Radioresistance and radiosensitivity: a biophysical approach on bacterial cells robustness

Abstract

The study of radiosensitivity and radioresistance of organisms exposed to ionizing radiation has acquired additional relevance since a new bio-concept, coined as The primacy of Proteome over Genome, was proposed and demonstrated elsewhere a few years ago. According to that finding, genome integrity would require an actively functioning Proteome. However, when exposure to radiation takes place, Reactive Oxygen Species (ROS) from water radiolysis induce protein carbonylation (PC), an irreversible oxidative Proteome damage. The bio-models used in that study were the radiosensitive Escherichia coli and the extraordinarily robust Deinococcus radiodurans. The production of ROS induces protective reactions rendering them non-reactive forms. Protective entities present in the cytosol, moieties smaller than 3 kDa, shield the Proteome against ROS, yielding protection against carbonylation. Shown in the present study is the fact that the fate of proteins functionality is determined by the magnitude of the Protein Carbonylation Yield (Y_PC), a quantity here analytically defined using published Y_PC numerical results. Analytical Y_PC expressions for E. coli and D. radiodurans were the input for a phenomenological approach, where the radiobiological magnitudes P_P and P_N, the probabilities for production of protein damage and ROS neutralization, respectively, were also analytically deduced. These highly relevant magnitudes, associated with key radiosensitivity and radioresistance issues, are addressed and discussed in this study. Among the plethora of information and conclusions derived from the present study, those endowed with higher conceptual degree, vis-à-vis the “Primacy of Proteome over Genome” concept, are as follows: (1) the ROS neutralization process in D. radiodurans reaches a maximum at a dose interval corresponding to the repairing shoulder. Therefore, it is a signature of the higher efficiency of the PC neutralization process. (2) ROS neutralization in D. radiodurans is nearly one order of magnitude higher than in E. coli, thus accounting for its extraordinary radioresistance. (3) Both physical (ROS-induced carbonyl radicals) and biological (protein modifications) processes are imbedded in the Protein Carbonylation Yield. The amalgamation of these two processes was accomplished by means of a statistical formalism.

Appendices

Appendix 1: Shouldered curves

The exponential survival curve

Although not as iconic as shouldered curves, exponential curves are the most widely used curve category, and in virtually all areas of knowledge.

Considering that the Survival Function S(D) decreases to S(D) − dS when the dose increases from D to D + dD, the differential decrement dS is simultaneously proportional to S and dD. Therefore, dS ⁓ S·dD, and

$${\text{d}}S = - a.S.{\text{d}}D$$

(32)

The negative sign in Eq. 32 comes from the fact that dS/dD < 0, that is, the function S(D) is decreasing with D. This equation can be rearranged as,

$${\text{d}}S/S \, \equiv {\text{ d}}p \, = \, | - a \cdot {\text{d}}D| \, = a \cdot {\text{d}}D$$

(33)

where dp = dS/S is the differential probability for the occurrence of the variation from S(D) to S(D) − dS. From another rearrangement of Eq. 33, it is finally obtained

$${\text{d}}p/{\text{d}}D \, = a$$

(34)

By integration of Eq. 33, one trivially obtains that

$$S\left( D \right) \, = \, S\left( 0 \right).e^{ - aD}$$

(35)

However, it is the result expressed by Eq. 34 the one endowed with great conceptual relevance. This finding is simply stating that all single steps involved in the dose dependent evolution, from S(0) to S(D), are performed with the same probability per dose unit.

Resorting to Alpen’s interpretation (Alpen 1990) for the occurrence of an Exponential Surviving Function, we have that.

"The implication of the shape of this curve is that the loss of clonogenic potential is related to dose in an exponential fashion, and, presumably, this relationship indicates that simple, single events are responsible for the biological outcome".

According to the statistical concept here worked out (see details above), all simple, single events responsible for the biological outcome manifest themselves with the same probability per dose unit. This statistical concept hidden in the exponential function was brought to light thanks to Eq. 34, here worked out.

Application example

Curves representing Surviving Functions known as sigmoids, threshold type or simply shouldered curves, carry biophysical information in their structure, which goes beyond a mere mortality probability as a function of dose.

A shouldered function is the integral of a progenitor differential function. By way of example, let us consider the following, and arbitrarily conceived Survival Function,

$$S\left( D \right) \, = \, D^{3} /3 - D^{2} + \, 1 \, \left( {\text{arbitrary units}} \right)$$

(36)

This function exhibits an inflexion at D_i = 1.

An inflexion reveals the location of the progenitor function. In fact, S(D) is equal to the integral of

$${\text{d}}S/{\text{d}}D \, = \, D^{2} - \, 2D$$

(37)

which is the progenitor differential function of S(D).

Since

$${\text{d}}S/{\text{d}}D \, = \, D\left( {D - 2} \right)$$

(38)

this function is bounded between D = 0 and D = 2, with a minimum at D = 1, as illustrated in Fig. 11.

As discussed in Sect. 4 kGy wide Repairing Shoulder, the decrease in S per unit dose, dS/dD, corresponds to the increase in the killing yield Y_K(D) per unit dose, dY_K/dD. Therefore,

dY_K/dD  =  − dS/dD ≥ 0, where dS/dD ≤ 0, and

$${\text{d}}Y_{K} /{\text{d}}D \, = \, 2D - D^{2}$$

(39)

It is shown in Fig. 11 below the analytically obtained functions dY_K/dD, dS/dD, and S(D)—see details above.

