broerse, g.iv. barendsen h.b. kal, a.j. van der kogel (editors) radiobiological institute tno rijswijk, the netherlands

radiation research reviews and summaries on

chemistry, physics biology and medicine

proceedings of the

seventh international congress of

radiation research

amsterdam july 3-8, 1983

martinus nijhoff publishers

VII

CONTENTS

P R E F A C E ν

SPECIAL AND SEMI -PLENARY L E C T U R E S

51 RISKS OF IONIZING RADIATION, THEIR UNCERTAINTIES AND 1 IMPACT UPON SOCIETY L.M. van Putten

52 NEW APPROACHES FOR THE IMPROVEMENT OF RADIOTHERAPY 13 J.F. Fowler

53 POTENTIAL EFFECTS ON HEALTH OF RADIOACTIVE WASTE DISPOSAL 23 Y. S o u s s e l i e r , N. Parmentier

54 REPAIR MECHANISMS IN RADIATION-INDUCED CELL TRANSFORMATION 33 M.M. E l k i n d , A. Han, C.K. H i l l and F. Buonaguro

55 RADIATION CHEMISTRY AND BIOLOGICAL EFFECTS 43 J.L. Magee

56 STUDIES ON RADIATION-INDUCED GENETIC DAMAGE IN MAMMALS: 53 PAST ACHIEVEMENTS AND FUTURE TASKS OF RESEARCH K. Sankaranarayanan

57 REVISIONS IN THE DOSIMETRY OF THE ATOMIC BOMB SURVIVORS 63 W.K. S i n c l a i r

58 MODELS OF CELLULAR RADIATION ACTION 75 AM. K e l l e r e r

59 RADIOBIOLOGICAL APPROACHES TO RADIATION LATE EFFECTS 87 T. Sugahara, T. Aoyama, O. Nikaido and F. Sato

CHEMISTRY AND PHYSICS

Al-R NONHOMOGENEOUS KINETICS AND THE RADIATION PHYSICS/CHEMISTRY 97 /BIOLOGY INTERFACES G.R. Freeman

Al-S PRIMARY PROCESSES IN RADIATION PHYSICS AND CHEMISTRY 107 R. V o l t z

Al-S PRIMARY PROCESSES IN RADIATION PHYSICS AND CHEMISTRY 113 J.M. Warman

A2-R SOME CONTRIBUTIONS OF RADIATION CHEMISTRY TO 119 GENERAL CHEMISTRY G.V. Buxton

A2-S RADIATION CHEMISTRY: GENERAL CHEMISTRY 129 K.-D. Asmus

A3-R RADIATION CHEMISTRY: DNA AND MODEL SYSTEMS 133 D. S c h u l t e - F r o h l i n d e

VIII

A3-S RADIATION CHEMISTRY OF DNA AND MODEL SYSTEMS 141 E.M. F i e l d e n

A3-S RADIATION CHEMISTRY: DNA AND MODEL SYSTEMS 145 G. Scholes

A4-R RADIATION CHEMISTRY: MOLECULAR SYSTEMS OF BIOCHEMICAL 151 INTEREST OTHER THAN DNA L.K. Pat t e r s o n

A4-S RADIATION CHEMISTRY: OTHER MOLECULES OF BIOLOGICAL INTEREST 161 C. von Sonntag

A4-S RADIATION CHEMISTRY: OTHER MOLECULES OF BIOLOGICAL INTEREST 165 A.J. Swallow

A5-R NANOSECOND TIME-RESOLVED DETECTION AND STUDY OF RADICALS 17 3 R.W. Fessenden

A5-S TECHNIQUES IN RADIATION CHEMISTRY 181 P. Wardman

BIOLOGY

Bl-R EARLY MECHANISMS IN RADIATION-INDUCED BIOLOGICAL DAMAGE 187 E.L. Powers

B l - S RADIATION BIOCHEMISTRY: MECHANISMS OF DAMAGE 195 J . K i e f e r

B l - S RADIATION BIOCHEMISTRY: MECHANISMS OF DAMAGE 199 B.D. Michael

B2-R DNA-REPAIR: PROGRESS AND PROBLEMS 205 R.B. P a i n t e r

B2-S DNA DAMAGE AND REPAIR IN CELLS 213 W.A. Cramp

B2-S DNA DAMAGE AND REPAIR IN CELLS 217 A. S a r a s i n

B3-R RADIATION EFFECTS ON DNA AND MEMBRANES 225 A. Cole

B3-S RADIATION EFFECTS ON MEMBRANES 231 A.W.T. Konings

B3-S COMPARISON OF DIFFERENT KINDS OF RADIATION DAMAGE 235 AT THE MOLECULAR LEVEL P.H.M. Lohman

B4-R MUTAGENESIS AND CHROMOSOME CHANGES 239 A.T. Natarajan

B4-S MUTAGENESIS AND CHROMOSOME CHANGES 249 D.T. Goodhead

B4-S CELLULAR EFFECTS: MUTAGENESIS AND CHROMOSOME CHANGES 257 M.S. S a s a k i

IX

B5-R LETHAL, SUBLETHAL AND POTENTIALLY LETHAL RADIATION DAMAGE 263 W. P o h l i t

B5-S CELLULAR TARGETS, "HITS", "EVENTS", CHEMICAL LESIONS AND 271 THEIR REPAIR J.D. Chapman

B5-S LETHAL, SUBLETHAL AND POTENTIALLY LETHAL DAMAGE IN CELLS 277 L . J . Tolmach

B6-R RADIOSENSITIZERS AND RADIOPROTECTORS: CURRENT STATUS 281 AND FUTURE PROSPECTS J.Μ. Brown

B6-S SENSITISATION AND PROTECTION 291 I . J . S t r a t f o r d

B6-S CHEMICAL PROTECTION 297 O. Vos

B7-R CELL-CELL CONTACT AND REPAIR OF RADIATION DAMAGE 303 J.S. Rasey

B7-S REPAIR IN CELLS, CELL CONTACT 311 R.E. Durand

B7-S SURVIVAL OF IRRADIATED MAMMALIAN CELLS IN CULTURE: THE 317 CHEMISTRY OF LESIONS AND THEIR REPAIR AND THE ROLE OF POLY(ADP-RIBOSE) SYNTHESIS P. Todd

