5
!"#$ &'( !)&*$ +, -&./+0+1$.21$34 5"623"+' &'( 7"8)9 !.&:$/"'8 BIOCH 590: Biomacromolecules, Part I Spring 2010 Copyright: Jianhan Chen Main References: 1. Chapters 5 & 7 of van Holde 2. Chapters 6 & 7 of Tinoco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aximum free energy Minimum entropy Minimum free energy Maximum entropy ?/&'3*+/9 DE ("623"+' 2'($/ & .+'.$'9/&B+' 8/&("$'9> NLNJQK 54 ("623"+' .+'39&'9 J)+A ,&39 & 32D39&'.$ ("623$3K ! L T ", N "3 2'",+/0 J"U$ VNWVQ L TK H' 0+39 .&3$3> .+'.$'9/&B+' $C+1C$3 A"9) B0$ &3 & /$3219 +, ("623"+'> NLNJQ>9K .+2*1$( A"9) X".=Y3 Z/39 1&A> A$ )&C$ !+1C"'8 9)"3 [("6$/$'B&1 $G2&B+'\ /$G2"/$3 3+].&11$( "'"B&1 &'( D+2'(&/E .+'("B+'3> NJ9LTK &'( NJQL^KU X".=Y3 X"/39 &'( !$.+'( 7&A3 J.K M"&')&' N)$' _ J = "D #C #x X".=Y3 ` 39 7&A "C "t = # "J "x "C "t = D " 2 C "x 2 X".=Y3 O '( 7&A

0+1$.21$34% 5623+'%&'(%78)9%!.&:$/'8%people.chem.umass.edu/.../bioch590/bioch590-4-diffusion.pdf · 2010-03-01 · PQ&0*1$4%("623"+'%+,%5nF%"'%N$113% J.K%M"&')&'%N)$'% o% cytoplasm

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Page 1: 0+1$.21$34% 5623+'%&'(%78)9%!.&:$/'8%people.chem.umass.edu/.../bioch590/bioch590-4-diffusion.pdf · 2010-03-01 · PQ&0*1$4%("623"+'%+,%5nF%"'%N$113% J.K%M"&')&'%N)$'% o% cytoplasm

!"#$%&'(%!)&*$%+,%-&./+0+1$.21$34%5"623"+'%&'(%7"8)9%!.&:$/"'8%

BIOCH 590: Biomacromolecules, Part I Spring 2010

Copyright: Jianhan Chen

Main References: 1. Chapters 5 & 7 of van Holde 2. Chapters 6 & 7 of Tinoco

;&'(+0%<&1=>%5"623"+'%&'(%?/&'3*+/9%

•  ;&'(+0%@/+A'"&'%0+B+'%+,%0+1$.21$34%("623"+'%–  5/"C$'%DE%9)$/0&1%$'$/8E%%

–  F%,2'(&0$'9&1%*/+.$33%9)&9%2'($/1"$3%C"/92&11E%&11%D"+0+1$.21$%3$*&/&B+'%9$.)'"G2$3%

–  H'B0&9$1E%/$1&9$(%9+%0&33>%3"#$%&'(%3)&*$%%

•  ?/&'3*+/9%*/+.$334%("623"+'%2'($/%"'I2$'.$%–  -$&32/$(%DE%J0&33K%I+A%!%L%0&33%J+/%0+1$K%*$/%2'"9%&/$&%*$/%3$.+'(%

J.K%M"&')&'%N)$'% O%

?)$/0+(E'&0".%PG2"1"D/"20%

•  <"9)+29%$Q9$/'&1%"'I2$'.$>%0"'"020%,/$$%$'$/8E%&.)"$C$(%A"9)%2'",+/0%.+'.$'9/&B+'%("39/"D2B+'3%–  !$*&/&B+'%/$G2"/$%$Q9$/'&1%A+/=R%

