Download Classical Over Barrier model

GEANT4-DNA
New physics models
…from cell to DNA
Christophe Champion
FKPPL Workshop
Seoul March 8-10, 2011
From water to DNA:
The classical Trajectory Monte Carlo - Classical Over Barrier model
(CTMC-COB)
ZP
Y
vP
X
RP
b
zP
Z
ZT

re1
Input dynamical data :
e1
Each simulation starts and stops at large internuclear distance (≈100 a.u.)
the projectile velocity (VP)
the impact parameter (b)
the initial conditions for the target
The classical Trajectory Monte Carlo - Classical Over Barrier model
(CTMC-COB)
The molecular binding energies
The classical Trajectory Monte Carlo - Classical Over Barrier model
(CTMC-COB)
General features of the classical models
Movements of the particles described by Newton laws
Initial targets information = the knowledge of the binding energies
Classical criteria for describing the ionizing processes
Total cross sections:
 i  2
bmax
 P (b)bdb
i
0
N i b 
Pi (b) 
N tot b 
The classical Trajectory Monte Carlo - Classical Over Barrier model
(CTMC-COB)
COB (Classical Over Barrier) criteria
RR
Target
Projectile
e5
Projectile
Target
Target
e1
Potential over barrier
Bound target electrons
(c)
(b)
(a)
Molecular electron
Potentielover
overbarrier
barrier
Potential
e2
e4
Projectile
R=R1
e11
ee2 2 eee333
Target electrons
e4 ee45 e5
Captured electrons
Target electrons
The classical Trajectory Monte Carlo - Classical Over Barrier model
(CTMC-COB)
COB (Classical Over Barrier) criteria
The Classical Trajectory Monte Carlo - Classical Over Barrier model
(CTMC-COB)
COB (Classical Over Barrier) criteria
R
Projectile
Target
Potential over barrier
e1
e2
Target electrons
Potential seen by the bound electron e1:
e4
R=R1
Projectile
Molecular electron
Target
e1
e2
Potential over barrier
VP   ZP
and
 
re1  RP
Target electrons
(b)
R
Target
Potentiel over barrier
e2
e4
Projectile
(c)
at the beginning of the simulation
e1
e3
e5
Bound target electrons
where
e3
e4 e5
 
VT  1 re1  RT


RT  0
e5
(a)

 
 
Vtot (re1 )  VP (re1  RP )  VT (re1  RT )
where
e3
Captured electrons
The classical Trajectory Monte Carlo - Classical Over Barrier model
(CTMC-COB)
Propagation of the system
At each step Δt (≈10-2 a.u.) COB and d conditions are tested:
At each time
T and/or
e-)
 1 for each involved particleZ Pi (i = ZP,
1
Z P step ZtT and
T  2
V  r1 , r2   


V (r1 )  

r

a
r12  a
r

R

a
r1  a 
2
r1  R  a
2
ˆ
ˆ
ˆ
r

x
i

y
j

z
k
For the nexti time i step :i t’ = t i + Δt



ri  vt.viv iˆ  v ˆj  v kˆ
i
xi
yi
zi
 

ri  ri  ri
 


 

vi  F
t.aim a iˆ  a ˆj  a kˆ vi  vi  vi
i
i
x
y
z

i
i
i

The classical Trajectory Monte Carlo - Classical Over Barrier model
(CTMC-COB)
Conditions and criteria of the final state
E
i
P (T )
1  
2
 vi  vP (T )  
2
Z P (T )
1
  

2

j  i ri  r j
ri  RP (T )
kinetic energy of the electron
relatively to the target or the
projectile
potential energy of the electron
relatively to the target or the
projectile
if EPi  0 the electron i is captured
if ETi  0 the electron i remains bound to the target
if EPi  0 and ETi  0 the electron i is ejected
The classical Trajectory Monte Carlo - Classical Over Barrier model
(CTMC-COB)
Total cross sections for the main ionizing processes induced by charged particles
Abbas et al., Phys. Med. Biol. 53, N1-N11 (2008)
Lekadir et al., NIM B 267, 1011-1014 (2009)
Lekadir et al., Phys. Rev. A 79, 062710 (2009)
From water to DNA: Quantum mechanical approaches:
Coulomb Born approximation (CB1)
Continuum Distorted Wave – Eikonal Initial State (CDW-EIS)
Champion et al., Phys. Med. Biol. 55, 6053-6067 (2010)
Target description
LCAO: Linear Combination of Atomic Orbitals
Bernahrdt and Paretzke (Int. J. Mass Spectrom. 599 (2003))
 