SOMATIC AND G E N E T I C E F F E C T S

Cl-R RADIATION BIOLOGY OF THE HEMOPOIETIC AND 325 IMMUNOLOGICAL TISSUES D.W. van Bekkum

Cl- S HAEMATOPOIETIC AND IMMUNE SYSTEMS 331 J.F. Duplan

Cl-S RADIATION AND THE HEMOPOIETIC SYSTEM 335 H.M. Vriesendorp

C2-R LATE EFFECTS OF RADIATION: HOST FACTORS 341 R.J.M. F r y and J.B. S t o r e r

C2-S MECHANISMS OF LATE EFFECTS IN VARIOUS TISSUES 349 G. P a t r i c k

C2-S MECHANISMS OF LATE EFFECTS IN VARIOUS TISSUES 353 R.L. U l l r i c h

C3-R THE MAIN VARIABLES INVOLVED IN THE RADIATION ACTION ON 3 55 EMBRYO AND FOETUS P. M e t a l l i

C3-S TERATOGENIC EFFECTS 3 59 G. Konermann

C4-R SOME GROWING POINTS IN MAMMALIAN RADIATION GENETICS 367 A.G. S e a r l e

χ

C4-S GENETIC EFFECTS 373 S. Abrahamson

C5-R RADIATION TRANSFORMATION IN VITRO 377 J.B. L i t t l e

C5-S IN VITRO CELL TRANSFORMATION 385 C. Borek

C6-R TUMOUR INDUCTION IN DIFFERENT TISSUES 391 G. S i l i n i

C6-S TUMOR INDUCTION IN DIFFERENT TISSUES 401 C.J. S h e l l a b a r g e r

C7-S CARCINOGENESIS BY INCORPORATED ISOTOPES 407 V. V o l f

C8-R CURRENT STATUS OF HUMAN RADIOEPIDEMIOLOGY 413 G.W. Beebe

C8-S CANCER EPIDEMIOLOGY AND RISK ASSESSMENT 421 C.E. Land

TUMOUR BIOLOGY AND THERAPY

Dl-R RADIATION EFFECTS ON TUMOURS 427 Η. Jung

Dl-S EFFECTS ON TUMOURS, CELL SURVIVAL, GROWTH DELAY 435 J . Denekamp

Dl-S RESPONSES OF TUMOURS TO RADIOTHERAPY 441 H.B. K a l

D2-R CELL POPULATION KINETICS AND THE RESPONSE OF TUMOURS 447 TO TREATMENT G. G. S t e e l

D2-S TUMOUR AND NORMAL TISSUE PROLIFERATION KINETICS 453 A.F. Hermens

D3-R EFFECTS ON NORMAL TISSUES: TOLERANCE 459 H. R. Withers

D3-S EFFECTS ON NORMAL TISSUES "467 J.W. Hopewell

D3-S EFFECTS ON NORMAL TISSUES 475 K.R. T r o t t

D4-R THERAPEUTIC APPLICATION OF NEUTRONS AND HIGH-LET RADIATION 481 A. Wambersie

D4-S HIGH LET RADIATION 491 S.B. C u r t i s

D4-S HIGH LET RADIATION 495 S.B. F i e l d

XI

D5-R MODIFICATION OF RADIATION RESPONSE BY CHEMICAL AGENTS: 501 PROBLEMS AND PROSPECTS G.Ε. Adams

D5-S MODIFICATION OF RADIOSENSITIVITY BY RADIOPROTECTORS 507 E.P. Malaise

D5-S MODIFICATION OF RADIOSENSITIVITY BY RADIOSENSITIZERS 511 A.H.W. Nias

D6-R HYPERTHERMIA IN CANCER THERAPY 517 W.C. Dewey

D6-S HYPERTHERMIA AND RADIATION - IN VITRO STUDIES 527 G.M. Hahn

D6-S HYPERTHERMIA. REVIEW OF ANIMAL AND CLINICAL STUDIES 535 J . Overgaard

D7-R RADIO-CHEMOTHERAPY 539 N.M. Bleehen

D7-S COMBINED RADIO- AND CHEMOTHERAPY 547 E. van der Schueren

DOSIMETRY, RADIONUCLIDES AND TECHNOLOGY

E l - R MICRODOS IMETRY 551 D. Harder

E l - S MICRODOSIMETRY 563 N. Parmentier

E2-R DOSIMETRY: PHYSICAL ASPECTS 571 D.K. Bewley

E2-S DOSIMETRY: PHYSICAL ASPECTS 579 G. Burger

E2-S DOSIMETRY: PHYSICAL ASPECTS 585 J.A. Dennis

E3-R DOSIMETRY: BIOLOGICAL INDICATORS 589 D.C. Lloyd

E3-S DOSIMETRY: BIOLOGICAL INDICATORS 597 M.R. Raju and D.C. Lloyd

E4-R RADIOECOLOGY AND NUCLEAR POWER IN PERSPECTIVE 603 R. Kirchmann

E4-S RADIOECOLOGY: MARINE AND TERRESTRIAL 613 D.S. Woodhead

E5-R RADIONUCLIDES: METABOLISM, TOXICITY, WASTE 621 W. Jacobi

E5-S; RADIONUCLIDES: TOXICOLOGY; METABOLISM, WASTE 635 A.L. Carsten

XII

E6-R VALUE OF RADIATION FOR CROP IMPROVEMENT 641 B. Si g u r b j o r n s s o n , A. Micke, Β. Donini, S. Daskalov, Τ. Hermelin and Η. Brunner

E6-S RADIATION EFFECTS AND MUTAGENESIS IN PLANTS 653 B.V. Conger

E7-R TECHNOLOGICAL ASPECTS OF RADIATION 657 A. Charlesby

E7-S TECHNOLOGICAL APPLICATIONS OF RADIATION 667 J . Simon

AUTHOR INDEX 6 7 3

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MODELS OF CELLULAR RADIATION ACTION

Α.Μ.Kellerer I n s t i t u t für Medizinische Strahlenkunde der Universität Würzburg,

Versbacher Str.53 D-8700 Würzburg, Germany

I . Introductory Remarks

Modelsj as t he e thymo logy o f t h e word says , a r e measures o f o u r knowledge o f the mechanisms u n d e r l y i n g ob se rved phenomena. In r a d i o b i o l o g y they are more o f t e n t e s t i m o n y t o ou r l a c k o f knowledge o f fundamenta l mechanisms; i n t h i s sense the p r e s e n t deve lopment i s one away f rom models towards ac ­t u a l d e t a i l e d knowledge. But models - f a u l t y as t hey may be - a r e s t i l l r e q u i r e d as g u i d e p o s t s towards new e x p e r i m e n t s and as c o n c e p t u a l f r ame ­work t h a t f a c i l i t a t e s d i s c u s s i o n . They w i l l be u s e f u l o n l y i f t hey a re not taken t o o l i t e r a l l y , and a t the p r e s e n t s t a t e o f knowledge, no r a d i o -b i o l o o i s t oupht t o a im a t p r e c i s e and comp le te agreement between h i s equa­t i o n s and t h e e x p e r i m e n t a l d a t a . What one can hope f o r , i s m e r e l y the i d e n t i f i c a t i o n o f r e c u r r e n t t r e n d s and o f e s s e n t i a l c h a r a c t e r i s t i c s o f t he d o s e - e f f e c t r e l a t i o n s i n t h e i r dependence on p a r a m e t e r s , such as r a ­d i a t i o n q u a l i t y , dose r a t e , o r oxygen t e n s i o n .