J.K%M"&')&'%N)$'% S%

Maximum free energy Minimum entropy

Minimum free energy Maximum entropy

•  ?/&'3*+/9%DE%("623"+'%2'($/%&%.+'.$'9/&B+'%8/&("$'9>%NLNJQK%%

% %%

–  54%("623"+'%.+'39&'9%J)+A%,&39%&%32D39&'.$%("623$3K%%–  !"L%T%",%N%"3%2'",+/0%J"U$%VNWVQ%L%TK%

•  H'%0+39%.&3$3>%.+'.$'9/&B+'%$C+1C$3%A"9)%B0$%&3%&%/$3219%+,%("623"+'>%NLNJQ>9K%

%%% %.+2*1$(%A"9)%X".=Y3%Z/39%1&A>%A$%)&C$%

–  !+1C"'8%9)"3%[("6$/$'B&1%$G2&B+'\%/$G2"/$3%3+].&11$(%"'"B&1%&'(%D+2'(&/E%.+'("B+'3>%NJ9LTK%&'(%NJQL^KU%

X".=Y3%X"/39%&'(%!$.+'(%7&A3%

J.K%M"&')&'%N)$'% _%

!

J = "D#C#x

X".=Y3%`39%7&A%

!

"C"t

= #"J"x

!

"C"t

= D"2C"x 2

X".=Y3%O'(%7&A%

Page 2: 0+1$.21$34% 5623+'%&'(%78)9%!.&:$/'8%people.chem.umass.edu/.../bioch590/bioch590-4-diffusion.pdf · 2010-03-01 · PQ&0*1$4%("623"+'%+,%5nF%"'%N$113% J.K%M"&')&'%N)$'% o% cytoplasm

`5%5"623"+'%A"9)%N+'.$'9/&B+'%H0*213$%

•  NLNT%A"9)"'%&'%9)"'%31&D%+,%9)".='$33%V%•  NLT%&9%QLa^%&9%&11%B0$%•  !+12B+'4%

J.K%M"&')&'%N)$'% b%

!

C(x, t) =C0"2 #Dt

e$x2 / 4Dt

0 x

small t

large t>>0

t=0, C=C0 within !

C(x

,t)

t="

-$&'%!G2&/$%5"3*1&.$0$'9%

–  FC$/&8$%*+3"B+'4%cQd%L%T%–  -$&'%3G2&/$%("3*1&.$0$'94%cQOd%e%T%

•  H'($$(>%5%0$&32/$3%9)$%("623"+'%3*$$(R%

•  ;$1&B+'%9+%/&'(+0%A&1=34%&C&"1&D1$%,/+0%3"021&B+'%

–  5E'&0".%1"8)9%3.&:$/"'8%0$&32/$0$'9%+,%5%J3$$%1&9$/%31"($3K%

J.K%M"&')&'%N)$'% f%

0 x

small t

large t>>0

t=0, C=C0 within !

C(x

,t)

!

C(x, t) =C0"2 #Dt

e$x2 / 4Dt

!

x 2 =x 2c(x,t)dt"c(x,t)dt"

=x 2e#x

2 / 4Dtdt"e#x

2 / 4Dtdt"= 2Dt

5"623"+'%&'(%-+1$.21&/%!"#$W!)&*$%

•  P"'39$"'Y3%/$1&B+'4%5%L%=?W,%–  ,4%,/".B+'&1%.+$g."$'9%J/$3"39&'.$%9+%0+C$0$'9%9)/+28)%3+1C$'9Kh%

–  ,%"3%($9$/0"'$(%DE%9)$%3"#$%&'(%3)&*$%+,%9)$%0+1$.21$%&3%A$11%&3%9)$%C"3.+3"9E%+,%9)$%3+1C$'9%

•  X+/%3*)$/".&1%*&/B.1$3%+,%/&("23%/4%,%L%fij/%J!9+=$3Y3%1&AK%–  j4%3+1C$'9%C"3.+3"9E%

•  N+0D"'$%!9+=$3Y3%1&A%&'(%P"'39$"'Y3%/$1&B+'%

•  5$C"&B+'%,/+0%3*)$/".&1%3)&*$%JA"9)%9)$%3&0$%C+120$K%&1A&E3%1$&(3%9+%1&/8$/%,/".B+'%J&'(%30&11$/%("623"+'%.+'39&'9K%–  %[$6$.BC$\%)E(/+(E'&0".%/&("23%+k$'%/$*+/9$(%&34%/%L%=?Wfij5%

–  N&'%D$%0"31$&("'8%,+/%"//$821&/1E%3)&*$(%0+1$.21$3%

J.K%M"&')&'%N)$'% l%

!

