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PART-­‐1  Comprehensive  Exam-­‐  June  2012  Section-­‐1  (Part  A)  9AM  –  1PM  

 Instructions:  Attempt  8  of  the  15  questions  in  this  section.  You  have  to  pass  6  (six).  Please  spend  no  more  than  30  minutes  on  each  question.  Begin  the  answer  to  each  question  on  a  fresh  page  

   Q1.  a.  Adaptation   is   a   fundamental  property  of   signaling   systems;   e.g.  when  you  enter   a  dark   room,   your  eyes   eventually   adjust   to   the   low   light   level.   Suggest   three   key   molecular/cellular   strategies   (in   any  biological  context)  by  which  a  signaling  system  can  adapt  to  time-­‐dependent  inputs.    b.   For   a   signaling   circuit   capable   of   adaptation,   plot   the   downstream  output  when   the   input   has   the  following  form  (you  may  assume  that  the  adaptation  mechanism  operates  on  the  timescale  of  several  minutes):    

   Q2.  A   genome-­‐wide   screen   in   humans   finds   a   recessive   mutation   in   a   gene   with   a   strong   link   to  cardiovascular  disease.    The  gene  encodes  a  ubiquitously  expressed  protein  with  no  predicted  function.  Describe   in   some   detail   two   different   strategies   that   you   could   follow   in   your   lab   to   establish   the  function  of  this  protein.        Q3.  a.   In   contrast   to   the   case   for   soluble   globular   proteins,   almost   all   residues   in   the   transmembrane  portions  of   integral  membrane  proteins   are  ordered   into   secondary   structure  elements   such   as   alpha  helices  and  beta  sheets.  Provide  a  biophysical  explanation.  

 b.   An   alpha   helix   is   a   coiled   structure  with   a   pitch   of   5.4   Angstroms,   and   3.6   residues   per   turn.   The  "hydrophobic   thickness"   of   a   lipid   bilayer   is   about   30   Angstroms.   In   a   few   sentences,   describe   an  algorithm  to  identify  putative  trans-­‐membrane  alpha-­‐helical  segments  of  an  integral  membrane  protein  of  known  sequence.  

 c.   There   are   over   300  membrane   proteins   of   known   structure.   Among   these,   it   is   observed   that   the  number  of  residues  of  trans-­‐membrane  alpha-­‐helical  segments  can  vary.  What  would  you  predict  to  be  the  main  structural  difference  between  short  and  long  trans-­‐membrane  segments?      

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Q4  a)   Studies   reveal   that   plants   that   live   at   high   elevations   tend   to   have   a   higher   proportion   of   self-­‐fertilization.   Can   you   think   of   reasons   why   this   might   be   the   case?  What   assumption   would   you   be  making?  (Hint:  pollination)    b)   Primula   are  high  elevation  plants   that   live   in   the  Himalayas,   among  other  places   in   the  world.   The  flowers  only  outcross,  and  do  not  self  fertilize.  However,  the  highest  number  of  species  co-­‐occur  at  high  elevations.   For   example,   elevations   between   4000-­‐4500  may   have   four   species,  while   those   at   3500-­‐4000  has   two  and  only  one  occurs  between  3000-­‐3500m.  How  might  multiple,  non-­‐selfing  species  co-­‐exist  at  high  elevations?      Q5  A  cylindrical  non-­‐myelinated  axon  is  stimulated  at  both  ends,  so  that  action  potentials  propagate  toward  each  other.  The  axon  has  the  usual  HH  channels  Na  and  K  delayed  rectifier.                

a) Draw  the  membrane  potential  Vm  at  the  midpoint  position  x  as  a  function  of  time  b) Draw  Vm  at  y  as  a  function  of  time,  aligned  on  the  time  axis  with  the  above  graph.  c) Draw  the  open  fraction  of  the  inactivation  gate  h  of  sodium  channels  at  y,  as  a  function  of  time,  

aligned  with  the  above  graphs.  d) Draw  Vm  vs.  position,  1  msec  after  the  APs  have  collided,  that  is,  1  msec  after  the  peaks  overlap.  e) Do  the  APs  continue  after  the  collision?  With  reference  to  these  figures,  explain.  

   Q6.  Dale’s  principle  holds  that  a  single  neuron  uses  one  and  the  same  substance  as  its  transmitter  across  all  of   its   synapses.  However,   recent   studies   show  that  many  neurons  are  capable  of   releasing  more   than  one  transmitter  (co-­‐transmission),  and  sometimes  the  same  neuron  releases  different  transmitters  from  different   terminals.   You   are   given   a   culture   of  medium   spiny   neurons   from   the   striatum   of   the   star-­‐nosed  mole.    

a) Describe  at  least  two  different  methods  by  which  you  will  determine  the  number  of  transmitters  that  MSNs  use.    

b) How   will   you   determine   which   transmitters   are   released   at   each   contact?   (Hint:   MSNs   are  known  to  contain  GABA,  enkephalin,  dynorphin,  and  SubstanceP).    

