BMB170a_2011_LECTURE6

BMB170a_2011_LECTURE6 -...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 5)565/6789:;%(<#*&$/3'( 1$=&>#$(?@(-=&(9A( •! !""#$"%&$'( •! )*+,'( •! -./"*0$#'( •! 1%#"$(2#*&$/3(%''$04./$'( ( 5%=&$#/%.(2*'&I&#%3'.%+*3%.( &#%3'.*=%+*3( D$=5( D$=!( )*K/L$K(,#*0(M/=N3$#(O(D=8$N0%3(D=/$3=$(EF;;PG(A9;H9QPFI?( B>(!"#$%(C%&>#$(D&#>=&(5/*.(EF;;;G(:H99:FI:(E9,JAG( •! D$=5('&%4/./R$'(>3,*.K$K( '&%&$(,*#(K$./S$#T(&*( 0$04#%3$( •! D$=!(=%>'$'(#$.$%'$( D$=5( •! UTK#*28*4/=( '>#,%=$(*3('/K$( •! <#$'>0$K(&*( '$V>$'&$#( ,*.K/3"( /3&$#0$K/%&$'( ,*#(0$04#%3$( K$./S$#T( B>(!"#$%(C%&>#$(D&#>=&(5/*.(EF;;;G(:H99:FI:(E9,JAG( UTK#*28*4/=( UTK#*28/./=( W#/""$#(,%=&*#( UTK#*28*4/=( UTK#*28/./=( •! •! •! •! W#/""$#(,%=&*#(,*>3K(/3(%..($>4%=&$#/%( )$04$#(*,(%("#*>2(*,(#/4*'*0$(%''*=/%&$K(=8%2$#*3$'( 5/3K'(&*(P;D('>4>3/&(%&($J/&(&>33$.( U$.2'(3%'=$3&(2#*&$/3'(,*.K( 5%3(.%4H(X$#4/&R(!"#$%(C%&>#$(EF;;QG(QA9HPY;I?(E9ZF?(O(9ZF4G( W#/""$#(,%=&*#(0$=8%3/'0( •! W#/""$#(,%=&*#(Z%/&'(%&( $J/&(&>33$.( •! 7%S/&T(,%=/./&%&$'( ,*.K/3"( •! M8$3(&8$(3%'=$3&( K*0%/3(/'(4/"($3*>"8( WX(,%..'(*[( 5%3(.%4H(X$#4/&R(!"#$%(C%&>#$(EF;;QG(QA9HPY;I?( !0T.*/K(K/'$%'$'( Disease (&!'(!)(78/+(O(\*4'*3(!33(]$S(5/*=8$0(EF;;?G(:PHAAA( Aggregating protein or peptide Num res A Neurodegenerative diseases Alzheimer's disease c Amyloid ! peptide 40 or 42 f Spongiform encephalopathies c,e Prion protein or frags thereof 253 Parkinson's disease c "-Synuclein 140 Dementia with Lewy bodies c "-Synuclein 140 Frontotemp dem. w/ Parkinsonism c Tau 352–441 f Amyotrophic lateral sclerosis c Superoxide dismutase 1 153 Huntington's disease d Huntingtin with polyQ expansion 3144 g Spinocerebellar ataxias d Ataxins with polyQ expansion 816 g,h Spinocerebellar ataxia 17 d TATA box-bind prot w/ polyQ expansion 339 g Spinal and bulbar muscular atrophy d Androgen receptor w/ polyQ expansion 919 g Hered. Dentat.-pallidoluysian atr. d Atrophin-1 with polyQ expansion 1185 g Familial British dementia d ABri 23 Familial Danish dementia d ADan 23 Nonneuropathic systemic amyloidoses AL amyloidosis c Immunoglobulin light chains or frags 90 f AA amyloidosis c frags of serum amyloid A protein 76–104 f Familial Mediterranean fever c frags of serum amyloid A protein 76–104 f Senile systemic amyloidosis c Wild-type transthyretin 127 Familial amyloidotic polyneuropathy d Mutants of transthyretin 127 Hemodialysis-related amyloidosis c !2-microglobulin 99 ApoAI amyloidosis d N-term frags of apolipoprotein AI 80–93 f ApoAII amyloidosis d N-term frag of apolipoprotein AII 98 i ApoAIV amyloidosis c N-term frag of apolipoprotein AIV 70 Finnish hereditary amyloidosis d frags of gelsolin mutants 71 Lysozyme amyloidosis d Mutants of lysozyme 130 Fibrinogen amyloidosis d Variants of fibrinogen "-chain 27–81 f 120 Icel. hered. cerebral amyloid angio. d Mutant of cystatin C Nonneuropathic localized diseases Type II diabetes c Amylin, also (IAPP) 37 Medullary carcinoma of the thyroid c Calcitonin 32 Atrial amyloidosis c Atrial natriuretic factor 28 40 or 42 f Heredi cereb. haem. w/ amyloidosis d Mutants of amyloid ! peptide Pituitary prolactinoma Prolactin 199 Injection-localized amyloidosis c Insulin 21 + 30 j Aortic medial amyloidosis c Medin 50 k Hereditary lattice corneal dystrophy d Mainly C-ter fragof kerato-epithelin 50–200 f Corneal amylodosis w/ trichiasis c Lactoferrin 692 Cataract c #-Crystallins Variable 46 Calcifying epith. odontogenic tumors cunk Pulmonary alveolar proteinosis d Lung surfactant protein C 35 Inclusion-body myositis c Amyloid ! peptide 40 or 42 f Cutaneous lichen amyloidosis c Keratins Variable Native structure of protein or peptide B Nat Unf Nat Unf (res 1–120) and "-helical (res 121–230) Nat Unf Nat Unf Nat Unf All-!, Ig like Largely Nat Unf All-!, AXH domain (res 562–694); the rest are unk "+!, TBP like (res 159–339); unk (res 1–158) All-", nucl receptor ligand-binding dom (res 669–919) unk Nat Unf Nat Unf All-!, Ig like All-", unk fold All-", unk fold All-!, prealbumin like All-!, prealbumin like All-!, Ig like Nat Unf unk unk Nat Unf "+!, lysozyme fold unk "+!, cystatin like Nat Unf Nat Unf Nat Unf Nat Unf All-", 4-helical cytokines All-", insulin like unk unk "+!, peri-binding protein like II All-!, #-crystallin like unk unk Nat Unf unk \*4'*3(C%&>#$(EF;;AG(QF?H__Q( (!('=8$0%+=(#$2#$'$3&%+*3(*,(&8$("$3$#%.(0$=8%3/'0(*,(%""#$"%+*3(&*(,*#0(%0T.*/K(L4#/.'^(( `I'8$$&'(%3K(%0T.*/K(L4#/.'( bCCccCd( $S/$Z'H( C$.'*3(O(a/'$34$#"(7-D5(EF;;?G(9?HF?;( M$&R$.(E$KG(!==*>3&'(78$0(]$'(EF;;?G(AY(EYG(( C$.'*3(!"#$%#C%&>#$(EF;;PG(QAPH::A( !0T.*/K(,*#0%+*3(/3(&#%3'&8T#$+3(I(K/'2.%=$0$3&(*,(`('&#%3K( D$#%"(!"#$%#CD5(EF;;FG(YH:AQIY( #$S/$Z(WT=N*(7-D5(EF;;QG(9QHY?( Domain swapping and amyloid formation eK*0%/3f('Z%22$K(]C%'$(!(*./"*0$#'f( U/3"$(.**2($J2%3K$K( Z/&8(bc9;c(/3'$#&( !0T.*/KI./N$(L4#/.'