The subsequent remarks w i l l , a c c o r d i n g l y , dea l w i t h problems and p r o p o s i ­t i o n s r a t h e r than e q u a t i o n s and n u m e r i c a l d a t a . Re levan t as a l o o k back t o the r o l e o f t a r g e t t h e o r y and t he more q u e s t i o n a b l e r o l e o f m u l t i -t a r g e t o r m u l t i - h i t t h e o r y c o u l d be , i t w i l l be o m i t t e d . N e i t h e r can a f u l l s y nop s i s o f models o f c e l l u l a r r a d i a t i o n a c t i o n be a t t e m p t e d w i t h i n t he c o n s t r a i n t s o f t h e a l l o t t e d space.

I I . The Linear-Quadratic Dose Dependence

There a r e s i m p l e and f undamenta l c o n c l u s i o n s t h a t f o l l o w f r o m m i c r o d o s i -met ry - t he te rm microdosimetry b e i n g used i n i t s gene ra l sense as the phy s i c s o f t he m i c r o s c o p i c d i s t r i b u t i o n o f energy impa r ted by i o n i z i n g r a d i a t i o n s . One o f t h e most g e n e r a l c o n c l u s i o n s i s t h a t at low doses any dose-effect relation for autonomous c e l l s must be linear. A low dose i n t he m i c r o d o s i m e t r i c sense i s one where a charged p a r t i c l e appears i n o n l y a minor f r a c t i o n o f a l l c e l l s , o r c e l l n u c l e i . The number o f such c e l l s i s then e v i d e n t l y p r o p o r t i o n a l t o absorbed dose. For s p a r s e l y i o n i z i n g r a d i a t i o n s low doses a re f r a c t i o n s o f one mGy, f o r d e n s i l y i o n i z i n g r a ­d i a t i o n s low doses a r e f r a c t i o n s o f one Gy. The t e r m autonomous was i n t r o ­duced by H.H.Rossi (20) t o r e f e r t o t he c o n d i t i o n t h a t the f a t e o f the exposed c e l l i s u n a f f e c t e d by r a d i a t i o n e f f e c t s on i t s ne i ghbou r s o r on the t i s s u e as a w h o l e .

Support by Euratom (Contract BI0-286-81D(B)) i s acknowledged.

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For genetic e f f e c t s t he e x i s t e n c e o f a l i n e a r component a t low doses f o l ­l ows , t h e r e f o r e , f r om f i r s t p r i n c i p l e s o f m i c r o d o s i m e t r y . Dose r e l a t i o n s f o r chromosome a b e r r a t i o n s must have a l i n e a r component; e s t i m a t e s o f he ­r e d i t a r y r i s k s o f i o n i z i n g r a d i a t i o n s can e q u a l l y u t i l i z e the p o s t u l a t e o f a l i n e a r r e l a t i o n a t low doses ( 2 3 , 3 2 ) . The s i t u a t i o n f o r radiation, car­cinogenesis i s more c o m p l i c a t e d ; l i n e a r i t y can not be p o s t u l a t e d even f o r v e r y low doses , as i n t e r - c e l l u l a r processes and t i s s u e f a c t o r s can p l ay , and have been shown t o p l a y ( 3 6 , 2 8 , 2 9 ) , an i m p o r t a n t r o l e .

A t i n t e r m e d i a t e and h i g h e r doses the dose dependence f o r c e l l u l a r e f f e c t s i s more complex and a v a r i e t y o f e q u a t i o n s has been emp loyed . However, the linear-quadratic dependence on absorbed dose has t aken a predominant r o l e i n r e cen t yea r s and, a t l e a s t f o r c e l l i n a c t i v a t i o n and chromosome abe r r a ­t i o n s , i t i s u s u a l l y adequa te . I t has o c c a s i o n a l l y been s a i d t h a t the l i n ­e a r - q u a d r a t i c dependence is t r i v i a l because any obse rved f u n c t i o n can, i n i t s i n i t i a l p a r t , be a p p r o x i m a t e d by a l i n e a r t e r m , a 1 i n e a r - q u a d r a t i : t e r m , o r i f more p r e c i s i o n i s r e q u i r e d , by a c o m b i n a t i o n o f h i g he r povers o f absorbed dose. Th i s t r u i s m may be m i s l e a d i n g i f i t c oncea l s the f a : t t h a t the l i n e a r - q u a d r a t i c r e l a t i o n cover s the obse rved d a t a o f many e<pe r i -ments w i t h mammalian c e l l s o ve r an a p p r e c i a b l e range o f absorbed doses, and t h a t i t i s t h e r e f o r e more than a m a t h e m a t i c a l t r i v i a l i t y . Subsequent c o n s i d e r a t i o n s on the RBE-dose r e l a t i o n w i l l c o n f i r m the p o i n t .

I t i s w e l l known t h a t t h e r e a re a t h i g h e r doses d e v i a t i o n s f rom the 1 n e a r -q u a d r a t i c dependence. Th i s wou ld r e q u i r e a s e p a r a t e c o n s i d e r a t i o n , bu: i n t he c o n t e x t o f the p r e s e n t d i s c u s s i o n i t may mere l y be n o t e d t h a t the t a i l o f t he dose r e l a t i o n i s f r e q u e n t l y i n f l u e n c e d by t e c h n i c a l i t i e s o f the e x ­p e r i m e n t and i s l e s s i n d i c a t i v e o f ba s i c mechanisms. T h i s a spec t is t i e r e -f o r e o m i t t e d f r om the p r e s e n t s u r vey o f e s s e n t i a l s .

