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Representing Development
David Osumi-Sutherland – FlyBase
Fabian Neuhaus - National Institute of Standards and Technology
Stage
Campos-Ortega and Hartenstein, 1997
VNE = Ventral neurectoderm
Neuroblast delamination from the ventral neurectoderm
Neuroblast
ganglion mother cell
Ventral neurectodermcells
{Ventral Neurectoderm
(VNE)
Figure from Doe, 1992, Development:116
Stage
ventral nerve cord primordium
(ganglion mother cell)
Campos-Ortega and Hartenstein, 1997
Stage
ventral nerve cord primordium
Campos-Ortega and Hartenstein, 1997
late stage 8 stage 10
early ES10
late stage 11
Neuroblast delamination from VNE to VNC primordium
Each circle is a specific neuroblast (NB) typeColours denote gene expression
Figure from Doe, 1992, Development:116
Development of U2 neuron
U2 neuronGMC 7-1b
during stage 12
NB7-1VNE
during stage 8 during stage 9
VNC prim VNC
during stage 17develops_from
part
Stage specific part relations such as these cannot be recorded using standard OBO relations
Limitations of current system
ES8 ES9 ES10 ES11 ES12
GMC
VNC prim
GMC 7-1bis_a
part part
ganglion mother cell GMC 7-1b neuroblast NB 7-1develops_from neuroblast NB7-1 is_a neuroblastis_a ganglion mother cell (GMC)
NB7-1
develops_from
Needed – system to connect anatomy to stage
Needed – system for capturing thesestage specific part relations
time
ES = embryonic stage
What is developmental time?
In any developmental process, (e.g.- development of a whole organism) many events happen in an invariant order.
These events can be used as markers of developmental progress or time. This is the basis of many standard stage series.
These marker events can be the birth, death, or transformation an anatomical structure. the beginning, end and key point in a developmental processes
System for ordering events
Events are treated as instants – they have no time dimension.
There are only 2 types of timing relationships between event instances (e, f):
e before f (<)
e simultaneous f (≈)
both can be derived from
before_or_simultaneous_ with (≤) :
definition: e<f := e≤f AND NOT f≤e
definition: e≈f := e≤f AND f≤e
x
p
α(x) ω(x)ω(p)α(q)
Timing relations between instances of occurrents, continuants
Events:α(p) - beginning of pω(p) - end of an paxiom: α(o) before ω(o)Time
x starts_during p := (α(p) before α(x)) AND (α(x) before ω(p))
q
α(p) ω(q)
Reference Processes
The invariability of the order of two events is always relative to some reference process: X before Y during oogenesis many instances of oogenesis occur in parallel in an
adult female, but with no shared starting time so, relative to the life of an adult female, X and Y
have no invariant order.
Drosophila Oogenesis
Ternary relations ?
Reference processes could be recorded using ternary relations (A before B during C...)
But these are not supported in OWL or OBO, or by their respective editing tools – Protege and OBO-Edit.
How to avoid using ternary relations
For each type for which timing is to be captured – record a reference occurrent.
A reference_occurrent B := all Continuant or Occurrent types have only one
reference process. all occurrents occur only once during their
reference process if Aa is an occurrant, then a part_of
(ref_occurrant(a)) if Aa is a continuant, then a participates_in
(ref_occurrant(a))
referenceoccurrent(x, y) -> (Universal(x) & is_a(y,Occurrent)).
referenceoccurrent(x, y) & referenceoccurrent(x, z) -> (y =z).
referenceoccurrent(x, y) & is_a(x,Occurrent) ->
all x1 (I(x, x1) ->
(I(y, refoccurrent(x1))
& ilo_part(x1,refoccurrent(x1))
& all y1 (I(y,y1) & ilo_part(x1, y1) -> (y1 = refoccurrent(x1)))
)).
referenceoccurrent(x, y) & is_a(x,Continuant) ->
all x1 (I(x, x1) ->
(I(y, refoccurrent(x1))
& participates_in(x1,refoccurrent(x1))
& all y1 (I(y,y1) & participates_in(x1, y1) -> (y1 = refoccurrent(x1)))
)).
