27
Life at Low D Lecture II: Virtual Lab
Life at Low D
Lecture II: Virtual Lab
Bend Energy
Energy required to bend filament of Length L into circular arc of Radius, R
22 R
LEIUBend
LR
Bend Energy
Energy required to bend filament of Length L into circular arc of Radius, R
22 R
LEIUBend
LR
dssR
EILUU
L
arcsall
oBendBend
02
)(
1
2
0sLs
Bend Energy
dssR
EILUU
L
arcsall
oBendBend
02
)(
1
2
0sLs
R
dds
Bend Energy
dssR
EILUU
L
arcsall
oBendBend
02
)(
1
2
0sLs
Rdds R
dds
Bend Energy
dssR
EILUU
L
arcsall
oBendBend
02
)(
1
2
0sLs
Rdds ds
d
R
1R
dds
Bend Energy
dssR
EILUU
L
arcsall
oBendBend
02
)(
1
2
0sLs
Rdds ds
d
R
1R
dds
2
2
1
ds
d
R
Bend Energy
dsds
dEILU
L
Bend
0
2
2
)2()1( BendBend UU
)1(
)2(
Bend Energy
dsds
dEILU
L
Bend
0
2
2
)1(
),( ii yx
),( 11 ii yx
Bend Energy
dsds
dEILU
L
Bend
0
2
2
)1(
),( ii yx
),( 11 ii yx 2
12
1 iiiii yyxxds ids
Bend Energy
dsds
dEILU
L
Bend
0
2
2
)1(
),( ii yx
),( 11 ii yx 2
12
1 iiiii yyxxds
ii
iii xx
yy
1
1]tan[
ids
i
Bend Energy
dsds
dEILU
L
Bend
0
2
2
)1(
),( ii yx
),( 11 ii yx 2
12
1 iiiii yyxxds
ii
iii xx
yy
1
1]tan[
ids
i
)(s
s
Bend Energy
dsds
dEILU
L
Bend
0
2
2
)(s
s
n
sL
nq
Ls
cos)(2
)(
Bend Energy
dsds
dEILU
L
Bend
0
2
2
)(s
s
n
sL
n
L
nq
Lds
d sin)(
2
n
sL
nq
Ls
cos)(2
)(
Bend Energy
dsds
dEILU
L
Bend
0
2
2
)(s
s
m n
sL
m
L
mks
L
n
L
nq
Lds
d sin)(sin)(
22
n
sL
nq
Ls
cos)(2
)(
n
sL
n
L
nq
Lds
d sin)(
2
Bend Energy
dsds
dEILU
L
Bend
0
2
2
)(s
s
dssL
ns
L
m
L
m
L
nkq
Lds
ds
d L
mn
L
sinsin)()(
2
0,0
2
n
sL
nq
Ls
cos)(2
)(
n
sL
n
L
nq
Lds
d sin)(
2
m n
sL
m
L
mks
L
n
L
nq
Lds
d sin)(sin)(
22
Bend Energy
dsds
dEILU
L
Bend
0
2
2
)(s
s
mn
L 2
n
sL
nq
Ls
cos)(2
)(
n
sL
n
L
nq
Lds
d sin)(
2
m n
sL
m
L
mks
L
n
L
nq
Lds
d sin)(sin)(
22
dssL
ns
L
m
L
m
L
nkq
Lds
ds
d L
mn
L
sinsin)()(
2
0,0
2
Bend Energy
dsds
dEILU
L
Bend
0
2
2
)(s
s
n
L
qqdsds
d 22
0
2
n
sL
nq
Ls
cos)(2
)(
n
sL
n
L
nq
Lds
d sin)(
2
m n
sL
m
L
mks
L
n
L
nq
Lds
d sin)(sin)(
22
Bend Energy
dsds
dEILU
L
Bend
0
2
2
)(s
s
n
Bend qqEIL
U 22
2
n
sL
nq
Ls
cos)(2
)(
Bend Energy
dsds
dEILU
L
Bend
0
2
2
)(s
s
n
Bend qqEIL
U 22
2
qqEIL
TkB22
22
1
n
sL
nq
Ls
cos)(2
)(
Bend Energy
dsds
dEILU
L
Bend
0
2
2
)(s
s
n
Bend qqEIL
U 22
2
qqEIL
TkB22
22
1 2
2 1
LqEI
Tkq B
n
sL
nq
Ls
cos)(2
)(
Bend Energy
dsds
dEILU
L
Bend
0
2
2
)(s
s
n
Bend qqEIL
U 22
2
qqEIL
TkB22
22
1
n
sL
nq
Ls
cos)(2
)(
2
2 11
Lqq
2
2 11
Lqq
22
11
Lqq
Persistence Length
2
2 11
Lqq
22
11
Lqq
Persistence Length
Persistence Length
2
2 11
Lqq
22
11
Lqq
fd virus
Actin
MT
x
Persistence Length
2
2 11
Lqq
22
11
Lqq
fd virus
Actin
MT
2
2 11
Lqq
22
11
Lqq
Persistence Length
mfd 1.23.7
mactin 9.19.13
mmMT 3.0.6.1
x
fd virus
Actin
MT
