Why do biologists use so many diagrams.3.1.a To  be  presented  at  the  biennial  meeting  of  the  Philosophy  of  Science  Association,     November  2012,  and  then  published  in  revised  form  in  Philosophy  of  Science     Why  do  biologists  use  so  many  diagrams?     Benjamin  Sheredos,  Daniel  C.  Burnston,  Adele  Abrahamsen   and  William  Bechtel   University  of  California,  San  Diego     Abstract     Diagrams  have  distinctive  characteristics  that  make  them  an  effective   medium  for  communicating  research  findings,  but  they  are  even  more   impressive  as  tools  for  scientific  reasoning.  Focusing  on  circadian  rhythm   research  in  biology  to  explore  these  roles,  we  examine  diagrammatic  formats   that  have  been  devised  (a)  to  identify  and  illuminate  circadian  phenomena   and  (b)  to  develop  and  modify  mechanistic  explanations  of  these  phenomena.       1.  Prevalence  and  importance  of  diagrams  in  biology     If  you  walk  into  a  talk  and  do  not  know  beforehand  whether  it  is  a  philosophy  or  biology   talk,  a  glance  at  the  speaker’s  slides  will  provide  the  answer.  Philosophers  favor  text,   whereas  biologists  shoehorn  multiple  images  and  diagrams  into  most  of  their  slides.   Likewise,  if  you  attend  a  philosophy  reading  group  or  a  biology  journal  club  you  can  readily   identify  a  major  difference.  Instead  of  verbally  laying  out  the  argument  of  the  paper  under   study,  the  presenter  in  a  journal  club  conveys  hypotheses,  methods,  and  results  largely  by   working  through  diagrams  from  the  paper.  This  reflects  a  more  fundamental  contrast   between  philosophers  and  biologists:  their  affinity  for  text  versus  diagrams  is  not  just  a   matter  of  how  they  communicate  once  their  work  is  done,  but  shapes  every  stage  of  inquiry.   Whereas  philosophers  construct,  evaluate,  and  revise  arguments,  and  in  doing  so  construct   and  revise  sentences  that  convey  the  arguments,  biologists  seek  to  characterize   phenomena  in  nature  and  to  discover  the  mechanisms  responsible  for  them.  Diagrams  are   essential  tools  for  biologists  as  they  put  forward,  evaluate,  and  revise  their  accounts  of   phenomena  and  mechanisms.       Diagrams  play  these  roles  in  science  more  generally,  but  we  have  chosen  to  focus  on   biology  –  in  particular,  on  the  research  topic  of  circadian  rhythms  –  to  begin  to  get  traction   on  this  understudied  aspect  of  the  scientific  process.  Circadian  rhythms  are  oscillations  in   organisms  with  an  approximately  24-­‐hour  cycle  (circa  =  about  +  dies  =  day).  They  are   endogenously  generated  but  entrained  to  the  day-­‐night  cycle  in  specific  locales  at  different   times  of  the  year.  They  have  been  identified  in  numerous  organisms—not  only  animals  but   also  plants,  fungi,  and  even  cyanobacteria—and  characterize  a  vast  array  of  physiological   processes  (e.g.,  basic  metabolism  and  body  temperature)  and  behaviors  (e.g.,  locomotion,   sleep,  and  responding  to  stimuli).       2.  Diagrams  and  mechanistic  explanation     Diagrams  play  a  central  role  in  biology  because  they  are  highly  suited  to  two  key  tasks:  (1)   displaying  phenomena  at  various  levels  of  detail,  and  (2)  constructing  mechanistic   explanations  for  those  phenomena.,  Philosophers  of  biology  have  increased  their  attention   Sheredos,  Burnston,  Abrahamsen,  and  Bechtel     p.  2   to  those  tasks  over  the  last  two  decades,  construing  mechanisms  as  systems  that  produce  a   phenomenon  of  interest  by  means  of  the  organized  and  coordinated  operations  performed   by  their  parts  (Bechtel  and  Richardson  1993/2010;  Bechtel  and  Abrahamsen  2005;   Machamer,  Darden,  and  Craver  2000).  To  advance  a  mechanistic  explanation,  biologists   must  characterize  the  phenomenon  of  interest  (e.g.,  circadian  oscillations  in  activity),     identify  the  mechanism  they  take  to  be  responsible  (e.g.,  a  molecular  “clock”),  decompose  it   into  its  parts  and  operations,  and  recompose  it  (conceptually,  physically,  or   mathematically)  to  show  that  the  coordinated  performance  of  these  operations  does   indeed  generate  the  phenomenon.  