   Q  7.  Tic-­‐tac-­‐toe,  or  Noughts-­‐and-­‐crosses,   is  a   two-­‐player  game  you  are  probably   familiar  with.    On  a  board  consisting   of   9   squares,   arranged   in   a   3x3  matrix,   players   play   alternately.  On   their   turn,   each   player  writes  a  symbol   in  an  empty  square  of   their  choice.  One  player  uses  the  symbol  X,   the  other  uses  the  symbol  O.    A  player  wins  if  they  get  three  of  their  symbols  lined  up  in  a  row,  column  or  diagonal.    If  all  nine  squares  are  filled  up  without  this  happening  for  either  player,  then  the  game  is  a  draw.    Write  out  a  

x   y  

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set  of   rules,  which   if   followed  exactly,  would  allow  me  to  play   tic-­‐tac-­‐toe  perfectly  against  all  possible  opponents.  That  is,  whether  I  play  first  or  second,  the  rules  should  make  me  play  the  best  possible  move  for  every  situation  that  arises  on  the  board.    Q8.  Assume  the  chance  of   it   raining  each  day   in  Bangalore   is  60%.  You  are  equally  unhappy  when  you  get  wet  and  when  you  carry  an  umbrella  on  a  non-­‐rainy  day.  You  are  also  equally  happy  when  you  have  an  umbrella  to  protect  you  on  a  rainy  day  and  when  you  are  not  burdened  by  an  umbrella  on  a  non-­‐rainy  day.  Then  which  of  the  following  strategies  will  leave  you  most  happy  in  the  long  run?  (i)  Always  carry  an  umbrella,   (ii)  Never   carry  an  umbrella,   (iii)  Carry  an  umbrella  60%  of   the   time,   (iv)    Carry  an  umbrella  50%   of   the   time.     Justify   your   answer.     (You   can   assume   that   the   60%   chance   of   rain   is   all   the  information  you  have  -­‐-­‐  you  cannot  look  out  the  window  to  see  if  rain  clouds  are  appearing,  how  long  it  rains  is  irrelevant,  there  is  no  correlation  between  it  raining  one  day  and  it  raining  the  next  day,  etc.)      Q9.  Consider   a   population   of   stem   cells   (P)   which   must   go   through   an   intermediate   state   (Q)   before  ultimately   differentiating   into   some   final   cell   type   (R).   We   model   the   P→Q   and   Q→R   transitions   in  analogy  to  a  chemical-­‐kinetic  model  of  three  reactants  (where  p,  q,  r  are  concentrations;  α   ,β  are  rate  constants),  or  a  model  of  water  flow  between  three  tanks  of   identical  size  and  shape  (where  p,q,r  are  water  levels,  and  α  ,βreflect  the  efficiency  of  flow  through  the  taps):  

 

 

 

 

 

 

Such  a  system  is  represented  by  the  following  ordinary  differential  equations:  

 

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(i) dpdt

= −αp, (ii) dqdt

=αp −βq, (iii) drdt

= βq.  

Assume  that  initially  all  cells  are  in  the  undifferentiated  state  P,  so  that    

€

p(0) = p0, q(0) = 0, r(0) = 0.    a.     For  any  time  t,  what  is  the  value  of  

€

p(t) + q(t) + r(t)?  [Hint:  You  don’t  need  calculus  to  answer  this.]    b.     Solve  for  p(t).  [Hint:  radioactive  decay.]    c.   Verify  that  the  following  function  gives  the  number  of  cells  in  state  Q:  

   

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q(t) = p0α

β −αe−αt − e−βt( )  

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  [Hint:  Differentiate  this  function  wrt  t  and  check  that  it  satisfies  Eq.  (ii).]    d.   Suppose  that  the  two  rate  constants  are  equal:  

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α = β .  Then  it  turns  out  that  q(t)  has  the  form:  

€

q(t) = ute−wt .  Find  the  values  of  u  and  w.  

  Hint:  

€

df (x)dx

= limβ →α

f (β) − f (α)β −α

.  Substitute  

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f (x) = −e−xt ,  evaluate  at  

€

x =α .  

e.   Again  assuming

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α = β ,  at  what  time  t  will  the  number  of  cells  in  the  intermediate  pool  be  greatest?  (You  may  leave  your  answer  in  terms  of  u  and  w).  

f.   For  p0  =  1,  

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α = β =1,  sketch  

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p(t), q(t), r(t) .  Be  as  precise  as  possible,  label  axes  and  all  special  points.    

