According to the theory and definition of radiation biology, the following formula can be deduced.
y, - hydrogen content of a biological material.
W, - Mass of dry matter of microbial cells, unit: kg, 0 < W ≦ 1.0.
MH2O=( 1-W ) × DH2O×GH2O ( 4 )
In formula 4,
1-W, - Mass of water in microbial cells, unit: kg, 0 < 1-W ≦ 1.0.
DH2O, - Absorption rate of ray by H2O in microbial cells.
GH2O, - Free radical yield of H2O in microbial cells, unit: mol/J.
Calculation of total free radicals ( M t ),
Mt=D KAgCr2O7×〔W × Dm×Gm+(1-W)×DH2O×GH2O〕 ( 5 )
In formula 5,
DKAgCr2O7, - Absorbed dose corresponding to a certain biological effect, unit: Gy.
Free radicals conservation equation, according to the definition of total free radicals and the principle of free radicals conservation.
Di×〔Wi×Dm×Gm+(1-Wi)×DH2O×GH2O〕
=Dn×〔Wn×Dm×Gm+(1-Wn)×DH2O×GH2O〕 ( 6 )
In formula 6,
Di, Dn, -Absorbed dose of microorganisms or bioactive macromolecules with different water content when the same biological effect caused, unit: Gy.
Theory application and verification. The free radical conservation equation was applied to quantitative calculation, and the calculation results were analyzed and verified.
Calculation of dose absorption rate of RNase. The H content of RNase calculated from the molecular formula of RNase ( C9H14N4O3 ) is 0.06237. The D37 value of RNase was obtained from literature7, which are D37(RNase) = 420 kGy, D37 (0.5%RNase) = 4.0 kGy.
The H value and D37 value are substituted into formula 1 and formula 2 and calculated, then obtained DRNase = 0.9574 D KAgCr2O7.
Calculation of free radical yield of RNase. DH20 = 1.0017 DKAgCr2O7, DRNase = 0.9574 DKAgCr2O7, GH20 = 600.088 × 10− 9 mol/J, D37(RNase) = 420 kGy, D37(0.5%RNase) = 4 kGy.
The algebraic value above are substituted into formula 6 to calculate, and obtained GRNase = 5.958 × 10− 9 mol/J.
Calculation of free radical of RNase and value of D 37 at low water content. Let the water content of RNase be: 0.00, 10%, 20%, 30%, 40%, 50% and 60%. The values of including water content and related parameters of DH20, DRNase, GH20 and GRNase were substituted into formula 3, formula 4, and formula 6. The percentage of direct and indirect action (That is: free radicals percentage) and the corresponding D37 value at different water content was calculated. The results are shown in Table 1.
Table 1 ratios of indirect and Direct action and corresponding D 37 values
at different water contents
Water content (%) | 0.00 | 0.10 | 0.20 | 0.30 | 0.40 | 0.50 | 0.60 |
G H20(×10− 9 mol/J) | 0.00 | 60.09 | 121.76 | 180.26 | 240.35 | 300.44 | 360.53 |
G H20/(GH20་GRNase) | 0.00 | 92.13 | 96.39 | 97.83 | 98.60 | 99.06 | 99.37 |
D37( kGy) | 420.00 | 36.73 | 18.96 | 13.00 | 9.83 | 7.90 | 6.60 |
In Table 1, the quantitative calculation results by the free radical conservation equation show that when RNase is in a dry state, the biological effects of radiation are completely produced by the direct action of rays. The D37 value is as high as 420 kGy without indirect action at this time. When the water content rises to 10%, more than 90% of the radiation effect is produced by the indirect action derived from water radiolysis, and the direct action ratio is less than 10%, and the D37 value drops from 420 kGy to 36.73 kGy. When the water content of RNase reaches 50%, the ratio of direct action is less than 1%. These calculation results are consistent with radiation biology theory and research results.
Calculation of free radical of RNase and D 37 value at high water content. Let the water content of RNase be: 0.99500, 0.99750, 0.99900, 0.99950, 0.99975, 0.99990. The values of water content and related parameters are substituted into formula 3, formula 4, and formula 6 and calculated. The results are shown in Table 2.
Table 2
Ratios of free radical and values of D37 in dilute solution of RNase
Water content (%) | 0.99500 | 0.99750 | 0.99900 | 0.99950 | 0.99975 | 0.99990 |
GRNase (× 10− 9 mol/J) | 0.02852 | 0.01426 | 0.00570 | 0.00285 | 0.00143 | 0.00057 |
GRNase/(GH20་GRNase) × 10− 7 | 477 | 238 | 95.0 | 47.5 | 23.7 | 9.49 |
D37( Gy) | 4007.0 | 3997.0 | 3991.0 | 3989.0 | 3988.0 | 3987.0 |
In Table 2, the quantitative calculation results of the free radical conservation equation show that when the water content of RNase reaches 99.50%, the biological effects of radiation are mainly caused by indirect action, and the ratio of direct action is less than 5/100,000. When it reaches 99.90%, the direct action ratio is less than one hundred thousandths. Its D37 value also drops below 4.00 kGy, and gradually changes linearly. These quantitative calculation results are consistent with actual results. See Fig. 1 for details.
This result is completely consistent with the research result of Yijing Chen17. It also shows that the free radical conservation equation is in line with objective reality.
Influence of water content on target volume. According to target theory, by analysis of the RNase activity survival curve, RNase is a biological macromolecule that can be inactivated with a single target click. The target volume can be calculated according to the formula v = 1/D373. See Table 3.