D =kT6"#r

X/".B+'%;&B+%

•  ?)$%0"'"0&1%,/".B+'%.+$g."$'9%"3%8"C$'%DE%0&33%&'(%*&/B&1%3*$."Z.%C+120$4%

•  ?)$'%9)$%/&B+%+,%0$&32/$(%,/".B+'%.+$g."$'9%J,K%A"9)%,T%"3%"'(".&BC$%+,%9)$%0+1$.21&/%3)&*$%J&'(%3+1C&B+'K%–  ",%,W,T%"3%02.)%8/$&9$/%9)&'%2'"9E>%9)$%*&/B.1$%"3%3"8'"Z.&'91E%$1+'8&9$(%

&'(W+/%)"8)1E%3+1C&9$(%J9)$%1&9$/%1$&(3%9+%1&/8$/%$6$.BC$%3"#$K%

J.K%M"&')&'%N)$'% m%

!

f0 = 6"#r0 = 6"# 3mV 4"

$

% &

'

( )

1/ 3

fibrinogen alpha chain

Page 3: 0+1$.21$34% 5623+'%&'(%78)9%!.&:$/'8%people.chem.umass.edu/.../bioch590/bioch590-4-diffusion.pdf · 2010-03-01 · PQ&0*1$4%("623"+'%+,%5nF%"'%N$113% J.K%M"&')&'%N)$'% o% cytoplasm

PQ&0*1$4%("623"+'%+,%5nF%"'%N$113%

J.K%M"&')&'%N)$'% o%

cytoplasm nucleus

dextran control Ref: Lukas et al, J. Biol. Chem. (2000)

!$("0$'9&B+'%

•  N+'.$/'3%9)$%0+B+'%+,%0+1$.21$3%"'%3+12B+'3%+/%*&/B.1$3%"'%323*$'3"+'3%"'%/$3*+'3$%9+%&'%$Q9$/'&1%,+/.$%32.)%&3%8/&C"9E>%.$'9/",28&1%,+/.$%+/%$1$.9/".%,+/.$%

•  @&1&'.$%+,%,+/.$3%–  X.%L%0/pO%J.$'9/",28&1%,+/.$K%

–  XD%L%]0T/pO%JD2+E&'.EK%

–  X(%L%],%C%J,/".B+'K%

% %%%%%X.%q%XD%q%X(%L%T %%% %0/pO%r0T/pO%r,C%L%T%

–  #4%3$("0$'9&B+'%.+$g."$'9%J)&3%9)$%2'"9%+,%B0$K%

–  H,%0L0T>%3%L%T%J'+%3$("0$'9&B+'K%J.K%M"&')&'%N)$'% `T%!

s =v

r" 2 =m #m0

f=

m(1# v $)f : partial specific volume

!

v

-+C"'8%@+2'(&/E%!$("0$'9&B+'%

•  F'&1EB.&1%219/&.$'9/",28$%.+2*1$(%A"9)%3.&''"'8%&D3+/*B+'%+*B.&1%3E39$0%–  !*$$(%+,%0+C"'8%D+2'(&/E4%C%L%(/W%(9%L%3%/pO%%%–  X/+0%0$&32/$0$'9%+,%3>%("623"+'%.+'39&'9%J+/%,/".B+'K%"3%.&1.21&9$(>%

A)".)%"'%92/'%.&'%D$%23$(%9+%+D9&"'%9)$%)E(/+(E'&0".%/&("23%

J.K%M"&')&'%N)$'% ``% J.K%M"&')&'%N)$'% `O%

Sedimentation Coefficients of common biological materials

(in Svedbergs)