(=*3&%/3( 3%+S$(]3%'$(!(0*.$=>.$'( 1/>(!"#$%#CD5(EF;;9G(_HF99g(D%04%'8/S%3(!"#$%#C%&>#$(EF;;PG(QA:HF??( !0T.*/K(2#*&$/3( 2%&8Z%T'( !(>3/L$K(S/$Z(*,('*0$(*,(&8$( &T2$'(*,('&#>=&>#$(&8%&(=%3(4$( ,*#0$K(4T(2*.T2$2+K$(=8%/3'( 78/+(O(\*4'*3(!33(]$S(5/*=8$0(EF;;?G(:PHAAA( 5%=&$#/%.(/3=.>'/*3(4*K/$'( •! 5%=&$#/%('&*#$( >3Z%3&$K(2#*&$/3(/3( 4*K/$'('$2%#%&$(,#*0( &8$/#(=T&*2.%'0( •! 78%2$#*3$'('&%/3(&8$( $K"$'(/3(&8/'(/0%"$( 7%##/h(O(i/..%S$#K$(EF;;PG(j(5%=&(9_:E9;GHAPYYI?;9( k3=.>'/*3(4*K/$'( k3=.>'/*3(4*K/$'( 8%S$(%0T.*/K( =8%#%=&$#( M%3"^^]/$N(EF;;_G(<1*D(5/*.*"T(!>">'&(( <#*&$/3(0*+,'( •! D$=*3K%#T(D&#>=&>#$( •! )*+,(l('0%..$'&(,*.K/3"('&#>=&>#$( •! \*0%/3(EK$L3$'(&*2*.*"TG(l(,*.K/3"(#$"/*3( •! )*3*0$#( •! -./"*0$#( )*K>.%#('0%..(K*0%/3'( •! <#*&$/3'(/3S*.S$K(/3(=$..(#$">.%+*3( •! k3&$#%=+*3(K*0%/3'(I(#$=*"3/+*3(0*K>.$'( –! W%#"$&(%3(%=+S/&T(&*(%('>4=$..>.%#(.*=%+*3( –! k3K$2$3K$3&.T(,*.K$K(0*K>.$'( •! 5/3K(2%#&3$#'(%.*3$( •! 7.*'$(%0/3*(&$#0/3/(I(4/3K/3"(*3(*22*'/&$('>#,%=$( –! X%0/./$'(K/S/K$K(4T('$V>$3=$@('&#>=&>#$(%3K(./"%3K( •! •! •! •! <#*./3$I#/=8(EDUA@(MM(O(aiU9G( <8*'28*&T#*'/3$(EDUW(O(<W5G( <8*'28*'$#/3$6&8#$*3/3$(EXU!@(<\5@(M\Q;G( <8*'28*./2/K'(E<U(O(XdiaG( –! 7%3(=*04/3$(/3(%3T(*#K$#(,*#('2$=/L=(,>3=+*3( k3&$#%=+*3(\*0%/3'( Petsko G.A., Ringe, D., Protein Structure and Function 2004, figure 3-2 (upper), pg. 89. k3&$#%=+*3(\*0%/3'( Petsko G.A., Ringe, D., Protein Structure and Function 2004, figure 3-2 (middle), pg. 89. k3&$#%=+*3(\*0%/3'( Petsko G.A., Ringe, D., Protein Structure and Function 2004, figure 3-2 (lower), pg. 89. M\Q;(/3(%=+*3( •! ]!7m9(I(%('=%[*.K(2#*&$/3( •! k3&$#%=&'('/0>.&%3$*>'.T(Z/&8('$S$#%.( '/"3%./3"(0*.$=>.$'( •! 1/3N'(&#%3'.%+*3(&*(&8$('/"3%.(&#%3'K>=+*3( 2%&8Z%T( D$3">2&%(!"#$%(CD)5(EF;;QG(99HYP:I?F( C/''*3(!"#$%(a)5-(#$2*#&'(EF;;QG(PE9FG99A:IQ9( )*'%/=(2#*&$/3'( •! •! •! •! k"(l(/00>3*".*4>./3(K*0%/3( X39(l(L4#*3$=+3(&T2$(k( m#/3".$(l(4/3K'(%(0$K/%&*#( XR(l(,#/RR.$K(7]\(K*0%/3(l( 4/3K'(M3&(2%&8Z%T(2#*&$/3'( •! abX(K*0%/3(l(2#*&$/3(4/3K/3"( K*0%/3( W/''>$(2.%'0/3*"$3(%=+S%&*#( $=$2&*#(&T#*'/3$(N/3%'$( k"(K*0%/3(E9%VNG( X#*0(X/"^(F^A9( m#/3".$(I(9&2N( m*''/%N*[(.%4( abX(K*0%/3(l(9%2*( XR(l(9/nT( 1$%8T(.%4( X39(K*0%/3(EF#NTG( X/"^(F^F:(X#*0(&8$(&$J&( <#*&$/3(N/3%'$'( X/"^(99^Q(E98=N(O(9L3G( WZ*(K*0%/3'(/3(%3(%=+S$(%3K( /3%=+S$(,*#0(E=T=./3IK$2$3K$3&( N/3%'$G( D*.>4.$(N/3%'$'( DUF(K*0%/3(E9'2'G(( k3%=+S$(D#=(&T#*'/3$(N/3%'$( X/"^(99^P@(99^?