Early  in  the  discovery  process  scientists  may  identify   only  a  few  parts  and  operations,  and  hypothesize  a  relatively  simple  mechanism  that  can  be   recomposed  by  mentally  imagining  a  short  sequence  or  cycle  of  operations  (e.g.,  a  single   gene  expression  feedback  loop  was  initially  posited  for  the  molecular  clock).  At  least  in   biology,  further  research  generally  uncovers  additional  parts  and  operations  with  complex   organization  and  dynamics  (e.g.,  multiple  interacting  feedback  mechanisms  constituting  the   overall  molecular  clock  mechanism).         While  a  simple  mechanistic  account  might  be  presented  linguistically  in  the  form  of  a   narrative  about  how  each  part  in  succession  performs  its  operation,  diagrams  generally   provide  particularly  useful  representational  formats  for  conceptualizing  and  reasoning   about  mechanisms.1  By  displaying  just  a  few  common  graphical  elements  in  two   dimensions,  a  diagram  can  visually  depict  a  phenomenon  or  the  organized  parts  and   operations  of  an  explanatory  mechanism  (Bechtel  and  Abrahamsen  2005;  Perini  2005).   Available  elements  include  labels,  line  drawings,  iconic  symbols,  noniconic  symbols   (  shapes,  colors),  and  –  the  device  most  often  used  for  operations  –  various  styles  of  arrows.   The  spatial  arrangement  of  these  elements  can  convey  spatial,  temporal,  or  functional   relations  that  help  characterize  a  phenomenon  or  mechanism.  Deploying  our  spatial   cognition  on  diagrams  has  certain  advantages  over  language-­‐based  reasoning  in   constructing  mechanistic  explanations.  Notably,  scientists  can  mentally  animate  (Hegarty   2004)  a  static  diagram  to  simulate  the  succession  of  operations  by  which  a  simple   sequential  mechanism  produces  a  phenomenon.  Simultaneous  operations  are  more   challenging.2         The  primary  role  of  diagrams  for  scientists  is  not  to  provide  a  visual  format  for   communicating  the  phenomena  discovered  or  the  mechanistic  accounts  that  explain  them.     Rather,  diagrams  of  mechanisms  are  comparable  to  the  plans  a  designer  develops  before                                                                                                                   1  Defining  and  classifying  diagrams  is  beyond  the  scope  of  this  paper;  therefore,  we  focus   on  clear  exemplars  and  set  aside  such  formats  as  micrographs  and  animations.   2  As  researchers  recognize  the  complicated  interaction  of  components  in  a  mechanism  and   the  complex  dynamics  emerging  from  multiple  simultaneous  operations,  they  often  turn  to   computational  modeling  and  the  tools  of  dynamic  systems  analysis  to  understand  how  the   mechanism  will  behave,  giving  rise  to  what  Bechtel  and  Abrahamsen  (2011)  characterize   as  dynamic  mechanistic  explanations.  Jones  and  Wolkenhauer  (in  press)  provide  a  valuable   account  of  how  diagrams  contribute  to  the  construction  of  such  computational  models.  It  is   also  worth  noting  that  linguistic  reasoning  has  its  own  advantages.  We  would  posit  that  the   more  complex  the  mechanism,  the  more  beneficial  is  a  coordinated  deployment  of   linguistic,  diagrammatic  and  computational  resources.     Sheredos,  Burnston,  Abrahamsen,  and  Bechtel     p.  3   building  a  new  machine.  These  are  used  not  just  to  tell  those  actually  constructing  the   machine  how  to  make  it;  they  also  figure  in  the  design  process.  Before  producing  the  final   plans,  the  designer  tries  out  different  designs  and  evaluates  whether  they  are  likely  to   result  in  a  working  and  efficient  machine.  Often  the  initial  sketches  of  these  plans  reveal   serious  problems  that  must  be  overcome,  resulting  in  revisions  to  the  plans.  The  biologist  is   not  creating  the  machine  (except  in  fields  such  as  synthetic  biology),  but  is  trying  to  reverse   engineer  it.  Still,  she  needs  to  go  through  many  of  the  same  processes  as  a  designer— sketching  an  initial  diagram,  identifying  ways  in  which  it  is  inadequate,  and  modifying  the   diagram  repeatedly  until  it  is  judged  a  satisfactory  mechanistic  account  of  the  targeted   phenomenon.  