ifl timbales - uni-muenchen.de...macromolecules 1 le 106 biophysics of 552019 problem set 1 a volume...
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Biophysics of Macromolecules 552019PROBLEM SET 1
a Volume of E coli
U I R2 L If.to Guy z.io fu
1 6 to 18ms 1µmk Ifl
b Inn timbalesle
0.6 molecules
lflRoughly 1 molecule per E
coli cell
1mmales
re600 ooo molealesTfl
Roughly 106 molecules perE coli
In6 io 3u ules 6 e wdec
IflRoughly 109 molecules per E coli
c Spacing on cubic lattice D c 43
1 nM D ls 6.623 43
Fisto 6in 1µm
I m M Dlo 3 6.1023
43
x Gmin D I Eee
d Mass of E coli assuming SHE1000k
ME coli SHO VEcoli 10313mg 101 3
to 15kg A pg
e E coli is slightly denser thanwater
SE coli re 1100181up due to proteinnucleic acid content One consequence is
that you can sediment E coli bycentrifugate
f 30µm Is corresponds to res bodysbush
world class human swimmers swim the
room freestylein a twin
the current world record is justunder 47 s i
V human toffs 2 F zlbodglength
s i
Great white shades are re 5 m longand swim up to 30mph 13
Vs hah 134g 2.5 bodgleagthS
so E coli out swim bothhumans and
sharks normalizedto body size
taxinATPhydrolysisUdordious _4 ee 91 inseneral
i e the Coulomb energyof two charges q qz
at a distance ran
Energychange in hydrolysisBE Emp Emp
Enos 1 uto t2 m
top Btof atopphosphate phosphate phosphate
EADp I eoO m
E e.CIzt2o Iu1e24TEEo0.1hm f 6 to 194
For E A AE yet 8.85 lo MI 0.1 lo Tmµ2w2
2.3 lo BN.us 330 welluwater E 580 17
560652For 2 80 AE _56845 7 EBT
van der Waals interaction withrepulsive term
Ecr 4 e f E6
a Minimum of the energy at f r
IF I o 4 e f it t 6
it offs sofa
If o8 r
8r ft 80
l M 0
Energy at minimum
Ecr I 4 e fEIgeyTzfo6I 4E f o 3 A Z E
b Plot of the functionsee watlab code for details
c InterpretentioneffheterinThe Fg term as attractive and due to
induced dipole induced dipole dispersion
forces at intermediatedistances The free
dependencecan be derivedfrom2nd order perturbation
theoryThefray term
B repulsive at shortdistances
it keeps atomsfromoverlappingand can bethoughtof
as a manifestation of the Pauli exclusion principlesometimes it is also par r2