Table 3 Changes of target volume of RNase at different water contents
Water content (%)
|
0.000
|
0.100
|
0.200
|
0.300
|
0.400
|
0.500
|
0.600
|
D37( kGy)
|
420.0
|
36.73
|
18.96
|
13.00
|
9.83
|
7.900
|
6.600
|
Target volume (×10-20cm3)
|
3.897
|
44.56
|
86.32
|
125.90
|
166.50
|
207.07
|
247.98
|
In Table
3, the calculation results of the free radical conservation equation show that the target volume of RNase is positively correlated with the water content of RNase. When the water content of RNase increases by 10%, the target volume increases by more than 11 times. When the water content increases to 50%, the target volume increased by 53 times. Although the target theory calculates all doses on the target volume, which reduces the calculated target volume by hundreds of times, the increase in water content does not affect the multiple of the target volume expansion. As the target volume increases, the energy of radiation absorbed increases, and the free radicals generated increase, thereby the dose of radiation has been greatly reduced. This result explains the reason why the value of D
37 drops by 90% when the water content increases from zero to 10% by the view of target theory.
Relationship between water content and number of target. When drawing the dose survival curve of a biological cell at any water content in a radiation experiment, the free radical conservation equation can be used to calculate the D37 value of the biological cell at any water content, and multiple cell survival curves with different slopes can be drawn. It can be seen that for the same biological cell, when its water content is different, the N value (number of targets or number of hits) derived from the survival curve is also different18. According to the Target Theory, as the water content increases, the number of times of hit also increases19. It can also be said that as the water content increases, the number of targets hit also increases. This proves the reliability of the free radical conservation equation based on the target theory. |
Quantitative calculation of radiation effects of DNA molecules. The radiation death of biological cells is mainly caused by the double-strand break or aberration of DNA molecules. A large number of cell dose survival curves show that the survival rate of biological cells is linearly related to the absorbed dose20. |
In an aerobic environment, calf thymus DNA powder was irradiated with γ-rays, and the double-strand breaks rate was 0.16 molecules/100 eV, and the single-strand breaks rate was 3.4 molecules/100eV21. The free radical yield of DNA molecules calculated, GDNA=3.72 molecules/100 eV, which is converted into GDNA=3.854 × 10− 7 mol/J. According to the molecular formula of calf thymus DNA, the hydrogen content YH(calf thymus DNA) = 0.0252. |
The Y value Substituted into formula 1 and calculated, |
(µen/ρ)DNA=2.7357 × 10− 3m2/kg。
the parameters of (µen/ρ)DNA and (µen/ρ)KAgCr2O7 Substituted into formula 2 and calculated,
DDNA/DKAgCr2O7=0.9242.
DH2O/DKAgCr2O7=1.0017, GH2O=6.0088 × 10− 7 mol/J. If the ratio of double-strand breaks caused by the radiation dose of 3 Gy absorbed by dry DNA powder is used as the basis for the calculation of radiation effects, then DDNA(calf thymus) = 3 Gy. Set the water content of DNA to 0, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, and substituted parameters such as GDNA, DDNA/DKAgCr2O7, GH2O, DH2O/DKAgCr2O7 into formula 3, formula 4, formula 5, formula 6, and calculated. The results are shown in Table 4.
Table 4
Quantitative calculation of radiation effects of DNA molecules
Water content (%) | 0.00 | 0.10 | 0.20 | 0.30 | 0.40 | 0.50 | 0.60 | 0.70 | 0.80 | 0.90 |
Direct action (%) | 1.0000 | 0.8419 | 0.7030 | 0.5800 | 0.4703 | 0.3718 | 0.2829 | 0.2023 | 0.1289 | 0.0617 |
Indirect action (%) | 0.0000 | 0.1581 | 0.2970 | 0.4200 | 0.5297 | 0.6282 | 0.7171 | 0.7977 | 0.8711 | 0.9383 |
Dose absorbed (Gy) | 3.00 | 2.81 | 2.64 | 2.49 | 2.35 | 2.23 | 2.12 | 2.02 | 1.93 | 1.85 |
In Table 4, the calculation results of the free radical conservation equation show that in the radiation process of DNA molecular, with the increase of water content, the direct action decreases and the indirect action increases. The magnitude of this change decreases with the increase of water content. The absorbed dose required to achieve the same radiation effect also changes according to this law.
Combined with the influence of water content on the relevant parameters of RNase, it can be seen that the stronger the anti-radiation ability of biological cells or biologically active macromolecules, the more significant the indirect action derived from water and the greater the range of absorbed dose changes. These quantitative calculation results are completely consistent with the radiation chemistry theory and research results.
Characterization parameters of radiation sensitivity and quantification. Due to the difference of water content, the absorbed dose when reaching a certain radiation effect is changing. A kind of biological cell can have multiple water content and different D37 values, so D37 cannot correctly express radiation sensitivity of biological cells or active macromolecules. However, higher biological cells are difficult to survive when the water content is less than 65%. The absorbed dose with a dryed state is only a virtual value, and it is not suitable to represent the radiation sensitivity of biological cells.
In the free radical conservation equation, there is an important parameter that can reflect biological radiation sensitivity. That is, the DG value (the product of dose absorption rate and free radical yield).
According to the definition,
DG = W1D1G1 + W2D2G2+W3D3G3 +……+WiDiGi+……+WnDnGn,
in which of this formula, Di is the relative dose absorption coefficient of component i in biological cells, and Gi is the free radical yield of component i in biological cells.
When the external radiation environment is constant, DG is a constant value for a specific biological cell or biological macromolecule and does not change with changes of water content. A biological cell or a biological macromolecule has only one DG value. The stronger the radiation resistance, the smaller the DG value. The larger the DG value, the stronger the radiation sensitivity. Although the DG value of biological cells is extremely difficult to measure and calculate, it is very convenient to use the free radical conservation equation to calculate. Therefore, the DG value is very suitable for characterizing the radiation sensitivity of biological cells or biologically active macromolecules.