Moreover,  the  biologist  wants  to  end  up  not  merely  with  some  possible   mechanism  capable  of  producing  the  phenomenon,  but  rather  with  the  one  actually  present   in  the  biological  system.  In  what  follows,  we  will  examine  how  diagrams  are  put  to  work  in   biology,  focusing  on  two  key  tasks:  delineating  phenomena,  and  constructing  mechanistic   accounts  to  explain  them.         3.  Diagrams  to  delineate  the  phenomenon     An  initial  delineation  of  the  phenomenon  to  be  explained  is  a  crucial  step  in  mechanistic   research.  This  remains  true  even  if,  in  the  course  of  discovering  the  mechanism,   researchers  revise  their  understanding  of  the  phenomenon.  Many  philosophical  accounts  of   mechanistic  explanation  have  focused  on  linguistic  descriptions  of  phenomena  (e.g.,  “in   fermentation,  sugar  is  converted  into  alcohol  and  carbon  dioxide  by  means  of  a  series  of   intermediate  reactions  within  yeast  cells”).  However,  scientists  focus  much  of  their  effort   on  obtaining  much  more  specific,  often  quantitative,  accounts  of  phenomena.  Numerical   data  involved  in  characterizing  a  phenomenon  may  be  presented  in  tables.  As  Bogen  and   Woodward  (1988)  made  clear,  however,  explanations  are  directed  not  at  the  data  but   rather  at  the  pattern  extracted  from  the  data—the  phenomenon.  Some  data  patterns  can  be   captured  in  one  or  a  few  equations,  such  as  the  logarithmic  function  relating  stimulus   intensity  (e.g.,  amplitude  of  a  tone)  to  the  sensation  evoked  (e.g.,  perceived  loudness).  By   plotting  these  values  on  a  graph,  the  phenomenon  of  a  nonlinear  relation  between   amplitude  and  loudness  is  immediately  evident.  The  graph  takes  advantage  of  spatial   cognition,  whereas  the  logrithmic  equation  makes  explicit  a  very  precise  claim  that  can  and   has  been  challenged  (e.g.,  by  those  who  argue  for  a  power  function).  Scientists  move  deftly   between  linguistic  descriptions,  diagrams,  and  equations  when  all  are  available,  using  each   to  its  best  advantage.       Diagrams  are  especially  useful  for  thinking  about  dynamic  phenomena  –  patterns  of  change   over  time.  Circadian  phenomena  are  dynamic,  so  diagrams  conveying  them  generally   incorporate  time  in  some  way  (as  the  abscissa  on  a  line  graph,  as  the  order  of  arrows  in  a   sketch  of  a  mechanism,  as  points  along  the  trajectory  in  a  state  space,  etc.).  Moreover,   research  on  circadian  oscillations  often  targets  the  interaction  between  endogenous   control  (by  an  internal  clock)  and  exogenous  timing  cues,  commonly  referred  to  as   Zeitgebers.  Hence,  what  was  needed  was  a  way  of  diagramming  the  activity  of  an  organism,   such  as  a  mouse  running  on  a  wheel,  that  revealed  at  a  glance  its  rhythmicity  and  the   impact  of  Zeitgebers.     Sheredos,  Burnston,  Abrahamsen,  and  Bechtel     p.  4   Circadian  researchers  settled  on  a  distinctive  format,  the  actogram.  Figure  1  illustrates  the   diagrammatic  devices  that  satisfy  the  desiderata  Time  of  day  is  represented  horizontally   and  successive  days  are  represented  vertically  (one  line  of  data  per  day).    Activity  is   tracked  along  each  line—e.g.,  a  single  hash  mark  each  time  a  mouse  rotates  a  wheel.  The   bars  at  the  top  use  white  vs.  black  to  represent  the  24-­‐hour  light-­‐dark  conditions.  Here  the   mouse  was  exposed  to  light  from  hours  4-­‐16  during  the  first  phase  of  the  study  (specified   elsewhere  as  Days  1-­‐7).  During  the  other  twelve  hours  of  Days  1-­‐7,  and  all  24  hours   beginning  Day  8,  the  mouse  was  kept  in  darkness.  On  Day  18,  four  hours  after  onset  of   activity,  the  mouse’s  rhythm  was  perturbed  by  a  pulse  of  light.  The  large  gray  arrow  directs   the  reader’s  attention  to  the  effects  of  this  isolated  Zeitgeber.     .           Figure  1.  A  basic  actogram  in  which  the  top  bar  indicates  a  normal  light-­‐dark  cycle   for  the  first  phase  of  the  study  (Days  1-­‐7)_and  constant  darkness  thereafter.  The   gray  arrow  identifies  the  day  a  light  pulse  was  administered.  (From   http://www.photosensorybiology.org/id16.html.)     The  actogram  offers  a  relatively  transparent  representation  of  the  animal’s  behavior;  that   is,  readers  who  have  learned  its  conventions  should  be  able  to  see  through  the  diagram  to   the  multiple  behavioral  phenomena  that  it  visually  depicts.3  Figure  1  offers  this  kind  of   access  to  at  least  four  circadian  phenomena.  First,  in  rows  1-­‐7  it  can  be  seen  that  the  hash   marks  occur  in  consolidated  bands  bounded  by  the  black  segments  of  the  upper  bar.  This   indicates  that  when  Zeitgebers  are  present  (light  alternating  with  dark),  virtually  all  wheel-­‐ running  occurs  in  the  dark:  the  animal  is  nocturnal.  Second,  the  fact  that  the  hash  marks   continue  to  appear  in  consolidated  bands  after  row  7  (when  the  animal  is  free-­‐running  in   the  absence  of  Zeitgebers)  indicates  that  the  animal  can  endogenously  maintain  a  robust   division  between  periods  of  rest  and  of  activity.  Third,  these  later  bands  of  hash  marks   ‘drift’  leftward,  indicating  that  the  animal  begins  its  activity  a  bit  earlier  each  day.   Maintenance  of  a  free-­‐running  period  somewhat  less  than  24  hours  is  the  core   phenomenon  of  circadian  rhythmicity.  Fourth,  the  pulse  of  light  flagged  by  the  gray  arrow   brings  an  abrupt  cessation  of  activity  on  Day  18  and  inserts  a  phase  delay  (seen  as  a                                                                                                                   3  See  Cheng  (2011)  for  a  more  extensive  discussion  of  semantic  transparency.  Note  also   that  some  phenomena  are  less  transparently  conveyed  by  diagrams  than  others.   Presumably,  the  spatial  cognition  deployed  in  less  transparent  cases  is  effortful  to  some   degree  and/or    coordinated  with  propositional  cognition.   Sheredos,  Burnston,  Abrahamsen,  and  Bechtel     p.  5   rightward  “jump”  in  the  bands  of  hash  marks)  into  what  was  otherwise  a  continuing   pattern  of  phase  advance  (left-­‐ward  “drift”)  under  constant  darkness.  This  reset   phenomenon  is  one  aspect  of  the  more  general  phenomenon  of  entrainment.       Thus,  actograms  make  circadian  rhythmicity  in  an  animal’s  activity  visually  accessible.  But   when  chronobiologists  attempt  to  understand  the  molecular  mechanisms  that  produce   such  macroscopic  rhythmicity,  they  are  confronted  with  new  phenomena  that  call  for   different  diagrammatic  formats.  Notably,  the  concentration  levels  (relative  abundance)  of   many  types  of  molecules  within  cells  oscillate.  For  example,  Hardin,  Hall,  and  Rosbash   (1990)  demonstrated  the  circadian  oscillation  of  period  (per)  mRNA  in  Drosophila   melanogaster  (fruit  flies).4  In  Figure  2  (below)  we  reproduce  a  pair  of  diagrams  from  their   paper  that  illustrate  how  the  same  data  can  be  displayed  in  two  formats  that  differ   substantially  in  how  they  visually  depict  per  mRNA  oscillation.  Flies  had  previously  been   kept  for  three  days  in  a  light-­‐dark  cycle  of  12  hours  light,  12  hours  dark.  Starting  on  the   fourth  day  (hours  24-­‐48  in  Figure  2),  the  flies  were  placed  in  constant  darkness.  Every  four   hours  a  batch  of  flies  was  sent  for  processing  to  determine  per  mRNA  abundance  via  a   molecular  probe.  The  output  of  this  procedure,  the  Northern  blot,  is  shown  at  the  top  of   Figure  2.  Darker  regions  of  the  blot  visually  depict  greater  presence  of  per  mRNA  across  the   four  days.         Figure  2.  Two  diagrams  from  Hardin  et  al.’s  (1990)  original  portrayal  of  circadian   oscillation  in  per  mRNA  levels  in  Drosophila.  On  top  is  a  series  of  Northern  blots   (from  different  flies  every  4  hours).  Below  this  is  a  line  graph  of  the  same  data.  The   Zeitgeber  schedule  is  shown  at  the  bottom,  with  white  hatched  bars  depicting  the   intervals  in  which  lights  would  have  been  on  if  the  initial  light-­‐dark  cycle  had   continued.                                                                                                                     4  Much  of  the  early  research  on  molecular  mechanisms  is  nonmammalian,  including  the   discovery  of  per  mRNA  oscillations.  