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Analyzing observed or hidden heterogeneity on survival and mortality in an isogenic C. elegans cohort

View Article: PubMed Central - PubMed

ABSTRACT

It is generally difficult to understand the rates of human mortality from biological and biophysical standpoints because there are no cohorts or genetic homogeneity; in addition, information is limited regarding the various causes of death, such as the types of accidents and diseases. Despite such complexity, Gompertz’s rule is useful in humans. Thus, to characterize the rates of mortality from a demographic viewpoint, it would be interesting to research a single disease in one of the simplest organisms, the nematode C. elegans, which dies naturally under identically controlled circumstances without predators. Here, we report an example of the fact that heterogeneity on survival and mortality is observed through a single disease in a cohort of 100% genetically identical (isogenic) nematodes. Under the observed heterogeneity, we show that the diffusion theory, as a biophysical model, can precisely analyze the heterogeneity and conveniently estimate the degree of penetrance of a lifespan gene from the biodemographic data. In addition, we indicate that heterogeneity models are effective for the present heterogeneous data.

No MeSH data available.


Biodemographic data of the mev-1;fer-15 double-mutant cohort at 25°C. (A) Survival of the mev-1;fer-15 double mutant (360 animals, summed data from three trials) exposed to 90% oxygen concentration from day 4. The raw data were fitted by the non-linear least-squares method with Eq. 4, whose fitting parameters were determined as t0 =5.25 and z=1.24. The bold black curve shows the fitting curve analyzed as a single mode. (B) Mortality rates of (A). The expected mortality rates qx′ from our model were calculated by substituting the fitting equation of survival determined at (A) into Eq. 1. Here, the interval time Δx in Eq. 1 was varied as 1.0 (filled circles), 0.5 (green line), 0.1 (blue line), and 0.05 (red line). The experimental qx and predicted qx ′ values are black circles and small black solid circles (Δx=1.0), respectively. The bold black curve represents the force of mortality calculated from Eq. 6.
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f4-5_59: Biodemographic data of the mev-1;fer-15 double-mutant cohort at 25°C. (A) Survival of the mev-1;fer-15 double mutant (360 animals, summed data from three trials) exposed to 90% oxygen concentration from day 4. The raw data were fitted by the non-linear least-squares method with Eq. 4, whose fitting parameters were determined as t0 =5.25 and z=1.24. The bold black curve shows the fitting curve analyzed as a single mode. (B) Mortality rates of (A). The expected mortality rates qx′ from our model were calculated by substituting the fitting equation of survival determined at (A) into Eq. 1. Here, the interval time Δx in Eq. 1 was varied as 1.0 (filled circles), 0.5 (green line), 0.1 (blue line), and 0.05 (red line). The experimental qx and predicted qx ′ values are black circles and small black solid circles (Δx=1.0), respectively. The bold black curve represents the force of mortality calculated from Eq. 6.

Mentions: Moreover, we tested our model employing the oxygen-hypersensitive double mutant mev-1;fer-15 under highly oxidative stress (Fig. 4). When this mutant strain was exposed to a high oxygen concentration (90%) after maturation, its lifespan was remarkably shortened (Fig. 4A and ref. 5). The mortality rates, qx, reached a complete plateau at advanced ages, as shown in Fig. 4B. Here, we first fitted the survival using the equation of lifespan, Eq. 4. Then we calculated the predicted mortality, qx′, from our model by substituting the equation of survival with determined parameters in the previous step into Eq. 2. The qx′ values were in quite good agreement with the experimental qx values, as seen in Fig. 4B. On the other hand, μx was not at all coincident with qx or qx′. However, as the time interval Δx in Eq. 1 decreased from 1.0 to 0.05, qx′ gradually approached μx, and both matched up completely at Δx=0.01 (data not shown). This is a typical example that the rates of mortality do not always fit with the force of mortality because of the issues of qx-discreteness and μx-continuity.