Panel [B] of this figure represents a Survival Curve published elsewhere and adapted herein for purposes of illustration only, with the insertion of dY_K/dD (arbitrary units) at the approximate position of the inflection seen in the original figure (Alpen 1990, Fig. 7 2-B).

Fig. 11

Top: Graphic representation of Eqs. 37 and 39. A Pictorial representation of a Survival Curve over imposed on a progenitor differential function dY_K/dD (see text for details). B Same as in A but referring to a figure adapted from Fig. 7.2-B of Alpen (1990)

Appendix 2: Complementary Conceptualization

Protein carbonylation yield and the “zeros” of Y _PC

It is important to point out, once more, that as found elsewhere (see Krisko et al. 2012 and Krisko and Radman 2013): (1) the irradiation dose-range saturating PC in E. coli (Dsat), 0.9–1.0 kGy, has no effect on the proteome of D. radiodurans, which saturates PC at doses ≥ 10 kGy; (2) the correlation between the cell killing relative yield (Y_K) and the protein carbonylation yield, (Y_PC), is strikingly similar for the two bacteria. In fact, saturation of killing, that is, Y_K(E.col) = Y_K(D.rad) = 1(or 100%), occurs for Y_PC(E.col) = Y_PC(D.rad) ≈ 5–6.5 (nmol-carbonyl/mg-protein).

These PC saturation levels of 5–6.5 (nmol-carbonyl/mg-protein), the same for D. radiodurans and E. coli, is relative to the assumption that Y_PC(D = 0) = 0 for both bacteria. However, the present phenomenological data analysis reveals that.

Y_PC(Ecol, 0 kGy) = 11 (nmol-carbonyls/mg-prot.) and.

Y_PC(Dra, 0 kGy) = 1.6 (nmol-carbonyls/mg-prot.).

This result is in qualitative agreement with findings obtained by Michael Daly and collaborators (Daly et al. 2010) where, according to their study, Protein Carbonylation is found at much lower levels in non-irradiated D. radiodurans (D = 0 kGy) than in E. coli. In fact,

$$\left[ {Y_{{{\text{PC}}}} \left( {{\text{Ecol}}, \, 0 {\text{kGy}}} \right)} \right]/\left[ {{\text{Y}}_{PC} \left( {{\text{Dra}}, \, 0 {\text{kGy}}} \right)} \right] = 11/1.6 \, \approx \, 7$$

This is, also, closely consistent with the fact that low levels of protein carbonyls are signatures of resistance to oxidative stress, as pointed out elsewhere (Stadtman and Levine 2003).

The dynamics of PC-neutralization

As commented before, the probability P_N(Drad) rises steeply with Y_K in the death yield interval Y_K ≈ 0.2 to 0.6, while P_N(Ecol) is a monotonically increasing function of Y_K (see Fig. 6). These function variation characteristics are quantitatively appraised by the “derivative of P_N(Y_K) relatively to Y_K”, that is, dP_N/dY_K, which represents the slope of the P_N curves shown in Fig. 6. The calculations were numerically performed from,

$${\text{d}}P_{{\text{N}}} /{\text{d}}Y_{{\text{K}}} \approx \, \Delta P_{{\text{N}}} /\Delta Y_{{{\text{K}} }} \equiv \Phi \left( {Y_{{\text{K}}} } \right)$$

(40)

by assuming small ΔY_K increments equal to 0.1 kGy in the interval Y_K ≈ 0.2 to 0.6. Results, up to Φ(Y_K) saturation, are presented in Table.

Table 1 The functions Y_K and Φ were defined in the text

1.

The more profound meaning of Φ(Y_K), other than a mere curve-slope evaluation, is closely related to the speed at which the Proteome protection systems of D. radiodurans and E. coli (analytically represented by P_N), respond to increases of the cell death yield (Y_K). Since Y_K is proportional to the radiation dose and, consequently, to the ROS produced, Φ(Y_K) also evaluates the rate at which the protection system responds to radiation injuries to the Proteome. Interestingly, Φ(Ecol) seems to be insensitive to increasing ROS (see Table 1), which correlates with the smaller population of available moieties, comparatively to D. radiodurans.

“Reading” of results formatted as probabilities

Presented below are two examples on how to correctly interpret probability formatted results.

• (a)

  D. radiodurans: P_N = 0.55 (kGy) ^− 1 when Y_K = 0.3

In an irradiation of D. radiodurans at a given dose, where 30% of its remaining cell population has died, its protective entities neutralized 55% of the ROS still active, per kGy. The dose associated with Y_K = 0.3 in D. radiodurans is D = 1.45 kGy.

• (b)

  E. coli: PN = 0.2 (kGy) ^− 1 when Y_K = 0.3

In this other example, 30% of the remaining E. coli cell population died, and its protective entities neutralized 20% of the ROS still active, per kGy. The dose associated with Y_K = 0.3 in E. coli is D = 0.10 kGy.

Quite salient from these two examples are as follows:

• i. The same cell casualties (Y_K = 0.3) inflicted on D. radiodurans and E. coli were provoked by radiation doses of 1.45 kGy and 0.10 kGy, respectively. The dose imparted to D. radiodurans is thus approximately 15 times (1.45/0.1) higher than in E.coli.

• ii. The ROS neutralization process in D. radiodurans is nearly thrice (0.55/0.2) more effective than in E. coli.