A  role  for  per  is  conserved  in  the  mouse  circadian   mechanism.   Sheredos,  Burnston,  Abrahamsen,  and  Bechtel     p.  6   Below  the  Northern  blots,  the  same  data  are  displayed  in  a  line  graph.  Here  numeric  values   for  per  MRNA  are  displayed  in  a  format  that  makes  their  oscillation  immediately  apparent.   Moreover,  a  quick  check  of  the  horizontal  scale  confirms  that  the  period  of  oscillation  is   circadian:  there  are  four  peaks  in  four  days.  Closer  examination  reveals  that  the  peak   occurs  slightly  earlier  on  Day  4,  indicating  a  slightly  shorter  period  in  the  absence  of  a   Zeitgeber.  Actograms  provide  a  better  visual  display  of  such  variations  in  period,  but  are   less  suitable  for  conveying  variations  in  amplitude.       4.  Diagrams  to  identify  the  parts,  operations,  and  organization  of  a  mechanism     A  major  use  of  diagrams  in  mechanistic  science  is  to  present  a  proposed  mechanism  by   spatially  displaying,  at  some  chosen  level  of  detail,  its  parts  and  operations  and  the  way   they  are  envisaged  as  working  together  to  produce  a  phenomenon.  Such  diagrams  typically   utilize  a  two-­‐dimensional  space  in  which  elements  representing  different  parts  and   operations  of  the  mechanism  can  be  laid  out  so  as  to  depict  key  aspects  of  their  spatial,     temporal,  and  functional  organization.  As  noted  in  Section  2,  a  variety  of  labels,  line   drawings  and  symbols  can  be  used  to  distinguish  different  kinds  of  parts.  Parts  perform   operations  that  affect  other  parts  and  lead  to  or  interact  with  other  operations.  One  or   more  styles  of  arrows,  often  labeled,  are  typically  chosen  for  displaying  these  operations.       As  static  structures,  diagrams  do  not  directly  show  how  the  mechanism  produces  the   phenomenon.  Unless  a  computational  model  is  available,  researchers  must  animate  the   diagram  by  mentally  simulating  the  different  operations  and  their  consequences   (sometimes  off-­‐loading  this  effort  by  developing  animated  diagrams).  Such  mental   simulation  lacks  quantitative  precision  and  can  be  highly  fallible.  A  researcher  may   overestimate  the  capabilities  of  a  component  part  or  neglect  important  consequences  of  a   particular  operation,  such  as  how  it  might  alter  another  part.  Moreover,  diagrams   themselves  are  generally  subject  to  revision  and  quite  often  wrong.  Since  their   representational  content  constrains  what  can  be  mentally  simulated,  key  gaps  in  a  diagram   will  yield  inaccurate  simulations.  On  the  positive  side,  the  diagram  helps  the  researcher   keep  track  of  what  must  enter  into  each  stage  of  simulation.  In  short,  diagrams  are  an   imperfect  but  necessary  tool.       A  crucial  step  in  discovering  the  molecular  mechanism  responsible  for  circadian  rhythms   was  Konopka  and  Benzer’s  (1971)  discovery  of  per,  the  Drosophila  gene  whose  mRNA   levels  became  the  focus  of  Hardin,  Hall,  and  Rosbash’s  (1990)  research.  In  addition  to   showing  circadian  oscillations  in  per  mRNA,  Hardin  et  al  ascertained  that  the  PER  protein   also  oscillated  with  a  period  of  approximately  24  hours  but  peaked  several  hours  later  than   per  mRNA.  Hardin  et  al.  recognized  these  oscillations  as  a  circadian  phenomenon  at  the   molecular  level,  but  also  had  the  idea  that  per  mRNA  and  PER  might  be  parts  of  the   mechanism  that  explained  behavioral  circadian  oscillations.  Combining  this  with  their   knowledge  that  negative  feedback  is  a  mode  of  organization  capable  of  producing   oscillations,  they  proposed  three  variations  of  a  molecular  mechanism  whose  oscillatory   dynamics  could  be  responsible  for,  and  thereby  explain,  behavioral  oscillations.    In  all  three   variations,  PER  served  to  inhibit  per  transcription  or  translation  in  a  negative  feedback   loop.  These  are  diagrammed,  somewhat  idiosyncratically,  in  Figure  3.       Sheredos,  Burnston,  Abrahamsen,  and  Bechtel     p.  7     Figure  3.  