On t he b a s i s o f some obse rved d o s e - e f f e c t r e l a t i o n s a case can be made f o r t he l i n e a r - q u a d r a t i c r e l a t i o n ; o t h e r s are f a r more c o m p l i c a t e d . But t i e e v i dence has ga i ned a d d i t i o n a l w e i g h t by the s t udy o f RBE-dose r e l a t i o n s . Rossi (26) has emphas ized the p o i n t t h a t such s t u d i e s remove complex i ie s o f t h e d o s e - e f f e c t r e l a t i o n s wh i ch are independent o f r a d i a t i o n q u a l i y , and t h a t t hey have, a c c o r d i n g l y , g r e a t e r s i g n i f i c a n c e than the mere s udy o f t he d o s e - e f f e c t r e l a t i o n s . RBE-dose s t u d i e s have, i n d e e d , led t o t i e r e c o g n i t i o n o f l a r g e n e u t r o n RBEs a t low doses; they have a l s o demons r a t e d a dependence o f n e u t r o n RBE on dose t h a t p r o v i d e s s t r o n g e v i dence f o r l i n ­e a r i t y o f c e l l u l a r damage w i t h n e u t r o n s , and f o r q u a d r a t i c r e l a t i o n s v i t h γ - o r x - r a y s . From the s t u d i e s o f tumor i n d u c t i o n o r l i f e s h o r t e n i n g t appears t h a t any l i n e a r components f o r x - r a y s must be much l e s s than hose obse rved f o r c e l l u l a r i n a c t i ν i a t i on . In c o n c l u s i o n : RBE-dose relation'., rather than dose-effect relations, are the essential argument for the lin­ear-quadratic dependence of cellular damage on radiation dose.

P ragmat i c i m p l i c a t i o n s o f t he l i n e a r - q u a d r a t i c models a r e e v i d e n t and r e ­q u i r e o n l y b r i e f r e f e r e n c e . The ve r y concepts and q u a n t i t i e s o f r a d i a i i o n p r o t e c t i o n a re l i n k e d t o l i n e a r i t y , a l t h o u g h t h i s i s n o t a lways s u f f i c i e n t ­l y a p p r e c i a t e d . The e s t a b l i s h e d n o t i o n s may by now be so f a m i l i a r tha t one tends t o o v e r l o o k t he fundamenta l d i f f e r e n c e o f p h i l o s o p h y between r ac i a -t i o n r i s k assessment w i t h i t s l i n e a r p o s t u l a t e s and t o x i c o l o g y w i t h t i e more common a s s umpt i on o f a t h r e s h o l d .

R a d i a t i o n p r o t e c t i o n i s , o f cou r se , no t the o n l y a rea where assumed ot i n ­f e r r e d d o s e - e f f e c t r e l a t i o n s f o r c e l l u l a r e f f e c t s have p r a g m a t i c impl c a ­t i o n s . R a d i a t i o n t h e r a p y is ano the r area w i t h i t s own e m p i r i c a l o r seri -

S8 77

e m p i r i c a l mode l s . The l i n e a r - q u a d r a t i c model i s , n e v e r t h e l e s s , r e l e v a n t . Th i s may appear s u r p r i s i n g i n v iew o f t he E l l i s f o r m u l a t h a t a c c o u n t s f o r the i n f l u e n c e o f p r o t r a c t i o n and f r a c t i o n a t i o n . One can show, a l t h o u g h t h i s i s n o t w i d e l y known, t h a t t h i s f o r m u l a c o r r e spond s t o t he a s sumpt ion o f a power f u n c t i o n f o r the s u r v i v a l cu r ve ( w i t h E l l i s ' o r i g i n a l c o e f f i ­c i e n t s : In S ^ D ) . Nobody expec t s a c e l l u l a r d o s e - e f f e c t r e l a t i o n t o f o l l o w such a r e l a t i o n t h a t has ze ro s l o p e a t t he o r i g i n . Th i s w o u l d seem t o i n v a l i d a t e the E l l i s - f o r m u l a , and, i n d e e d , more r e a l i s t i c t r e a t m e n t s i n terms o f t he l i n e a r - q u a d r a t i c r e l a t i o n have been proposed by Fowle r and S te rn (9) and by Barendsen ( 2 ) . Of c o u r s e , t h i s does no t i n v a l i d a t e the E l l i s - f o r m u l a and i t s i m p o r t a n t r o l e as a c l i n i c a l g u i d e l i n e , w i t h i n the l i m i t e d range o f c o n v e n t i o n a l f r a c t i o n a t i o n schemes. One can r e p l a c e the broken power o f dose by a c l o s e l y c o i n c i d e n t l i n e a r - q u a d r a t i c t e r m (16) and o b t a i n s then a f o r m u l a t h a t i s n e a r l y unchanged in the range o f v a l i ­d i t y o f t he E l l i s - e q u a t i o n , b u t g i v e s m e a n i n g f u l v a l ue s even a t l ower do ­ses and dose r a t e s and c o u l d t h e r e f o r e be u s e f u l a l s o i n i n t r a c a v i t a r y t h e r a p y . The example t e s t i f i e s t o the f a c t t h a t t h e r e i s no t o n l y t h e o r e ­t i c a l i n t e r e s t i n models o f c e l l u l a r r a d i a t i o n a c t i o n , bu t a c o n t i n u i n g p r a c t i c a l need as w e l l .

I I I . The Evolution of Relevant Studies

The fundamenta l i dea i s s imp l e and has been r e cogn i z ed s i n c e t he work o f Lea and Sax on chromosome a b e r r a t i o n s ( 2 1 ) . A second order process o r dual action, as i t has been termed i n a l a t e r approach (19) , wou ld l ead t o a q u a d r a t i c dependence on absorbed dose i f the s p a t i a l d i s t r i b u t i o n o f energy impa r ted were u n i f o r m . In r e a l i t y an added l i n e a r component appears because energy i s i m p a r t e d t o the c e l l i n c o r r e l a t e d c l u s t e r s on the t r a c k s o f charged p a r t i c l e s ; even a t s m a l l e s t doses the l o c a l c o n c e n t r a t i o n s o f e n ­e rgy can be l a r g e , and they depend then o n l y on r a d i a t i o n q u a l i t y n o t on dose.

Fig. 1 Schematic diagram of the distribution of energy transfers (dots) in a cell nucleus exposed to sparsely ionizing and densily ionizing radiation.

