Models for Mechanisms of Protection against Damaging Effects of Radiation 161
where E is the remaining concentration of active enzyme at time te' and Eo
is the initial enzyme concentration at t = 0, because according to the mathematics of the model In(E/Eo) starts to vary parabolically with te, i.e. the
plot (3) should for small doses asymptotically fit a straight line through the
origin. If -.)1 denotes the slope of this line the mathematics of the model
shows that
(4)
where kE is the rate constant for the reaction of the enzyme E with the
radical X in which both enzyme and radical become inactivated. One next
has to plot
In (E/Eo) versus te
(5)
because according to the mathematics of the model In(E/Eo) versus te
should fit a straight line asymptotically for large doses D. Denoting this
line -.)2 te + Rl one has to calculate the quantity
(6)
and to plot
b versus Eo
(7)
which plot should fit a straight line according to the mathematics of the
model. Denoting this line R2 + .5"3EO one has to plot
R2 versus Po
(8)
where Po is the concentration of the substance whose protecting, or sensitizing, effect on the inactivation of the enzyme E is studied. According to the
mathematics of the model this plot should fit a straight line through the
origin denoted .)5PO with
(9)
where kp is the rate constant for the reaction between the radical X and
the protector, or sensitizer, P, leading to a change of the radical.
If by varying the quality of the protecting, or sensitizing, substance P a
variation is found in the rate constant kE this will indicate that the protecting, or sensitizing, effect of P is due to a masking effect of P on the enzyme
E, whereas if a variation is found in the rate constant kp this will indicate
that the protective, or sensitizing, effect of P is due to a scavenging effect of P
on the radical X.
It is therefore possible that we here have a new tool for elucidating the
basic mechanisms of the effects of protecting and sensitizing substances in
radiobiology. Consequently we have tentatively proposed to denote the
rate constants kE and k p the internal and external radiosensitivity coefficients,
respectively.
11 3. Symp. Quant. Bioi.
where E is the remaining concentration of active enzyme at time te' and Eo
is the initial enzyme concentration at t = 0, because according to the mathematics of the model In(E/Eo) starts to vary parabolically with te, i.e. the
plot (3) should for small doses asymptotically fit a straight line through the
origin. If -.)1 denotes the slope of this line the mathematics of the model
shows that
(4)
where kE is the rate constant for the reaction of the enzyme E with the
radical X in which both enzyme and radical become inactivated. One next
has to plot
In (E/Eo) versus te
(5)
because according to the mathematics of the model In(E/Eo) versus te
should fit a straight line asymptotically for large doses D. Denoting this
line -.)2 te + Rl one has to calculate the quantity
(6)
and to plot
b versus Eo
(7)
which plot should fit a straight line according to the mathematics of the
model. Denoting this line R2 + .5"3EO one has to plot
R2 versus Po
(8)
where Po is the concentration of the substance whose protecting, or sensitizing, effect on the inactivation of the enzyme E is studied. According to the
mathematics of the model this plot should fit a straight line through the
origin denoted .)5PO with
(9)
where kp is the rate constant for the reaction between the radical X and
the protector, or sensitizer, P, leading to a change of the radical.
If by varying the quality of the protecting, or sensitizing, substance P a
variation is found in the rate constant kE this will indicate that the protecting, or sensitizing, effect of P is due to a masking effect of P on the enzyme
E, whereas if a variation is found in the rate constant kp this will indicate
that the protective, or sensitizing, effect of P is due to a scavenging effect of P
on the radical X.
It is therefore possible that we here have a new tool for elucidating the
basic mechanisms of the effects of protecting and sensitizing substances in
radiobiology. Consequently we have tentatively proposed to denote the
rate constants kE and k p the internal and external radiosensitivity coefficients,
respectively.
11 3. Symp. Quant. Bioi.