1 S = 10-13 second

nucleic acids

Page 4: 0+1$.21$34% 5623+'%&'(%78)9%!.&:$/'8%people.chem.umass.edu/.../bioch590/bioch590-4-diffusion.pdf · 2010-03-01 · PQ&0*1$4%("623"+'%+,%5nF%"'%N$113% J.K%M"&')&'%N)$'% o% cytoplasm

!$("0$'9&B+'%PG2"1"D/"20%

•  PQ9$/'&1%"'I2$'.$%32.)%&3%.$'9/",28&1%+/%$1$.9/".%,+/.$%.&'%3)"k%9)$%$G2"1"D/"20%("39/"D2B+'%+,%.+'.$'9/&B+'%&'(%32.)%&%3)"k%($*$'(3%+'%&%/&'8$%+,%0+1$.21&/%*/+*$/B$3%"'.12("'8%0&33>%3"#$W3)&*$>%.)&/8$3%$9.%

J.K%M"&')&'%N)$'% `S%

Maximum free energy Minimum entropy

Minimum free energy Maximum entropy

!$("0$'9&B+'%PG2"1"D/"20%

•  F9%$G2"1"D/"20>%&%39$&(E]39&9$%.+'.$'9/&B+'%8/&("$'9%"3%$39&D1"3)$(4%D&.=I+A%(2$%9+%8/&("$'9%JM5K%&'(%+2s1+A%DE%.$'9/",28&1%3$("0$'9&B+'%JM!K%*$/,$.91E%.&'.$1%&9%$C$/E%*+"'9%

J.K%M"&')&'%N)$'% `_%

!

JD = "D dCdr

JS = vsC = sr# 2C, where s = m(1" v $) / f

JS + JD = sr# 2C "D dCdr

= 0

dCdr

=sr# 2

DC

d lnCd(r2)

=s# 2

2D=

m(1" v $)2kT

C(r) = C(r0)es# 2

2D(r 2"r0

2 )= C(r0)e

m(1"v $ )2kT

(r 2"r02 )

Molecular weight determined by fitting the gradient!

-&33%5$9$/0"'&B+'%DE%!$("0$'9&B+'%PGU%

•  tD9&"'$(%,/+0%Zu'8%NJ/K%

•  v$/E%&..2/&9$%&'(%A+/=3%+C$/%&%1&/8$%/&'8$%Jp%&(w239&D1$RK%•  n+'"'9$/&.B'8%0"Q92/$34%021B$Q*+'$'B&1%Zu'8%

•  H'9$/&.B'8%0"Q92/$34%/$G2"/$3%0+/$%.+0*1$Q%,2'.B+'&1%,+/03%,+/%(&9&%Zu'8%–  x"$1(3%D"'("'8%.+'39&'93R%

J.K%M"&')&'%N)$'% `b%

!

C(r) /C(r0) = em(1"v # )2kT

(r 2"r02 )

!

d lnCd(r2)

=m(1" v #)2kT

Biochem. J. (1996) 320 (39–47) Screenshot of SEDPHAT fitting analysis of protein-DNA binding

7"8)9%!.&:$/"'8%

•  <&C$]*&/B.1$%(2&1"9E%–  3.&:$/"'8%B$(%9+%9)$%A&C$%'&92/$>%A)"1$%*)+9+$1$.9/".%$6$.9%&'(%

&D3+/*B+'%$Q*1&"'$(%DE%9)$%*&/B.1$%'&92/$%

–  <&C$%'&92/$4%+3."11&B'8%$1$.9/".%&'(%0&8'$B.%.+0*+'$'93%J$1$.9/".%0&8'$B.%/&("&B+'>%+/%P-;K%

–  F%,$A%D&3".%/$1&B+'34%.%L%y%z%PL%)%z%

J.K%M"&')&'%N)$'% `f%

Page 5: 0+1$.21$34% 5623+'%&'(%78)9%!.&:$/'8%people.chem.umass.edu/.../bioch590/bioch590-4-diffusion.pdf · 2010-03-01 · PQ&0*1$4%("623"+'%+,%5nF%"'%N$113% J.K%M"&')&'%N)$'% o% cytoplasm