The s chemat i c d i a g r a m o f F i g . l can h e l p t o i n d i c a t e the concep t s and f a ­c i l i t a t e t he t e r m i n o l o g y . I t r e p r e s e n t s s c h e m a t i c a l l y the s i t u a t i o n o f a s p a r s e l y i o n i z i n g and a den se l y i o n i z i n g r a d i a t i o n . The d o t s s t a n d f o r energy transfers, and f r om these energy t r a n s f e r s s u b l e s i o n s may be p r o ­duced. One m i g h t c o n c e i v e o f the s u b l e s i o n s as s i n g l e s t r a n d DNA breaks (SSB) and o f the l e s i o n s as doub le s t r a n d breaks (DSB); b u t s u b l e s i o n s c o u l d a l s o be chromosome i n s t a b i l i t i e s and l e s i o n s c o u l d then be o b s e r v ­a b l e chromosome a b e r r a t i o n s . Even t he s chemat i c t w o - d i m e n s i o n a l d i ag ram i n d i c a t e s the p o t e n t i a l c o m p l e x i t y o f i n t e r a c t i o n s i n a random p a t t e r n o f energy t r a n s f e r s and r e s u l t i n g s u b l e s i o n s t h a t may i n t e r a c t p a i r w i s e . Ev­i d e n t l y t h e r e i s no l a c k o f p o s s i b l e models and f r e e p a r a m e t e r s . Whatever

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p o s t u l a t e s w i l l be i n v o k e d , i t i s p l a u s i b l e t o assume an i n t e r a c t i o n p r o ­b a b i l i t y between s u b l e s i o n s t h a t decreases w i t h d i s t a n c e o f i n i t i a l s epa ­r a t i o n . Lea assumed a c o n s t a n t i n t e r a c t i o n p r o b a b i l i t y up to a c r i t i c a l d i s t a n c e , and ze r o i n t e r a c t i o n p r o b a b i l i t y beyond t h i s range. Of c o u r s e , t h i s a s sumpt ion was i n t r o d u c e d no t as an a c t u a l p o s t u l a t e but n e r e l y as a p r a g m a t i c a p p r o x i m a t i o n .

W i t h t h i s e x p l a n a t i o n one can take a gene r a l v iew and c l a s s i f y the approach o f Lea o r s i m i l a r t r e a t m e n t s , as proximity models. The term re fe r s t o t he as sumpt ion t h a t s u b l e s i o n s a r e formed randomly by energy t r a n s f e r s and t h a t p a i r s o f n e i g h b o u r i n g s u b l e s i o n s i n t e r a c t w i t h p r o b a b i l i t / t h a t i n ­creases w i t h t h e i r p r o x i m i t y . From the d i a g r am o f F i g . l one sees i n t u i ­t i v e l y t h a t i n t e r a c t i o n o f intra-track s u b l e s i o n s must predominate i n t he case o f den se l y i o n i z i n g r a d i a t i o n s , w h i l e i n t e r a c t i o n s o f inter-track s u b l e s i o n s a r e more f r e q u e n t i n the case o f s p a r s e l y i o n i z i n g r a d i a t i o n s . In t he a c t u a l 3~d imens i ona l case i t i s even more u n l i k e l y t h a t energy t r a n s f e r s f r om independent p a r t i c l e t r a c k s come i n t o c l o s e p r o x i m i t y , w h i l e c l o s e ne i ghbou r s w i l l a lways e x i s t w i t h i n p a r t i c l e t r a c k s , and e s p e c i a l 1 y w i t h i n the t r a c k s o f den se l y i o n i z i n g p a r t i c l e s .

The u n s p e c i f i e d use o f t he te rm interaction probability o f energy t r a n s ­f e r s o r s u b l e s i o n s has i n t h e pas t l ed t o c o n f u s i o n . The t e r n does n o t r e ­f e r t o a direct i n t e r a c t i o n , b u t i s a probabilistic n o t i o n that r e f e r s -c e r t a i n l y f o r the i n t e r - t r a c k e f f e c t , b u t p r o b a b l y a l s o f o r the i n t r a - t r a c k f o r m a t i o n o f damage - t o t he outcome o f a complex c h a i n o f mo lecu la r and m e t a b o l i c e ven t s t h a t may l ead f r om the p r o d u c t i o n o f f r e e r a d i c a l s t o DNA-damage and then - w i t h s h o r t e r o r l o n ge r s p a t i a l and temporal s e p a r a ­t i o n - t o s u c c e s s f u l o r f a u l t y r e p a i r . The r e l e v a n t damage is never ' d i ­r e c t l y 1 produced by t he i n i t i a l processes o f energy t r a n s f e r . ) bv i ou s as t h i s p o i n t s hou ld be f r o m i t s o r i g i n a l use i n the c o n t e x t o f t i e f o r m a ­t i o n o f chromosome a b e r r a t i o n s , i t i s even now n o t s u f f i c i e n t l y a p p r e c i a t e d ; i n h e r e n t l y s i m i l a r n o t i o n s such as sublesion interaction o r nisrepair due to the formation of neighbouring lesions a r e then t r e a t e d as a l t e r n a t i v e s r a t h e r than d i f f e r e n t d e s i g n a t i o n s o f t he same p r o c e s s .

When m i c r o d o s i m e t r y was deve l oped by Rossi and h i s co l l e ague s a p o w e r f u l new t o o l f o r e x p e r i m e n t a l assessment o f r a d i a t i o n q u a l i t y becane a v a i l a b l e . One can d e t e r m i n e a c t u a l ene rgy c o n c e n t r a t i o n s w i t h i n m ic ro scop ic vo lumes . But one must r e a l i z e t h a t t h e f a m i l i a r m i c r o d o s i m e t r i c measurenents ans ­wer a q u e s t i o n t h a t i s n o t e n t i r e l y ana logous t o t he prob lem o~ the p r o x -

PHOXIKITY CONCEPT SITE CONCEPT Fig. 2

energy in specified proxiiity

froi randoi energy transfer

(utilizes coaputed

•icrodosiietric data)

\

(utilizes licrodosiietric

•easureients)

energy in site centered

at randoi point

\

Schematic diagram tc i l l u s t r a t e the relation of the prozimity and the s i t e concept. The proximity function i s utilized in the prox­imity model; i t i s linked by a general mathematical relation to the dose average of microdosimet­r i c quantities (17). The proximity concept permits a treatment in terms of distance dependent inter­action probabilities (20).

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i m i t y models . They do no t d e t e r m i n e the number o f n e i g h b o u r i n g energy t r a n s f e r s around a randomly chosen energy t r a n s f e r ; they s p e c i f y i n s t e a d the number o f t r a n s f e r s i n a randomly p o s i t i o n e d s i t e . A mode l , t h e r e f o r e , t h a t i s based on e x p e r i m e n t a l m i c r o d o s i m e t r i c da ta must be a s i t e model. The scheme o f F i g . 2 j u x t a p o s e s the two c o n c e p t s , t h a t have here been men­t i o n e d because they a r e r e c u r r e n t n o t i o n s i n a v a r i e t y o f models t h a t a r e not a lways phrased i n the m i c r o d o s i m e t r i c t e r m i n o l o g y . However, they a r e ment i oned a l s o t o emphasize the f a c t t h a t b o t h approaches are i n h e r e n t l y s i m i l a r i n i n v o k i n g l o c a l measures of energy concentration o ve r d i s t a n c e s t h a t a re r e l e v a n t t o the a c c u m u l a t i o n o r f i x a t i o n o f c e l l u l a r damage. S i t e and p r o x i m i t y models a re v a r i a t i o n s o f the same theme.

