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