(O(99^_( )$04#%3$( #$=$2&*#'( •! i$#T(0*K>.%#( •! \/0$#/R%+*3(.$%K'( &*(%=+S%+*3( •! ]%'(2%&8Z%T( X/"^(99^9;@(99^99(O(99^9F( b#*Z&8(*,(2#*&$/3( &*2*.*"/$'( •! <\5("#*Z&8(=*3+3>$'(&*( #/'$( •! b#*Z&8(*,(3$Z(&*2*.*"/$'( K*$'(3*&(=*##$.%&$(&*(<\5( b#*Z&8( <\5('&%&'(,#*0(8o2H66ZZZ^#='4^*#"6( X*.K'(/3(2#*&$/3('&#>=&>#$( ( •! !.%''("#=8/&$=&>#$(#*2*.*"T($*0*.*"*>'(%>2$#,%0/.T( –! -#$3"*@()/=8/$@(j*3$'@(j*3$'@(DZ/3K$..'@(%3K(W8*#3&*3(E9YY:G(e7!WUI(!(U/$#%#=8/=( 7.%''/L=%+*3(*,(<#*&$/3(\*0%/3(D&#>=&>#$'f(D&#>=&>#$(PH9;YA( –! 8o2H66ZZZ^=%&8K4^/3,*6( ( •! %&#>=&>#%.(!.%''/L=%+*3(&,('#*&$/3'( –! )>#R/3@(5#$33$#@(U>44%#K@(78*&8/%(E9YYPG(eD7-<H(%(%&#>=&>#%.(!.%''/L=%+*3(&,('#*&$/3'( K%&%4%'$(,*#(&8$(/3S$'+"%+*3(*,('$V>$3=$'(%3K('&#>=&>#$'f(j()*.(5/*.(FQ:HPA?( –! 8o2H66'=*2^4$#N$.$T^$K>6( ( •! (/'&%3=$()%&#/J(")*"30$3&+ –! U*.0(1@(m%%#/%/3$3(D@(]*'$3'&#*0(<@(D=8$3N$.(!^(EF;;_G(eD$%#=8/3"(2#*&$/3('&#>=&>#$( K%&%4%'$'(Z/&8(\%./1/&$(S^Af(5/*/3,*#0%+='(F;;_( •! %/02.$(,*K>.%#("#=8/&$=&>#$(-$'$%#=8(#**.( –! 7%3(.**N(>2(K/[$#$3&(K*0%/3'(&*('$$(8*Z(&8$Tp#$(%##%3"$K(/3(2#*&$/3'(%3K(=*02%#$(2#*&$/3'( ,#*0(K/[$#$3&("$3*0$'( –! D=8>.&R(!"#$%(E9YY_G(eD)!]W@(%('/02.$(0*K>.%#(%#=8/&$=&>#$(#$'$%#=8(&**.H(kK$3+L=%+*3(*,( '/"3%./3"(K*0%/3'f(<C!D(YPHP_P:( –! 8o2H66'0%#&^$04.I8$/K$.4$#"^K$6( SCOP# Structural Classification Of Proteins( 8o2H66'=*2^4$#N$.$T^$K>6( Brenner et al COSB (1997) 7:369" DALI" Distance matrix ALIgnment - fold similarities" Holm & Sanders Science (1996) 273:595" http://www.ebi.ac.uk/dali/" X>3=+*3(=%3($S*.S$('$2%#%&$.T( WZ*(K/[$#$3&('$#/3$(2#*&$%'$'( 78T0*&#T2'/3( D>4+./'/3( X/"^(F^A;(,#*0(&8$(&$J&( Why are proteins so big? Why do cells build oligomeric proteins? •! Minimum size –! Stability (small proteins have more disulfides or metals) –! Small proteins have large substrates (DNA binding) •! Monomers: many secreted proteins (e.g., toxins, hormones) •! Oligomers: many intracellular proteins –! average oligomeric state in E. coli is 4 •! Small monomers can diffuse to interact with large substrates –! e.g., electron transport proteins that interact with immobile substrates in lipid bilayer •! Enzymes that act on small substrates can be large - only limited by diffusion Goodsell & Olson (1993) Soluble proteins: size, shape, & function. TIBS 18: 65-68 Sample of soluble proteins drawn to relative scale Hormones Weird Shape Goodsell & Olson (1993) TIBS 18: 65-68 Toxins Electron transfer proteins