 Q10.  The  concentrations  of  tRNAs  for  different  codons  vary  across  tissues  in  humans.  What  do  you  expect  will  happen   when   the   codon   in   present   in   an  mRNA   being   translated   but   its   associated   tRNA   is   absent?  Explain   how   differing   tRNA   concentrations   could   lead   to   alternatively   folded   forms   of   a   protein  translated  from  the  same  mRNA  in  two  different  tissues.      Q  11.  

As   can   be   seen   from   the   figure,   two   complementary   strands   of   DNA   come  together  to  form  a  right  handed  antiparallel  double  helix.      

(i) What   are   the   possible   benefits   -­‐with   respect   to   function   of   DNA   as  genetic  material-­‐  of  adopting  this  arrangement?    

(ii)  Protein   factors   are   able   to   read   the   information   resident   in   this  arrangement  with  exquisite   specificity   to  bring   about  physiologically  distinct  outcomes.      

(iii) What   different   aspects   of   DNA   in   this   form   can   be   exploited   by  protein  factors  to  achieve  specific  binding?        

 Q  12.  Using  your  biceps  to  lift  a  weight  

The  figure  shows  a  simplified  sketch  of  the  biceps-­‐elbow  system.  The  muscle-­‐tendon  unit  represents  the  biceps,  and    is  the  external  mass  being  lifted.  Assume  that  bone  #1  is  attached  to  ground.  Dimensions  are  as  indicated  in  the  figure,  in  terms  of   .  

When  you  lift  a  weight,  like  in  the  weights  room  in  the  gym,  the  tension  in  the  biceps'  muscle-­‐tendon  unit  creates  a  torque  about  the  elbow  joint.  The  amount  of  torque  generated  depends  on  the  lever  arm  of  the  muscle-­‐tendon  unit  about  the  joint  centre  of  rotation.  This  lever  arm  is  called  the  `moment  arm'  of  the  muscle.  The  muscle-­‐tendon  unit  could  `bow-­‐string',  causing  the  moment  arm  to  depend  on  posture.  Calculate  the  moment  arm  of  the  biceps  about  the  

m

`0

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elbow  joint  using  the  musculoskeletal  geometry  depicted  in  the  figure.  Find  an  expression  for  the  moment  arm    as  a  function  only  of    and   .  

Q13.    Our  gut  grows  when  we  regularly  increase  food  intake  and  shrink  we  regularly  manage  to  diet  severely.  Imagine   a   simplified   gut  with   epithelial   cells   and   smooth  muscle.   Keep   in  mind   that   food   is   digested,  nutrients  taken  up  and  sensed  inside  the  animal.  Write  out  a  signalling  mechanism  that  can  detect  levels  of   food   intake  and   respond   to   it  by   increasing  gut   size  and   reducing   it  on   starvation.   Link   the   specific  signalling   pathways   you   choose,   their   ligands,   receptors,   output   with   the   cell   biology   of   secretion,  detection   of   systemic   read-­‐outs   of   nutrient   levels   and   how   this   detection   in   turn   feed   back   from   the  body  to  the  gut  to  regulate   its  size.    You  don’t  have  to  know  ‘the  answer’:  You   just  need  to  present  a  well-­‐thought  out  credible  answer.    Q14.  In  a  protein,  a  polypeptide  chain  can  fold-­‐back  on  itself:  This  common  ‘turn’  is  called  a  beta-­‐turn:  How  many  consecutive  amino  acid  residues  do  you  think  are  likely  to  be  involved  in  a  beta  turn?  Depending  on  the  numbers  of  consecutive  amino-­‐acid  residues  in  a  polypeptide  chain  involved  in  a  turn  the  nature  of  the  turn  can  vary.  Apart  from  the  beta-­‐turn,  can  you  mention  another  turn,  the  numbers  of  amino-­‐acid  residues  involved  and  the  nature  of  the  turn?    Q15.  Stem  cells  can  expand  the  size  of   tissues  they  make  by  switching   from  asymmetric  cell  division   (linear  increase   in   cell   number)   to   symmetric   (exponential)   division.   Write   down   a   plausible   molecular  mechanism   for   asymmetric   division  where  one  daughter  of   a   stem  cell   is   a   stem  cell   and   the  other   a  daughter,   which   divides   once   and   differentiates   its   two   progeny.   Write   another   plausible   molecular  mechanism  by  which  a  stem  cell  gives  rise  to  a  daughter  stem  cell  and  a  ‘transit’  cell  which  then  divides  to  give  two  more  transit  cells,  a  process  that  continues  for  6  rounds  of  symmetric   transit  cell  division.  The   amplified   transit   cells   then   divide   once  more   to   differentiate.   You   answer   need   not   be   based   on  what  we  have  learnt  from  research  on  this  question:  We  just  need  a  plausible  molecular  model  that  is  inspired  by  what  we  know  of   the  cell  biology  of   signalling,   sub-­‐cellular   localization  and   transcriptional  response.  