W i th t h i s c o n v e n t i o n on t e r m i n o l o g y one can now t r a c e b r i e f l y the d e v e l o p ­ment f r o m the work o f Lea t o c u r r e n t mode l s . As i s w e l l known, Lea and Sax have compared the dose r e l a t i o n s o f chromosome a b e r r a t i o n s f o r n e u t r o n s and x - r a y s . They used the e s t i m a t e d f r e q u e n c i e s o f i n t r a - t r a c k and i n t e r -t r a c k ne i ghbour s t o d e t e r m i n e i n t e r a c t i o n d i s t a n c e s o f s u b l e s i o n s , i . e . chromosome b r e a k s , and they deduced d i s t a n c e s up t o 1 pm, i . e . the c u r v e d shape o f the d o s e - e f f e c t r e l a t i o n f o r x - r a y s was e v i dence f o r l ong range i n t e r a c t i ons.

The approach o f Lea and Sax c o u l d have o f f e r e d i t s e l f t o ready t r a n s l a ­t i o n i n t o the concept s and q u a n t i t i e s o f m i c r o d o s i m e t r y . However, the f i r s t a p p l i c a t i o n o f m i c r o d o s i m e t r y took d i f f e r e n t and i ndependent l i n e s . An a t t e m p t was made by Rossi and coworker s (30 ,22 ) t o see w h e t h e r a c r i ­t i c a l t h r e s h o l d o f s p e c i f i c energy i n c e r t a i n assumed s i t e s wou ld c o r r e ­l a t e w i t h the e x p e r i m e n t a l d a t a . The l ack o f agreement w i t h e x p e r i m e n t a l r e s u l t s l ed t o the more g e n e r a l i z e d approach t h a t a s c r i b e s an i n c r e a s i n g e f f e c t p r o b a b i l i t y t o i n c r e a s i n g v a l ue s o f s p e c i f i c energy - one may n o t e t h a t t h e r e a re r e c e n t approaches (k) o f t he same n a t u r e . When t h i s assump­t i o n was t e s t e d a g a i n s t a v a r i e t y o f e x p e r i m e n t a l d a t a , the c o n c l u s i o n was drawn t h a t a q u a d r a t i c dependence on s p e c i f i c energy agreed w i t h a w i d e range o f e x p e r i m e n t a l d a t a . Th i s l e d t o t he m i c r o d o s i m e t r i c a n a l y s i s o f dua l r a d i a t i o n a c t i o n ( 1 9 ) . Subsequent l y t he c l o s e ana logy t o Lea ' s r e ­s u l t s f o r chromosome a b e r r a t i o n s was a p p r e c i a t e d .

From t h i s p o i n t o f i n i t i a l agreement t he deve lopment l e d t o the p r e s e n t s t a t e . Neary had ex tended the s t u d i e s o f Lea. From h i s work w i t h s o f t x - r a y s {2k) he i n f e r r e d i n t e r a c t i o n d i s t a n c e s t h a t tended t o be l e s s t han those e a r l i e r deduced. Goodhead and c o l l e a g u e s (11) ex tended the i n v e s t i ­g a t i o n s o f Neary t o s t i l l lower x - r a y e n e r g i e s and , found - as d i d V i r s i k and Harder i n t h e i r chromosome s t u d i e s ( 3^ ,35 ) " f u r t h e r e v i dence f o r s h o r t range i n t e r a c t i o n s . Th i s i s i n agreement w i t h e a r l i e r c o n c l u s i o n s f rom t r a c k segment work ( l ) and f r om s t u d i e s o f DNA damage by heavy ions ( 2 5 ) . The gene ra l c o n c l u s i o n i s t h a t t he p r o x i m i t y model w i t h c o n s t a n t i n t e r a c t i o n p r o b a b i l i t y o r t he ana logous s i t e model i s i n a d e q u a t e . An i n ­dependent and s imu l t aneou s d e r i v a t i o n o f t h i s r e s u l t came f rom e x p e r i m e n t s w i t h s p a t i a l l y c o r r e l a t e d heavy ions ( 2 7 , 1 8 ) . Rossi and h i s c o l l e a g u e s had shown i n these e x p e r i m e n t s , t h a t a m a j o r i t y o f t he i n t r a - t r a c k l e s i o n s a re formed f r om s h o r t range i n t e r a c t i o n s . Toge the r w i t h t he s i g m o i d shape o f the s u r v i v a l c u r v e , and the i m p l i e d r e q u i r e m e n t o f l ong range i n t e r a c t i o n s , t h i s l e d t o the c o n c l u s i o n o f an i n t e r a c t i o n p r o b a b i l i t y o f s u b l e s i o n s r a p i d l y d e c l i n i n g a t d i s t a n c e s be low 50 t o 100 nm, b u t r e a c h i n g o u t t o d i s t a n c e s o f t he o r d e r o f a m i c r o m e t e r .

At t h i s p o i n t t h e r e was remarkab le ag reement . There was a l s o agreement w i t h e a r l i e r r e s u l t s o f Chapman e t a l . ( 6 ) who had i d e n t i f i e d c h a r a c t e r i s -

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t i c d i f f e r e n c e s i n the e f f e c t o f m o d i f y i n g f a c t o r s on the l i n e a r i n t r a -t r a c k component and the q u a d r a t i c i n t e r - t r a c k component. I f the i n t r a - t r a c k a c t i o n p e r t a i n s t o much s h o r t e r d i s t a n c e s than the i n t e r - t r a c k a c t i o n , the marked d i f f e r e n c e s a re u n d e r s t a n d a b l e .

A s i m i l a r c o n s i d e r a t i o n p e r t a i n s t o t he OER. I f observed l e s i o n s r e s u l t f r o m a second o r d e r p rocess then - as e l e m e n t a r y arguments can show - the OER f o r the i n t r a - t r a c k e f f e c t s hou ld equa l the square o f the OER f o r the s u b l e s i o n s . For t he i n t e r - t r a c k e f f e c t t he OERs o f l e s i o n s and s u b l e s i o n s s h o u l d be the same. There i s , however, no e x p e r i m e n t a l ev idence t h a t t he OER f o r the l i n e a r component o f c e l l s u r v i v a l o r o t h e r c e l l u l a r e f f e c t s i s l a r g e r than t h a t f o r the q u a d r a t i c component. The sub l e s i on s i n v o l v e d i n the l i n e a r process must t h e r e f o r e have a c o n s i d e r a b l y s m a l l e r OER than i n the i n t e r - t r a c k mode. The reduced OER o f h i g h LET r a d i a t i o n s may, o f c o u r s e , i n v o l v e a d d i t i o n a l f a c t o r s , such as s a t u r a t i o n e f f e c t s .