Analyzing observed or hidden heterogeneity on survival and mortality in an isogenic C. elegans cohort
Biodemographic data of the mev-1;fer-15 double-mutant cohort at 25°C. (A) Survival of the mev-1;fer-15 double mutant (360 animals, summed data from three trials) exposed to 90% oxygen concentration from day 4. The raw data were fitted by the non-linear least-squares method with Eq. 4, whose fitting parameters were determined as t0 =5.25 and z=1.24. The bold black curve shows the fitting curve analyzed as a single mode. (B) Mortality rates of (A). The expected mortality rates qx′ from our model were calculated by substituting the fitting equation of survival determined at (A) into Eq. 1. Here, the interval time Δx in Eq. 1 was varied as 1.0 (filled circles), 0.5 (green line), 0.1 (blue line), and 0.05 (red line). The experimental qx and predicted qx ′ values are black circles and small black solid circles (Δx=1.0), respectively. The bold black curve represents the force of mortality calculated from Eq. 6.
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Related In: Results  -  Collection

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f4-5_59: Biodemographic data of the mev-1;fer-15 double-mutant cohort at 25°C. (A) Survival of the mev-1;fer-15 double mutant (360 animals, summed data from three trials) exposed to 90% oxygen concentration from day 4. The raw data were fitted by the non-linear least-squares method with Eq. 4, whose fitting parameters were determined as t0 =5.25 and z=1.24. The bold black curve shows the fitting curve analyzed as a single mode. (B) Mortality rates of (A). The expected mortality rates qx′ from our model were calculated by substituting the fitting equation of survival determined at (A) into Eq. 1. Here, the interval time Δx in Eq. 1 was varied as 1.0 (filled circles), 0.5 (green line), 0.1 (blue line), and 0.05 (red line). The experimental qx and predicted qx ′ values are black circles and small black solid circles (Δx=1.0), respectively. The bold black curve represents the force of mortality calculated from Eq. 6.
Mentions: Moreover, we tested our model employing the oxygen-hypersensitive double mutant mev-1;fer-15 under highly oxidative stress (Fig. 4). When this mutant strain was exposed to a high oxygen concentration (90%) after maturation, its lifespan was remarkably shortened (Fig. 4A and ref. 5). The mortality rates, qx, reached a complete plateau at advanced ages, as shown in Fig. 4B. Here, we first fitted the survival using the equation of lifespan, Eq. 4. Then we calculated the predicted mortality, qx′, from our model by substituting the equation of survival with determined parameters in the previous step into Eq. 2. The qx′ values were in quite good agreement with the experimental qx values, as seen in Fig. 4B. On the other hand, μx was not at all coincident with qx or qx′. However, as the time interval Δx in Eq. 1 decreased from 1.0 to 0.05, qx′ gradually approached μx, and both matched up completely at Δx=0.01 (data not shown). This is a typical example that the rates of mortality do not always fit with the force of mortality because of the issues of qx-discreteness and μx-continuity.

View Article: PubMed Central - PubMed

ABSTRACT

It is generally difficult to understand the rates of human mortality from biological and biophysical standpoints because there are no cohorts or genetic homogeneity; in addition, information is limited regarding the various causes of death, such as the types of accidents and diseases. Despite such complexity, Gompertz’s rule is useful in humans. Thus, to characterize the rates of mortality from a demographic viewpoint, it would be interesting to research a single disease in one of the simplest organisms, the nematode C. elegans, which dies naturally under identically controlled circumstances without predators. Here, we report an example of the fact that heterogeneity on survival and mortality is observed through a single disease in a cohort of 100% genetically identical (isogenic) nematodes. Under the observed heterogeneity, we show that the diffusion theory, as a biophysical model, can precisely analyze the heterogeneity and conveniently estimate the degree of penetrance of a lifespan gene from the biodemographic data. In addition, we indicate that heterogeneity models are effective for the present heterogeneous data.

No MeSH data available.