Division of reference process into a reference scale
ES7 ES8 ES9 ES10
time
ES6
cellular-ization
stomodeal invaginationgastrulation
germ band extension TP invagination
Stage
Unique Process
gastrulation reference_occurrent embryogenesis
embryonic stage 5 reference_occurrent embryogenesis
gastrulation begins_at_end_of embryonic stage 5
stomodeal invagination begins_at_end_of embryonic stage 9
ES5
begins_at_end_of – formal def
O begins_at_end_of P
↔ (O is_a Occurrent
& P is_a Occurrent
& o (O(o)∀
→ ∃ p (P(p)
& refoccurrent(o) = refoccurrent(p)
&(omega(p) ≈ alpha(o)))))
List of type level relations - 1
unique*1 Occurrent to unique Occurrent begins_at_end_of begins_during ends_during begins_before ends_after simultaneous_with * happens_during **1 Unique here means, happens only once during reference process
*2 non-essential but reduces number of relationships needed
ES8 ES9 ES10 ES11 ES12
GMC first_exists_during embryonic stage 8 (ES8):some instance of GMC starts to exist during* all instances of ES8 ANDAll instances of GMC (start to exist during* ES8 OR start to exist after the end of some instance of ES8)
*during is shorthand for 'the start of X is after the start of Y and before the end of Y'
GMC
DAG – graph-viewomitting timing relationships
Timing relations between types
Time
is_a inheritance of timing
ES8 ES9 ES10 ES11 ES12
GMCGMC 7-1bis_a
ganglion mother cell (GMC)first_exists_during embryonic stage 8 (ES8)ganglion mother cell GMC 7-1ball_begin_to_exist_during embryonic stage 9 (ES9)all_cease_to_exist_during embryonic stage 12 (ES12)is_a ganglion mother cell (GMC)
DAG – graph-viewomitting timing relationships
all_begin_to_exist_during – formal definition
C all_begin_to_exist_during O
↔ (C is_a Continuant
& O is_a Occurrent
& c t ( C (c,t)∀ ∀
→ ∃ o
( O(o)
& refoccurrent(c) = refoccurrent(o)
& (alpha(o) ≤ alpha(c))
& (alpha(c) ≤ omega(o)))))
List of type level timing relations - 2 unique*1 occurrent to non-unique continuant:
first_exists_during last_exists_during all_begin_to_exist_during *2
all_cease_to_exist_during *2
begins_to_exist_at_end_of begins_to_exist_after ceases_to_exist_before exists_only_during *2
*1 Unique here means, happens only once during reference process
*2 non-essential but reduced number of relationships needed
ES8 ES9 ES10 ES11 ES12
GMC
VNC prim
GMC 7-1bis_a
part* part*
We can’t record has_part here
Y has_part X: some X part_of all Y, no matter what stage.
DAG – graph-viewomitting timing relationships
ES13 ES14 ES15 ES16 ES17
VNC prim
U2 neuron
VNC
develops_from
time
ES12
part* part*
We can’t record part_of here
FALSE:Y part_of X: all U2 neuron part_of some VNC prim, for all stages that U2 neuron exists
Solution to the part problem:time_restricted_integral_part_of
(tri_part_of)
For any time point where some instance of X and some
instance of Y exist:
All instances of X part_of some instance of Y
AND
Some instance of X part_of all instances of Y
time_restricted_integral_part_of(C tr_part_of D)
↔ (C is_a Continuant
& D is_a Continuant
& ∀c ∀t (C (c, t)
→ ∃d (∃t₁ D( d, t₁) &(c part_of d at t₁)) &
∀t₂ ((c exists_at t₂) & (d exists_at t₂) →(c part_of d at t₂))))).
( C tr_has_part D)
↔ (C is_a Continuant
& D is_a Continuant
& ∀c ∀t (C (c, t)
→ ∃d (∃t₁ D( d, t₁) &(d part_of c at t₁)) &
∀t₂ ((c exists_at t₂) & (d exists_at t₂) →(d part_of c at t₂))))).
C tr_integral_part_of D ↔ (C tr_part_of D & D tr_has_part C )
ES8 ES9 ES10 ES11 ES12
GMC
VNC prim
GMC 7-1bis_a
tdi_part_ofDAG – graph-viewomitting timing relationships
tdi_part_of
NB7-1
develops_from
ganglion mother cell (GMC)first_exists_during embryonic stage 8 (ES8)tdi_part_of ventral nerve cord primordium (VNC prim)ganglion mother cell GMC 7-1bdevelops_from neuroblast NB7-1all_begin_to_exist_during embryonic stage 9 (ES9)all_cease_to_exist_during embryonic stage 9 (ES9)tdi_part_of ventral nerve cord primordium (VNC prim)
ES13 ES14 ES15 ES16 ES17
VNC prim
U2 neuron
U2 neurondevelops_from ganglion mother cell GMC 7-1bis_a motor neurontdi_part_of ventral nerve cord primordiumtdi_part_of ventral nerve cordall_begin_to_exist_during embryonic stage 13 (ES13)
GMC 7-1b
develops_from
VNC
tdi_part_oftdi_part_of
develops_from
time
ES12