Hardin  et  al.’s  (1990)  representation  of  three  versions  of  their  proposed   molecular  mechanism  for  circadian  oscillations  in  terms  of  a  negative  feedback  loop.   Question  marks  indicate  points  of  uncertainty  as  to  the  origin  and  termination  of  the   feedback  operation.     As  we  claimed  above,  diagrams  are  not  solely  vehicles  for  communicating  a  proposed   mechanistic  explanation;  they  also  can  serve  as  a  representational  tool  employed  in   reasoning  about  the  proposed  mechanism.  First,  a  diagram  can  be  used  to  envisage  how  a   particular  mechanism  functions  to  produce  a  phenomenon.  In  this  case,  the  phenomenon   involves  regular  oscillations.  To  understand  how  the  mechanism  produces  such  oscillations   a  viewer  would  begin  at  the  upper  left,  where  the  known  operations  of  transcription  into   mRNA  and  translation  into  a  protein  are  portrayed.  These  result  in  the  accumulation  of  PER   molecules,  represented  in  the  diagram  as  a  small  line  drawing  of  one  molecule.  Once  PER   accumulates,  feedback  must  inhibit  either  transcription  or  translation,  thereby  stopping   the  accumulation  of  PER.    The  existing  PER  will  gradually  degrade  (an  operation  not   explicitly  represented,  but  which  molecular  biologists  would  readily  infer).  As  it  degrades,   the  concentration  of  PER  will  decline.  This  will  release  the  transcription  and  translation   processes  from  inhibition,  and  synthesis  of  PER  will  begin  again.  When  repeated,  this  cycle   of  active  and  repressed  per  expression  will  result  in  the  observed  pattern  of  rhythmic   oscillations  in  both  per  mRNA  and  PER.     A  second  major  way  in  which  such  a  diagram  can  serve  reasoning  about  a  mechanism  is  by   making  it  clear  where  there  are  uncertainties  about  its  operations.  Note  how  little  of  Figure   3  is  put  forth  as  a  depiction  of  previous  discoveries  concerning  the  mechanisms  of  per   regulation.  The  bulk  of  the  diagram  serves  as  a  simultaneous  depiction  of  multiple  possible   mechanisms  (sketched  only  in  bare  outline)  that  could  explain  oscillations  of  per  mRNA   and  PER.  The  diagram  is  in  large  part  an  invitation  to  explanation,  not  a  record  of  it.  The   possible  mechanisms  sketched  here  as  (1)  –  (3)  could  each  theoretically  account  for  the   observed  oscillations.  In  (1),  PER  interacts  with  some  biochemical  substrate  or  process  “X”,   Sheredos,  Burnston,  Abrahamsen,  and  Bechtel     p.  8   which  then  somehow  regulates  either  the  per  gene  itself  (transcriptional  regulation),  or  the   transcribed  mRNA  (post-­‐transcriptional  regulation).  In  (2),  X  interacts  with  some  further   substrate  or  process  “Y,”  which  then  does  the  same.  In  (3),  the  behavior  of  the  organism   provides  the  necessary  feedback.  What  is  known  is  only  that  the  mechanism(s)  at  work  in   Drosophila  must  eventuate  in  regulation  of  per  mRNA  abundance.       Third,  the  constraints  presented  by  what  is  presented  in  the  diagram  serve  to  guide   hypothesizing  about  and  investigating  of  further  elements  of  the  proposed  mechanism.   Indeed,  both  the  unknowns  represented  by  the  question  marks  in  Figure  3  and  the   operations  specified  became  the  focus  of  subsequent  research.  For  example,  researchers   sought  not  merely  to  determine  where  PER  fed  back  to  inhibit  formation  of  more  PER,  but   how  it  did  so.  This  and  other  inquiries  quickly  led  to  the  discovery  of  many  additional   components  of  the  mechanism:  by  the  end  of  the  1990s  at  least  seven  different  genes,  as   well  as  their  transcripts  and  proteins,  were  viewed  as  part  of  the  clock  mechanism,  both  in   Drosophila  and  in  mammals.  Many  of  these  were  also  shown  to  oscillate,  but  at  different   phases  than  PER.       As  the  list  of  clock  parts  expanded  and  as  researchers  proposed  multiple  feedback  loops,  it   became  ever  more  crucial  to  be  able  to  represent  how  the  operations  performed  by   individual  parts  affected  other  parts,  and  researchers  regularly  produced  diagrams  to   illustrate  and  guide  their  reasoning.  On  the  left  in  Figure  4  is  a  fairly  typical  contemporary   diagram  of  the  mammalian  circadian  oscillator.    