1. Representing Development David Osumi-Sutherland – FlyBase Fabian Neuhaus - National Institute of Standards and Technology

2. Stage Campos-Ortega and Hartenstein, 1997 VNE = Ventral neurectoderm

3. Neuroblast delamination from the ventral neurectoderm Neuroblast ganglion mother cell Ventral neurectoderm cells { Ventral Neurectoderm (VNE)‏ Figure from Doe, 1992, Development:116

4. Stage ventral nerve cord primordium (ganglion mother cell)‏ Campos-Ortega and Hartenstein, 1997

5. Stage ventral nerve cord primordium Campos-Ortega and Hartenstein, 1997

6. late stage 8 stage 10 early ES10 late stage 11 Neuroblast delamination from VNE to VNC primordium Each circle is a specific neuroblast (NB) type Colours denote gene expression Figure from Doe, 1992, Development:116

7. Development of U2 neuron U2 neuron GMC 7-1b during stage 12 NB7-1 VNE during stage 8 during stage 9 VNC prim VNC during stage 17 develops_from part Stage specific part relations such as these cannot be recorded using standard OBO relations

8. Limitations of current system ES8ES9ES10ES11ES12 GMC VNC prim GMC 7-1b is_a part ganglion mother cell GMC 7-1bneuroblast NB 7-1 develops_from neuroblast NB7-1 is_a neuroblast is_a ganglion mother cell (GMC) NB7-1 develops_from Needed – system to connect anatomy to stage Needed – system for capturing these stage specific part relations time ES = embryonic stage

9. 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

10. 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

11. x p α(x)‏ ω(x)‏ ω(p)‏ α(q)‏ Timing relations between instances of occurrents, continuants Events: α(p) - beginning of p ω(p) - end of an p axiom: 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)‏

12. 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.

13. Drosophila Oogenesis

14. 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.

15. 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))‏

16. 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))) )).

17. Division of reference process into a reference scale ES7ES8ES9ES10 time ES6 cellular- ization stomodeal invagination gastrulation 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 ES 5

18. 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)))))‏

19. 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

20. ES8ES9ES10ES11ES12 GMC first_exists_during embryonic stage 8 (ES8): some instance of GMC starts to exist during* all instances of ES8 AND All 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-view omitting timing relationships Timing relations between types Time

21. is_a inheritance of timing ES8ES9ES10ES11ES12 GMCGMC 7-1b is_a ganglion mother cell (GMC)‏ first_exists_during embryonic stage 8 (ES8)‏ ganglion mother cell GMC 7-1b all_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-view omitting timing relationships

22. 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)) )))‏

23. 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

24. ES8ES9ES10ES11ES12 GMC VNC prim GMC 7-1b is_a part* We can’t record has_part here Y has_part X: some X part_of all Y, no matter what stage. DAG – graph-view omitting timing relationships

25. ES13ES14ES15ES16ES17 VNC prim U2 neuron VNC develops_from time ES12 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

26. 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

27. time_restricted_integral_part_of (C tr_part_of D) ↔ (C is_a Continuant & D is_a Continuant & ∀ c ∀ t (C (c, t) → ∃ d( ∃ t ₁ D( d, t ₁ ) & (c part_of d at t ₁ )) & ∀ t ₂ ((c exists_at t ₂ ) & (d exists_at t ₂ ) →(c part_of d at t ₂ ))))). ( C tr_has_part D) ↔ (C is_a Continuant & D is_a Continuant & ∀ c ∀ t (C (c, t) → ∃ d( ∃ t ₁ D( d, t ₁ ) & (d part_of c at t ₁ )) & ∀ t ₂ ((c exists_at t ₂ ) & (d exists_at t ₂ ) →(d part_of c at t ₂ ))))). C tr_integral_part_of D ↔ (C tr_part_of D & D tr_has_part C )‏

28. ES8ES9ES10ES11ES12 GMC VNC prim GMC 7-1b is_a tdi_part_of DAG – graph-view omitting 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 7-1b develops_from neuroblast NB7-1 all_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)‏

29. ES13ES14ES15ES16ES17 VNC prim U2 neuron develops_from ganglion mother cell GMC 7-1b is_a motor neuron tdi_part_of ventral nerve cord primordium tdi_part_of ventral nerve cord all_begin_to_exist_during embryonic stage 13 (ES13)‏ GMC 7-1b develops_from VNC tdi_part_of develops_from time ES12