IV, Interpretations

The q u a d r a t i c model has been r e j e c t e d by Goodhead (12,13) i n f a v o r o f a proposed i n t e r p r e t a t i o n t h a t he has l a b e l e d TERS. In the acronym TE s tands f o r threshold energy and f o r the a s sumpt ion t h a t a c r i t i c a l energy o f 100 t o 300 eV causes, i n s i t e s o f 3 nm d i a m e t e r , r e p a i r a b l e l e s i o n s , w h i l e more than 300 eV ( f o r m u t a t i o n s t w i c e the amount) cause non - r epa i r ab1e l e ­s i o n s , the predominant mode f o r den se l y i o n i z i n g r a d i a t i o n .

One may be r e l u c t a n t t o adopt the n o t i o n o f d e f i n e d 3 nm s i t e s w i t h two energy t h r e s h o l d s f o r two t ype s o f l e s i o n s ; b u t the p o s t u l a t e appears f l e x i b l e enough t o be r e p l a c e d by a p r o b a b i l i s t i c dependence. A more s e r i ­ous l i m i t a t i o n c o u l d be , t h a t s i t e s i z e s ( o r e f f e c t i v e s i z e s ) and t h r e s h ­o l d s ( o r e f f e c t i v e t h r e s h o l d s ) f o r two types o f p r e s e n t l y unde f i ned DNA-damage c o n f e r t o the model t o o many pa ramete r s t o a l l o w v e r i f i c a t i o n o r f a l s i f i c a t i o n . The prob lem i s common w i t h o t h e r models , t o o , bu t i t i s here p a r t i c u l a r l y e v i d e n t s i n c e t he pa ramete r s de te rm ine mere ly t he l i n e a r component. An independent f e a t u r e i s i nvoked t o account f o r the c u r v a t u r e o f t he dose dependence.

The a d d i t i o n a l f e a t u r e i s RS, repair saturation, the assumption t h a t among the e x t e n s i v e r e p a i r o f r a d i a t i o n induced damage i t 'seems l i k e l y t h a t a t l e a s t one o f these r e p a i r s tep s becomes less e f f i c i e n t w i t h i n ­c r e a s i n g r a d i a t i o n dose, p r o b a b l y due t o s a t u r a t i o n o f the r e p a i r s y s t e m 1 .

A dose dependent lo s s o f compensat ion o r r e p a i r e f f i c i e n c y had been i n ­voked b e f o r e most o f our p r e s e n t knowledge on enzymat i c r e p a i r mechanisms was a v a i l a b l e 0^ ,15 ) · However, f o r the p r e s e n t l y known mechanisms o f short patch, long patch, recombination, and SOS repair - even i f they were a l l o p e r a t i v e i n e u k a r y o t e s - i t i s d i f f i c u l t t o conce ive o f s a t u r a ­t i o n a t doses o f a few g r a y . I t i s , i n f a c t , d i f f i c u l t t o ana l y se these mechanisms excep t a t f a r h i g h e r doses. Exper iment s by V i r s i k and Harder (33) on chromosome a b e r r a t i o n s i n d i c a t e t h a t the h a l f t imes o f r e p a i r a r e independent o f dose. Recent work by B l ö c h e r and Pohl i t (3) g i ve s the a n a l ­ogous r e s u l t s f o r DSB r e p a i r i n mammalian c e l l s . The work o f Wheeler and Wierowski on DNA-repa i r i n t h e i r r a d i a t e d r a t b r a i n (37) cou l d be c i t e d in s uppo r t o f s a t u r a t i o n o f a s low r e p a i r component. However, t he data show unchanged r e p a i r t imes i n the r e l e v a n t dose range below 12 Gy, and any s low-down observed a t h i g h e r doses may w e l l be a t i s s u e e f f e c t . There i s , t h e r e f o r e , a t p r e s e n t no e x p e r i m e n t a l e v i dence and no f e a t u r e o f the known r e p a i r processes t h a t s u p p o r t s the idea o f r e p a i r s a t u r a t i o n o r r e -pai r o v e r l o a d .

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The dual a c t i o n m o d e l , o r any s u b l e s i o n i n t e r a c t i o n models o f s i m i l a r na ­t u r e , are s i m p l e r i n the sense t h a t t hey invoke m e r e l y one mechanism. But i t i s e v i d e n t t h a t t h e g e n e r a l f o r m u l a t i o n i n terms o f d i s t a n c e dependent i n t e r a c t i o n o f s u b l e s i o n s c o n t a i n s a l s o , in e f f e c t , many degrees o f f r e e ­dom. P re sen t d a t a a r e as y e t i n s u f f i c i e n t f o r the i d e n t i f i c a t i o n o f a c t u a l mechanisms. C e r t a i n f i r m c o n c l u s i o n s a r e n e v e r t h e l e s s r eached , as can be i l l u s t r a t e d by a f u r t h e r e l e m e n t a r y b u t gene ra l a p p l i c a t i o n o f m i c r o d o s i -m e t r i c d a t a , i n p a r t i c u l a r , o f t he proximity functions ( 1 7 ) .

1 0 0 -

% Fig. 3

The average partition (at a dose of 1 Gy) of energy im­parted around an energy trans­f e r into contributions on the same particle track (linear term in dose) and on other tracks (non-linear term in absorbed dose).

The data are based on com­puted Droximitij functions (8,?).'

300 i.00 500

Distance / nm

F i g . 3 shews t h a t the i n t r a - t r a c k n e i g h b o u r s domina te by f a r a t sma l l d i s t a n c e s . As f o l l o w s r e a d i l y , any c u r v e d dose dependence must r e f l e c t i n t e r a c t i o n o f s u b l e s i o n s o r a c c u m u l a t i o n o f r a d i a t i o n e f f e c t s o v e r d i s t a n c e s beyond the e x t e n s i o n o f t h e da rk a r e a s . T h i s r e q u i r e m e n t i s g e n e r a l , and e n t i r e l y independent o f t he proces ses t h a t may be i n v o k e d . DNA d o u b l e - s t r a n d breaks wou ld t h e r e ­f o r e appear n o t t o be t h e c r i t i c a l l e s i o n s , as i n d i c a t e d i n the d i ag ram o f F i g . 1 * .