Key  parts  are  indicated  by  upper-­‐case   labels:  italicized  for  genes  vs.  enclosed  in  colored  ovals  for  proteins.  When  proteins  serve   as  transcription  factors,  they  are  shown  attached  to  the  promoter  regions  (E-­‐box,  D-­‐box,   and  RRE)  of  the  respective  genes.       In  using  this  diagram  to  reason  about  the  mechanism,  researchers  follow  the  action  of   individual  proteins  and  the  ways  in  which  they  activate  or  repress  the  expression  of   specific  genes.  At  the  top  right  is  a  further-­‐specified  version  of  the  feedback  loop  first   proposed  by  Hardin  et  al.  in  which  PER  inhibits  its  own  transcription:  it  does  so  by   dimerizing  with  CRY  (Hardin  et  al.’s  substrate  “X”)  and  preventing  the  CLOCK/BMAL1   complex  (Hardin  et  al.’s  substrate  “Y”)  from  upregulating  per  transcription  at  the  E-­‐box   promoter  site.  There  is  also  a  second  feedback  loop  responsible  for  the  synthesis  of  CLOCK   and  BMAL1.  A  second  promoter  site  on  the  per  gene  has  been  identified,  and  its  activator   (DBP)  is  part  of  a  positive  feedback  loop.  It  should  be  obvious  that  as  the  understanding  of   the  mechanism  became  more  complicated,  diagrams  became  ever  more  crucial  both  in   representing  the  mechanism  and  in  reasoning  about  it.  We  should  note  that  research  on   this  mechanism  is  far  from  complete.  The  inhibitory  operations,  in  particular,  are  the  focus   of  important  ongoing  research  that  is  serving  to  identify  yet  additional  parts  and   operations.  Diagrams  such  as  these  serve  not  just  to  represent  and  facilitate  reasoning   about  the  mechanism  but  also  serve  as  guides  to  where  further  investigation  is  required   (even  if  these  are  not  always  explicitly  signaled  by  question  marks).       Sheredos,  Burnston,  Abrahamsen,  and  Bechtel     p.  9     Figure  4.  On  the  left  is  an  example  of  a  common  way  of  representing  the   mechanism  of  the  mammalian  circadian  clock,  labeling  genes  in  black  italics   and  the  proteins  they  express  in  colored  ovals  and  using  arrows  to  represent   feedback  loops  (Zhang  and  Kay  2010).  On  the  right  an  alternative   representation  (Ukai  and  Ueda  2010)  which  places  the  three  promoter  sites   at  the  center.  A  grey  line  from  the  promoter  to  the  gene  indicates  that  the   promoter  site  is  found  on  the  gene,  whereas  green  arrows  from  the  gene  to  a   promoter  box  indicate  that  the  protein  synthesized  from  the  gene  is  an   activator  at  that  promoter  site  and  a  while  a  squared-­‐off  magenta  line   indicates  that  the  protein  in  some  way  inhibits  the  expression  of  the  gene.     Once  a  basic  diagram  format  is  developed  and  researchers  become  familiar  with  its   conventions,  it  is  often  retained  by  other  researchers,  who  introduce  relatively  minor   modifications  to  capture  specific  features  of  a  given  account.  The  choice  of  a  diagrammatic   format  is  not  neutral,  and  researchers  sometimes  find  it  important  to  develop  alternative   formats  that  provide  a  different  perspective  on  the  mechanism.  Ueda,  for  example,  has   introduced  the  alternative  representation  shown  in  the  diagram  on  the  right  side  of  Figure   4.  It  presents  essentially  the  same  information  about  parts  and  operations  as  the  diagram   on  the  left,  but  shifts  attention  away  from  the  genes  and  proteins  to  the  promoter  regions  –   the  three  boxes  placed  in  the  center  of  the  figure.  The  different  genes  that  are  regulated  by   these  promoters  are  shown  in  colored  ovals  in  the  periphery  of  this  diagram.  The  proteins   they  express  are  assumed  but  not  depicted.  The  relation  of  the  boxes  to  the  genes  is   explained  in  the  figure  caption.       Ueda  adopted  this  format  as  part  of  his  argument  that  the  relations  between  the  three   promoter  regions  are  fundamental  to  the  functioning  of  the  clock.  Transcription  factors   bind  to  particular  promoters  at  different  times  of  day:  the  E/E’  box  in  morning,  the  D  box  in   midday,  and  the  RRE  at  nighttime.  