Carrier proteins Hydrolase Sample of enzymes drawn at relative scale a3RT0$'( 9;;I:P;(%%( Goodsell & Olson (1993) TIBS 18: 65-68 Examples of oligomeric proteins Homo-oligomers: •! Alcohol dehydrogenase (1HTB): 2 •! Phosphofructokinase (4PFK): 4 •! Glutamine synthetase (1FPY): 12 Hetero-oligomers •! Hemoglobin (2DHB): 4 - !2"2 •! Aspartate transcarbamylase (1AT1): 12 - C6R6 •! Protease/protease inhibitors (non-obligate oligomers) -./"*0$#'( m\b<(%.K*.%'$( 9Xc;( C$>#%0/K%'$( 9!Qc( \I%0/3*(%=/K( %0/3*&#%3',$#%'$( A\!!( 78*.$#%(&*J/3( 97U<( 1%=&%&$( K$8TK#*"$3%'$( 91\C( k3'>./3(QkCD( b#*aD(=*I=8%2$#*3/3( 9bA9( b%.%=&*3%&$( K$8TK#%&%'$( FbDU( )*.T4K$3>0(=*,%=&*#( 4/*'T3&8$'/'(2#*&$/3(7( 9am]( <#*&$%'*0$( 9b?P( AI K$8TK#*V>/3%&$( K$8TK#%&%'$( F\Uc(8/3*S/#>'(9!d)( Petsko G.A., Ringe, D., Protein Structure and Function 2004, figure 1-74 (upper), pg. 45. Advantages of quaternary structure •! Cooperativity and substrate feedback –! active site often located at subunit interface •! Evolution –! Mutations are amplified –! Bad mutations are hard to introduce •! Genetic economy –! Saves the need for long transcripts •! Reduces the error rate of synthesis –! If 1 error per 1000 residues: –! Single chain (1000 residues) –! Four chains (250 residues each) •! Reduce surface/volume # correct copies 37% 78% –! buries portions of protein surface –! reduce # ions needed to neutralize exposed charges –! reduce # ordered waters for hydration Goodsell & Olson (1993) Soluble proteins: size, shape, & function. TIBS 18: 65-68 Two types of association •! Isologous •! Heterologous: –! Intersubunit interactions are same for each monomer –! 2-fold axis of symmetry –! All dimers, some tetramers. –! Intersubunit interactions involve different surfaces on each monomer –! Interface has no element of symmetry –! Open-ended polymers or closed polymers( Prealbumin dimer (2PAB) Two monomers associate to extend the two "-sheets. Rabbit skeletal muscle aldolase (1EX5) Isologous tetramer with three twofold symmetry axes Chloramphenicol acetyltransferase (1CLA) Heterologous trimer (C3) Hemerythrin (1HMO) Octamer (two omitted) Each layer is a heterologous tetramer with fourfold symmetry. <#*&$/3I<#*&$/3(k3&$#,%=$'( •! k3&$#,%=$(!D!(./3$%#.T(#$.%&$K(&*()M( E#q;^?YG( •! !D!(4>#/$K(E2$#('>4>3/&G(S%#/$'(A?_^9( &*(Q:Q?^9(rF( •! !D!6)M(K$=#$%'$'(,#*0(2#*&*0$#(&*( K/0$#( •! UTK#*28*4/=/&T(%&(&8$(/3&$#,%=$H( –! $J&$#/*#s/3&$#,%=$s/3&$#/*#( –! !