3
3
N
N
d
d
j
(
3
)
(

,

,
E
)
 

(

,

,
E
)


s
e
e
j
s
e
e
d

d

dE
d

d

dE
j

1
j

1
s
e
e
s
e
e

3




(
3
)
(

,

,
E
)

g
.
.
(

,

,
E
)

i
i
at
,
i
s
e
e
(
3
)
j se
e
i
 at(3,)i ( s ,  e , Ee )  Ta ,b i
2



Z
Z
P
P


T

(
R
)
.
(
r
)

(
R
)
.
(
r
)
a
,
b
i
,
b
i
,
b
i
,
a
i
,
a


i
R
R

r
Quantum mechanical /classical approaches: CB1, CDW-EIS / CTMC-COB
Ionization of DNA bases impacted by light ions
Abbas et al., Phys. Med. Biol. 53, N1-N11 (2008)
Lekadir et al., NIM B 267, 1011-1014 (2009)
Lekadir et al., Phys. Rev. A 79, 062710 (2009)
Protons
2+
H + Cytosine
2
10
2
CDW-EIS
CBA
CTMC-COB
exp
-1
+
+
H + Guanine
H + Thymine
10
10
2
1
1
CBA
CDW-EIS
CTMC-COB
10
10
0
2+
2+
He + Thymine
10
10
10
He + Guanine
2
10
10
1
10
2
10
3
10
4
10
15
10
2
10
3
10
Incident proton energy (keV/amu)
4
10
5
2
10
1
CBA
CDW-EIS
CTMC-COB
10
0
6+
6+
C + Guanine
C + Thymine
10
3
10
2
10
1
10
0
1
0
-1
10
-16
10
-16
Total cross sections (10
10
0
3
2
cm )
2
-16
Total Cross Sections (10
10
10
C + Cytosine
2
1
cm )
10
6+
C + Adenine
He + Cytosine
Total cross sections (10 cm )
10
6+
2+
He + Adenine
+
+
H + Adenine
Carbon ions C6+
a-particles
0
10
1
10
2
10
3
10
1
10
2
10
3
Incident ion energy (keV/amu)
10
4
10
1
10
2
10
3
10
4
10
15
10
2
10
3
Incident ion energy (keV/amu)
10
4
10
5
Quantum mechanical approaches:
Continuum Distorted Wave – Eikonal Initial State (CDW-EIS)
Capture on DNA bases impacted by light ions
Protons
10
-13
10
-14
10
-15
10
-16
10
-17
10
-18
10
-19
H + Adenine
H + Cytosine
10
-20
10
-21
10
-22
10
-23
10
-13
10
-14
10
-15
10
-16
10
-17
10
-18
10
-19
10
-20
10
-21
10
-22
10
-23
10
-12
10
-13
10
-14
10
-15
10
-16
10
-17
10
-18
10
-19
10
-20
10
-21
10
-22
10
-23
10
-24
10
-25
-11
10
-12
10
-13
10
-14
10
-15
10
-16
10
-17
10
-18
10
-19
10
-20
10
-21
10
-22
10
-23
10
-24
10
-25
2
Total cross sections (cm )
2
10
CTMC-COB
CDW2 (CNDObis) (n=1 + n=2)
CDW2 (CNDObis) (n=1)
CDW2 (CNDObis) (n=2)
+
2
-11
10
+
H + Guanine
1
10
2
10
3
Incident energy (keV/amu)
6+
C
6+
+ Adenine
C
+ Cytosine
+
experimental
Total cross sections (cm )
10
-12
+
Total cross sections (cm )
Carbon ions C6+
H + Thymine
10
1
2
10
10
3
Incident energy (keV/amu)
4
10
CTMC-COB
CDW
CDW
CDW
CDW
CDW
(n=1+n=2+n=3+n=4)
(n=1)
(n=2)
(n=3)
(n=4)
6+
C
1
10
2
10
+ Guanine
3
10
C
10
1
6+
+ Thymine
2
10
Incident ion energy (keV/amu)
3
10
4
10
DNA versus liquid water:
GEANT4 simulations
Results
DNA 10 bp target
Nucleosome target
An increase of the mean energy value of energy deposits of the order of
25% for the 10 base pairs target and 25% for the nucleosome target