For  Ueda,  the  individual  genes  and  proteins  involved  are   just  the  vehicles  via  which  these  promoters  interact.  He  made  this  even  more  explicit  in  the   three  diagrams  shown  in  Figure  5.  Here  he  abstracts  from  the  genes  and  proteins  and   focuses  just  on  the  promoters,  using  arrows  to  indicate  when  products  from  the  sites  serve   to  activate  or  repress  activity  at  another  promoter.  He  shows  all  these  interactions  in  the   diagram  on  the  left,  but  further  decomposes  them  into  two  kinds  of  circuits  (motifs)  in  the   other  two  diagrams.  In  the  middle  is  a  delayed  negative  feedback  motif  in  which  proteins   Sheredos,  Burnston,  Abrahamsen,  and  Bechtel     p.  10   expressed  in  the  morning  regulate  expression  of  other  genes  at  midday,  which  then  repress   the  morning  element.  On  the  right  is  a  repressilator  motif  in  which  products  from  each   element  repress  further  operation  of  the  preceding  element.  Each  of  these  motifs  has  been   the  subject  of  experimental,  computational,  and  synthetic  biology  investigations  that  show   how  they  generate  oscillations  (Ukai-­‐Tadenuma  et  al.  2011).       Importantly,  in  choosing  to  represent  the  mechanism  as  in  Figure  5,  different  aspects  of  its   organization  and  functioning  become  salient.  By  emphasizing  the  overall  structure  of  the   mechanism,  the  overlapping  oscillations  are  made  more  salient  at  the  expense  of  detail   about  the  proteins  involved  in  the  regulatory  processes.  These  different  contents  provide   different  constraints  on  the  reasoning  that  can  be  performed  by  way  of  the  diagram,  and   can  lead  to  different  insights  about  the  mechanism  itself,  thus  helping  to  provide  a  more   complete  explanation  of  the  phenomenon.         Figure  5.  Hogenesch  and  Ueda’s  (2011)  diagrams  that  abstract  from  the  genes  and   proteins  of  the  circadian  oscillator  to  identify  the  basic  causal  circuit  (left),  which  he   then  decomposes  into  two  motifs  (center  and  right)  that  are  viewed  as  explaining   the  oscillatory  behavior  of  the  mechanism.       5.  Conclusion:  Diagrams  and  Mechanistic  Explanation       A  major  explanation  for  the  prevalence  of  diagrams  in  biology  is  the  role  they  play  in   mechanistic  explanation.  We  have  focused  on  their  role  in  two  pursuits—delineating  a   phenomenon  of  interest  and  constructing  mechanistic  accounts  to  explain  the  phenomenon.   A  number  of  diagrams  may  be  generated  in  making  progress  from  an  initial  account  to  the   one  proposed  in  public.  Each  specifies  the  parts,  operations,  and  organization  of  the  current   conception  of  the  mechanism.  Diagrams  also  play  other  roles  in  mechanistic  explanation.   For  example,  even  modestly  complex  mechanisms,  such  as  those  involving  negative   feedback  loops,  challenge  the  ability  of  theorists  to  figure  out  their  behavior  by  mentally   rehearsing  their  interactions.  To  visualize  dynamic  phenomena,  scientists  often  resort  to   other  types  of  diagrams,  such  as  phase  spaces  in  which  oscillations  appear  as  limit  cycles.   Such  diagrams  abstract  from  mechanistic  details  to  portray  how  the  overall  state  of  the   system  changes  over  time.       Having  identified  important  roles  diagrams  play  in  biology,  we  conclude  by  noting  three   ways  in  which  analysis  of  diagrams  contributes  to  philosophy  of  science.  We  have  begun  to   address  the  first:    from  diagrams  we  can  gain  a  (partial)  understanding  of  how  scientists   reason  about  a  phenomenon,  specifically  by  simulating  the  understood  elements  of  a   mechanism  encoded  in  a  diagram  to  see  if  they  are  adequate  to  explain  the  phenomenon.     Second,  diagrams  can  serve  as  a  vehicle  for  understanding  scientific  change  when  we   analyze  how  the  diagrams  within  a  field  evolve,  find  acceptance,  and  are  eventually   Sheredos,  Burnston,  Abrahamsen,  and  Bechtel     p.  11   discarded.  Third,  identifying  the  cognitive  elements  of  diagram  use,  including  their  design   and  the  learning  processes  required  to  interpret  them,  can  provide  insight  into  the   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