&*0'H(?_^9t(3*3I2*.%#( –! ]$'/K>$'H(Q?^:t(8TK#*28*4/=@(A9^Qt( 2*.%#@(F9^Yt(=8%#"$K( •! k3&$#,%=$(8%'(%u3/&T(,*#(8TK#*28*4/=( #$'/K>$'( •! !S$#%"$(;^__(UI4*3K'(2$#(9;;(rF(( j*3$'(O(W8*#&*3(<#*"(5/*28T'()*.(5/*.(E9YYPG(?AHA9( <#$K/=+3"(K/0$#(/3&$#,%=$( *+K/0$##,--./.( *+0*3*FQ9;rF( W8$(D$=!(!W<%'$(/'(N3*Z3(&*( 8%S$(%(K/0$#/=(,*#0g(8*Z$S$#@( /3(&8#$$(=#T'&%.(,*#0'(&8$#$( %#$(&8#$$(K/[$#$3&(/3&$#,%=$'v( ( M8/=8(/'(&8$(28T'/*.*"/=%.( K/0$#w( -'4*#3$(!"#$%(<C!D(EF;;QG(9;9EA;GH9;YA:IQF( 0"#F_FFrF( How do you know if something is a real oligomer or just crystal packing? •! Janin compiled database of 1320 pair-wise interfaces from 152 crystal forms of monomeric proteins with 1 molecule/a.u. •! Mean value of buried surface (B) is 570 Å2 (total, not per subunit). •! Probability of finding a non-specific contact burying surface area >B is proportional to B: p( B) " 4.2e# B / 260 Janin Nat Struct Biol (1997) 4: 973 5n*#N0%3(.%4H( 1$4#h3(!"#$%(7$..(E9YY_G(YAH999IFA( E9%?RG( 5$33$o(!"#$%(C%&>#$(EF;;;G(Q;AHQ?( E9K$QG( 7%3p&(%.Z%T'(2#$K/=&( •! WZ*(8*0*.*"*>'( 8*0*K/0$#'( •! WZ*(K/[$#$3&(2%=N/3"( •! 9!1-(O(9Xkc( i%.K%#(O(W8*#3&*3(j)5(F;;9EFGAYY( )*'&(=*00*3(0*K/L=%+*3'( •! UTK#*28*4/=(%KK/+*3( •! <8*'28*#T.%+*3( •! )T#/'&*T.%+*3( E0$04#%3$(%3=8*#/3"G( –! 7$3&#%.(2.%T$#(/3('/"3%../3"( –! ]$S$#'/4.$( –! m/3%'$'( •! <#$3T.%+*3(E0$04#%3$( %3=8*#/3"G( •! b<k(%3=8*#(E&%#"$+3"G( –! <8*'28%&%'$'( –! CI&$#0/3%.( –! 7I&$#0/3%.( •! b.T=*'T.%+*3( –! W#%3',$#(*,(%('>"%#(&*( !'3(*#(W8#6D$#( •! )*#$(&8%3(:;;(2#*&$/3'( •! 7*00*3(,*.K(ExFP;( #$'/K>$'G( •! WT2/=%..T(WT#(%3K(D$#6W8#( •! <#*&$/3('$#/3$I&8#$*3/3$( 28*'28%&%'$'( •! <#*&$/3(&T#*'/3$( 28*'28%&%'$'(E<W<G( •! U7EBGP](0*+,( %#$#(0*K/L=%+*3'( •! UTK#*JT.%+*3( –! ]$0$04$#(=*..%"$3( E8TK#*JT2#*./3$G( •! -J/K%+*3( –! \>$(&*(#$%=+S$(*JT"$3( –! WT2/=%..T(4%K(E$J=$2&(/3( =T'(K#/S$3(#$K*J( #$%=+*3'G( •! \$%0/K%+*3( –! D2*3&%3$*>'(=*3S$#'/*3( *,(!'3(O(b.3(&*(%=/K( •! )$&8T.%+*3( $">.%+*3( –! y'$'(DI%K$3*'T.( 0$&8/*3/3$( –! 5%=&$#/%.(=8$0*&%J/'( •! W#%3'0$04#%3$(#$=$2&*#'( &>#3$K(*3(%3K(*[( –! U/'&*3$(&%/.'( •! ]$0*S$'(=8%#"$( •! ]$.%J$'(8/'&*3$(2%=N/3"( •! !=$&T.%+*3( –! zI%0/3*(%3K({I%0/3*(*,( .T'/3$( –! <.%T'(%(4/"(#*.$(/3( &#%3'=#/2+*3( ...
View Full Document

This note was uploaded on 01/03/2012 for the course BI 170a taught by Professor List during the Fall '09 term at Caltech.

Ask a homework question - tutors are online