               

 

r ✓ `0

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PART-­‐1  Comprehensive  Exam-­‐  June  2012    

Part  1  (SECTION  B)  2PM  –  6PM    Instruction:  Attempt  any  ONE  of  the  following  questions  

 Projects  should  be  framed  using  the  following  format:  

• Abstract  –  300  words  or  less  • Introductory  paragraph  summarizing  the  background  and  framing  the  question  • Hypotheses  • Predictions  • Experimental  design  framed  to  test  the  hypotheses  • Analysis  

 Q1.  Reading  material:  Michael  Hasselmo’s  review    (Trends  in  Cognitive  Sciences  –  Vol  3,  1999)  on  associative  memories  and  modulation  by  acetylcholine.    Project   to   design:   Design   a   research   project   to   test   the   acetylcholine   gating   theory   for   associative  memory  in  the  hippocampal  slice  preparation.  Your  experiment  can  use  any  of  the  modern  techniques:  2-­‐photon  calcium  imaging,  channel  rhodopsin  and  optical  stimulation,  patch  recording,  transgenics  and  so  on.      Q2.  Reference:  Senavirathne  et  al.,  Single-­‐stranded  DNA  Scanning  and  Deamination  by  APOBEC3G  at  Single  Molecule  Resolution.  JBC,  2012  The   enzyme   APOBEC3G   (Apo3G)   catalyzes   C-­‐to-­‐U   deamination   reactions   in   single-­‐stranded   DNA  (ssDNA),   without   requiring   ATP   or   any   small-­‐molecule   co-­‐factors.   It   acts   at   the  motif   5’aaaCCCaaa3’,  deaminating  the  final  C.  When  there  are  multiple  motifs  on  a  single  ssDNA  molecule,  Apo3G  is  known  to  act   processively:   binding   to   a   substrate   strand,   catalyzing   multiple   deamination   reactions,   then  unbinding.   When   short   ssDNA   strands   are   incubated   with   Apo3G,   the   final   pattern   of   deamination  shows  an  asymmetry  or  polarity,  favouring  5’  motifs  over  3’  motifs.  Our  aim  is  to  explain  this  polarity.  

 A.  First,  consider  the  hypothesis  that  Apo3G  binds  DNA,  then  scans  unidirectionally,  deaminating  at  all  motifs   it   passes   until   it   unbinds.   In  which   direction  would   the   scanning   have   to   occur?   Is   this  model  tenable  given  the  facts  above?  

 B.   Senavirathne  et  al.   claim   that   their   single-­‐molecule  experiments  prove   that  Apo3G  scans   ssDNA  bi-­‐directionally  in  a  random  fashion,  based  on  the  symmetric  nature  of  their  transition  density  plots  (TDPs).  They   state:   “All   initial   binding   events   stem   from   zero   FRET  on   the   y-­‐axis,  with  most  occurring   at   ~0.2  FRET,   indicating   that  Apo3G  binds   preferentially   away   from   the   tethered  5’-­‐end”.   Strikingly   the   x-­‐axis  and   y-­‐axis   are   completely   symmetric   in   all   TDPs,   suggesting   that   Apo3G   preferentially   un-­‐binds   away  from  the  5’-­‐end  as  well.  Explain  why  this  might  be  so.    C.  Assuming  that  the  scanning  by  Apo3G  is   indeed  bidirectional  with  no  bias,  we  must  still  explain  the  polarized  deamination  pattern.  The  authors  present  a  model  involving  the  two  DNA-­‐binding  domains  (N-­‐terminal   CD1   and   C-­‐terminal   CD2)   of   Apo3G,   only   one   of   which   is   catalytically   active   (CD2).   In   their  model,  Apo3G  can  bind  DNA  in  two  distinct  orientations.    

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    (i)  Is  this  model  sufficient  to  explain  polarity?       (ii)  What  does  the  model  predict  for  a  long  stretch  of  linear  ssDNA?     (iii)  What  does  the  model  predict  for  circular  ssDNA?     (iv)  What  does  the  model  predict  for  short  linear  double-­‐stranded  DNA?    

