.

Because in practice chilling is not usually commerced
until some time up to about 1 h *post mortem*, we also considered
the effect if for the first 60 min the carcass was thermally insulated
and only then did chilling commerce (Fig. 8). Since
rigor will be reached in this period if the rate of pH fall is >0.025
units/min, regardless of the chilling rate, all curves coincide with the
cureve for the thermally insulated carcass at rates of pH fall greater
than this value. The insensivity of the denaturation to chilling rate for
these faster rates of pH fall is therefore even more apparent than in Fig.
6. For the slower rates of pH fall, the delay chill increases considerably,
the degree of denaturation, especially with the shorter half-cooling times.

The effect of the rate of chilling on the amounth of myosin denatured at rigor is shown in more detail in Fig. 9 for six different rates of pH fall, covering the extreme range from 0.001 units/min, typical for beff carcass, to 0.1 units/min, the highest observed in PSE pork. More rapid chilling always decrease the amount of myosin denatured at rigor, but the effect of chilling is most marked for the slower and intermediate rates of pH fall. At a rate of pH fall of 0.001 units/min, representing the normal rate for a beef carcass, a change in the half-cooling time from 100 to 700 min increases the fraction denatured 13-fold, from 0.0096 to 0.124. For a rate of pH fall of 0.001 units/min, representing a normal pig carcass, the same change in chilling regime would increase the fraction deantured from 0.028 to 0.50, an increase of 18-fold. For a rate of pH fall of 0.02 units/min, which is usually taken to represent a marginal case of PSE, it would increase the fraction denatured from 0.060 to 0.42 a 7-fold increase. However, at a rate of pH fall of change of chilling regime would increase the fraction denatured from 0.086 to 0.15, a factor of only 1.7.

Figure 10 shows the effect of varying the final pH of the carcass for the same wide range of rates of pH fall, assuming other conditions are standard. At low rates of pH fall, such as 0.001 units/min, typical of beef, the amount of myosin denatured at rigor increases only slightly with fall in the final pH. This is because when the carcass experiences very low pH values, its temperature has to fallen to such a level that the rate of denaturation is low. For pig carcasses, where the rate of pH fall are much higher, the final pH has a much more marked effect on the fraction denatured. For example, at a rate of fall of 0.01 units/min, corresponding to a normal pig carcass, a decrease in the final pH from 6 to 5 would raise the fraction denatured from 0.048 to 0.19. At the same rate of 0.02 units/min, corresponding to a marginal case of PSE, the same decrease in final pH would raise the fraction denatured from 0.053 to 0.40. With a rate of 0.04 units/min, the same decrease in final pH would raise the fraction denatured from 0.043 to 0.52, and at a rate of fall of 0.1 units/min, from 0.024 to 0.44.