S H O R T - R A N G E I N T E R A C T I O N

Fig. 4

Short-distance interaction of lesions by separate particles i s unlikely at doses of bio­logical interest.

( u n l i k e l y e x c e p t a t v e r y h i g h d o s e s )

There a r e , on t h e o t h e r hand, n o t a b l e r e s u l t s on a q u a d r a t i c , o r l i n e a r -q u a d r a t i c , dose-dependence f o r n o n - r e p a i r e d DSBs, n o t o n l y i n the da ta by Frankenberg ( 10 ) f o r y e a s t b u t a l s o i n t he r e s u l t s o f B l ö che r and Pohl i t (3) f o r E h r l i c h - A s c i t e s c e l l s . Such u n r e p a i r e d l e s i o n s m i gh t be r e l a t e d t o c e l l d e a t h , and t h e y may a l s o be i n v o l v e d i n o t h e r c e l l u l a r r a d i a t i o n e f ­f e c t s . However, t h i s w o u l d r e q u i r e t he i d e n t i f i c a t i o n o f the mechanism t h a t can a c c u m u l a t e damage o v e r d i s t a n c e s o f f r a c t i o n s o f a m i c r o m e t e r . Could energy c o n d u c t i o n i n t h e DNA-molecule be r e s p o n s i b l e f o r such i n t e r ­a c t i o n s ? Or c o u l d t h e l e s i o n s be caused by the f a i l u r e o f r e c o m b i n a t i o n o r SOS - r epa i r , i . e . forms o f r e p a i r where pa tches o f thousands o f n u c l e o ­t i d e s ( i . e . DNA t h r e a d s > 0.5 ym, i f e x t e n d e d ) a re r e p l a c e d , and where the presence o f a second DNA l e s i o n w i t h i n t h e rep l acement segment c o u l d cause t h e f a i l u r e o f r e p a i r ?

S8 82

Fig. 5 schematic diagram stands for interaction of carnage over very long DNA patches (>1000 nucleotides). This type of mis-repair could he envisaged if recombination- or SCS-repair is operative in eukaryotes. The inter-track effect predominates, because the mean number of neighbouring energy transfers on other tracks at distance χ is proportional to x%.

Whether e r r o r p rone and dual l e s i o n s e n s i t i v e s u p e r - l o n g patch r e p a i r i s r e l e v a n t t o the a c t i o n o f i o n i z i n g r a d i a t i o n s on e u k a r y o t i c c e l l s i s , a t t h i s p o i n t , mere s p e c u l a t i o n . But i t i s an i n t r i g u i n g s u p p o s i t i o n , i n view o f an observed q u a d r a t i c dose dependence f o r u n r e p a i r e d DSBs. I t i s f u r t h e r m o r e a t t r a c t i v e t o n o t e t h a t a l i n e a r array o f p o t e n t i a l t a r g e t s t h a t can p a i r w i s e i n t e r a c t w i l l lead t o a d i s t a n c e dependence of l e s i o n f o r m a t i o n t h a t i s p r o p o r t i o n a l t o 1/x 2 o r i s even s t eepe r (see the d i a ­gram o f F i g . 5 ) ; such dependences have, i n f a c t , been deduced from the c o r ­r e l a t e d i on e x p e r i m e n t s ( 1 8 ) and f r om the r e a n a l y s i s by Brenner and Z a i d e r o f the u l t r a s o f t x - r a y e x p e r i m e n t s ( 5 ) .

Dua ? r a d i a t i o n a c t i o n o r , more g e n e r a l l y , a second o rde r process i n t he a c t o n o f r a d i a t i o n on the c e l l , appears t o be the s i m p l e s t nodel c o n s i s t ­e n t w i t h e x p e r i m e n t a l d a t a . But t he u n d e r l y i n g processes a re l a r g e l y u n r e ­s o l v e d , and o t h e r o r a d d i t i o n a l mechanisms can n o t be exc luded . F u r t h e r progress i n the a n a l y s i s o f r e p a i r p roce s se s , and mechanisms o f energy t r a n s f e r i n and around the DNA w i l l be r e q u i r e d ; m i c r o d o s i m e t r i c s t u d i e s both on t h e nanometer and t he m i c r o m e t e r l e v e l w i l l be e q u a l l y i m p o r t a n t .

C u r t i s has r e c e n t l y b r o u g h t t o g e t h e r e s s e n t i a l s o f c u r r e n t models ( 8 ) . The r e s u l t i n g u n i f i e d t r e a t m e n t cove r s a broad range o f s u b l e s i o n - i n t e r a c t i o n o r n i s r e p a i r mode l s . As many o f these mode l s , i t d i s r e g a r d s or s i m p l i f i e s one m i c r o d o s i m e t r i c a s p e c t ; i t invokes a u n i f o r m , n o n - s t o c h a s t i c , i . e . dose dependent , i n c r e a s e o f i n t e r a c t i o n f r equency o r m i s r e p a i r p r o b a b i l i t y On π ί c r o d o s i m e t r i c p r i n c i p l e s one shou ld e x p e c t a dependence o f these p r o ­cesses on l o c a l energy c o n c e n t r a t i o n . The i n d i v i d u a l c e l l car not d i s c e r n the v a l ue o f the absorbed dose o r t he average y i e l d o f l e s i o r s ; i t can r e -spord o n l y t o t he energy i m p a r t e d t o i t s e l f , and t h i s may dev i a te g r e a t l y , i n c non -Po i s s on i an d i s t r i b u t i o n , f r om the s t a t i s t i c a l average. There may, a c c c r d i n g l y , be room f o r a f u r t h e r i n t e r l i n k a g e o f models .

As rrembers o f ou r s pec i e s we a re t he p r o d u c t o f f a u l t y DNA-repeir; as s c i e n t i s t s we owe ou r p r o f e s s i o n t o the e v o l u t i o n o f i m p e r f e c t t h e o r i e s and e r r o r - p r o n e i d ea s . The need f o r t r i a l and e r r o r can serve es an e x ­cuse even f o r a d i s c u s s i o n o f models t h a t expose more l i m i t a t i o n s o f knowledge than a c t u a l mechanisms o f c e l l u l a r r a d i a t i o n a c t i o n .

LONG-RANGE I N T E R A C T I O N

( l i k e l y o n l y f o r INTER-TRACK a c t i o n )

Fo r p a i r o f energy t r a n s f e r s w i t h s p e c i f i e d d i s t a n c e χ i n t e r a c t i o n p r o b a b i l i t y -v 1/

X2 ( i . e . s t e e p l y d e c r e a s i n g i n t e r a c t i o n f u n c t i o n ) .

V. Conclusion

S8 83

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