D.   Suggest   further  experiments   to   test   the   ‘two-­‐orientation’  hypothesis.  Be   specific,   stating  how  each  proposed  experiment  would  test  aspects  of  the  hypothesis.  

   

Q3  How   do   humans   throw   at   high   speeds,   yet   achieve   sufficient   accuracy?   Review   the   three   papers  provided   (Calvin,  1983,  Chowdhary  and  Challis,  1999,  Hore  and  Watts,  2011),  and  comment  upon   the  factors   that   govern   accuracy   of   projectile   release.  What   are   the  merits   and   limitations   of   the   type   of  analysis  carried  out  by  Calvin  (1983)  and  by  Chowdhary  and  Challis  (1999)?  Do  the  experimental  findings  of   Hore   and   Watts   (2011)   contradict   the   theoretical   calculations   before?   Design   an   experimental  protocol,   and   propose   a   concurrent   theoretical   model,   using   control   theory,   to   test   the   hypothesis  proposed   by   Hore   and   Watts   (2011).   How   will   you   design   an   experiment   to   try   and   falsify   your  theoretical  model?    W  H  Calvin.  A  stone’s   throw  and   its   launch  window:   timing  precision  and   its   implications   for   language  and  hominid  brains.  Journal  of  Theoretical  Biology,  104(1):121–135,  1983.  A   G   Chowdhary   and   J   H   Challis.   Timing   accuracy   in   human   throwing.   Journal   of   Theoretical   Biology,  201(4):219–229,  1999.  J  Hore  and  S  Watts.  Skilled  throwers  use  physics  to  time  ball  release  to  the  nearest  millisecond.  Journal  of  Neurophysiology,  106(4):2024–2033,  2011.    Q4.  Despite   intense   investigation,   auditory   transduction,   the   process   by   which   sound   is   detected   and  transduced  by  the  sensory  cells  in  the  vertebrate  inner  ear  remains  incompletely  understood.  It  is  widely  accepted   that   auditory   transduction   is   a   process   of  mechanotransduction,  which   culminates  with   the  activation  of  ion  channels  on  membranes  of  neurons  in  the  inner  ear.    However  despite  several  years  of  analysis  the  identity  of  these  ion  channels  remains  unresolved.    

Members  of  the  TRP  family  of  ion  channels  are  implicated  in  transducing  a  range  of  stimuli  in  a  large   number   of   species.   The   Corey   lab   has   suggested   that   TRPA1   might   be   the   mechanosensitive  channel  involved  in  auditory  transduction.  Please  read  the  primary  research  articles  from  the  Corey  lab  and  discuss  critically   the  evidence   for/against   the   idea   that  TRPA1  channels  are   the   final  mediators  of  auditory  transduction.  Suggest  additional  experiments  that  might  be  required  to  resolve  this  issue.      Q5.  1)Recent   studies   reveal   genomic   signatures   of   selection   on   genes   involved   in   unique   adaptations   to  hypoxia   (low  oxygen   levels)   in  humans   that   live   in  highlands,   like   the  Tibetan  Plateau   (1,  2).  Pikas  are  lagomorphs  (rabbit  family)  that  live  at  high  elevations  (cold,  hypoxic  environments)  or  at  high  lattitudes  (like   in  Canada,  cold  enviornments).  The  tree  below  shows  evolutionary  relationships  and  distributions  of   five   pika   species.   Describe   experiments   to   test  whether   (1)   Pikas   originally   evolved   adaptations   to  hypoxia   (2)   they   only   have   adaptations   to   cold   environments   and   (3)   they   are   adapted   to   cold   and  hypoxia.  

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References:  1)   Sequencing  of   50  Human  Exomes  Reveals  Adaptation   to  High  Altitude   Yi,   et   al.   Science  2   July  2010:  Vol.  329  no.  5987  pp.  75-­‐78.  DOI:10.1126/science.1190371  2)   Genetic  Evidence  for  High-­‐Altitude  Adaptation  in  Tibet  Simonson  et  al.,  Science  2  July  2010:  Vol.  329  no.  5987  pp.  72-­‐75  DOI:  10.1126/science.1189406        

   Q6:    Pacific   Salmon   are   born   in   fresh-­‐water,   migrate   to   the   sea   and   return   ‘home’   to   spawn.   Read   the  attached  paper  (Dittmann  and  Quinn,  1996;    http://jeb.biologists.org/content/199/1/83)  for  a  summary  of  the  process  and  what  was  understood  some  time.  Today,  as  an  experimental  physicist   interested  in  biology,  or  as  a  behavioural  biologist,  what  do  you  think  the  one  key  question  to  understand  homing  is?