!"'81$]{&/B.1$%!.&:$/"'8%

•  {+1&/"#$(%1"8)9%

•  |'*+1&/"#$(%1"8)9%

J.K%M"&')&'%N)$'% `l%

!

iI0

=16" 4# 4

r2$4sin2 %

!

iI0

=8" 4# 4

r2$4(1+ cos2%)

!.&:$/"'8%+,%-21B*1$%!0&11%{&/B.1$3%

•  ;&E1$"8)%!.&:$/"'84%",%*&/B.1$3%&/$%02.)%30&11$/%9)&'%9)$%A&C$1$'89)%JC"3"D1$%3*$.9/&4%SmT]lbT%'0K%–  !)+/9$/%A&C$1$'89)%JD12$%1"8)9K%3.&:$/$(%0+/$R%

•  H'%9)$%1"0"9%+,%1+A%.+'.$'9/&B+'4%

–  {+1&/"#&D"1"9E%}%"3%21B0&9$1E%1"'=$(%9+%0+1$.21&/%A$"8)9%J-K%&'(%.+'.$'9/&B+'%JNK4%

–  n+'%"($&1%3+12B+'34%@%L%O'(%C"/&1%.+$g."$'9%

J.K%M"&')&'%N)$'% `m%

!

iI0

= N 8"4# 4

r2$4(1+ cos2%)

!

R" #iI01+ cos2"

r2= KCM

!

KCR"

=1M

+ 2BC + ...

!.&:$/"'8%+,%7&/8$/%{&/B.1$3%

•  -$"%!.&:$/"'84%",%*&/B.1$%3"#$%"3%8/$&9$/%9)&'%9)$%A&C$1$'89)%–  !2.)%&3%C"/&1%*&/B.1$3h%+/%Q]/&E%&'(%'$29/+'%3.&:$/"'8%J30&11%yK%

–  -239%"'.12($%"',$/$'.$%D$9A$$'%1"8)9%3.&:$/$(%,/+0%&11%3.&:$/"'8%*"'93%A"9)"'%9)$%0+1$.21$%

–  {/+C"($%"',+/0&B+'%+'%0&33>%("0$'3"+'%&'(%$C$'%"'9$/'&1%39/2.92/$3R%

–  5$Z'$%3+].&11$(%*&/B.1$%,+/0%,&.9+/%$J~K%

–  P3B0&B+'%+,%-%/$G2"/$3%$Q9/&*+1&B+'%9+%NLT%&'(%~LT%J&%*/&.B.&1%1"0"9&B+'%(2$%9+%("6/&.B+'%$6$.93K%

J.K%M"&')&'%N)$'% `o%

!

KCR"

=1

P(")1M

+ 2BC#

$ %

&

' (

P(") =1) h2RG

2

3+ ...

RG2 =

12n2

rij2

j*

i*

5E'&0".%7"8)9%!.&:$/"'8%

•  -$&32/$%1"8)9%3.&:$/"'8%"'9$'3"9E%&3%&%,2'.B+'%+,%B0$%,/+0%&%30&11%C+120$%JA)$/$%1+.&1%.+'.$'9/&B+'%I2.92&9$3%32D39&'B&11E%(2$%9+%@/+A'"&'%0+B+'3K%–  ?)$%1&/8$/%5%"3>%9)$%,&39$/%3.&:$/"'8%"'9$'3"9E%A"11%I2.92&9$%–  N+00+'1E%&'&1E#$(%A"9)%&29+.+//$1&B+'%&'&1E3"34%

J.K%M"&')&'%N)$'% OT%

!

g(2)(") = i(t)i(t + " ) / i(t) 2

g(2)(") =1+ ce#2h 2D" , with h = 4$n%#1 sin(& /2)

t

i