Computational insights into Caenorhabditis elegans vulval development

Abstract

Studies of Caenorhabditis elegans vulval development provide a paradigm for pattern formation during animal development. The fates of the six vulval precursor cells are specified by the combined action of an inductive signal that activates the EGF receptor mitogen-activated PK signaling pathway (specifying a primary fate) and a lateral signal mediated by LIN-12/Notch (specifying a secondary fate). Here we use methods devised for the engineering of complex reactive systems to model a biological system. We have chosen the visual formalism of statecharts and use it to formalize Sternberg and Horvitz's 1989 model [Sternberg, P. W. & Horvitz, H. R. (1989) Cell 58, 679-693], which forms the basis for our current understanding of the interaction between these two signaling pathways. The construction and execution of our model suggest that different levels of the inductive signal induce a temporally graded response of the EGF receptor mitogen-activated PK pathway and make explicit the importance of this temporal response. Our model also suggests the existence of an additional mechanism operating during lateral specification that prohibits neighboring vulval precursor cells from assuming the primary fate.

Fig. 1.

Model for gene interactions during vulval induction. (A) Arrows represent activation, and bars represent inhibition. 1⁰, 1⁰-specific functions; 2⁰, 2⁰-specific functions; 3⁰, 3⁰-specific functions; LS, lateral signal. (B) ON, function is active; (ON), function is partially active; OFF, function is inactive. The thickness of each arrow indicates the strength of the interaction. [Reproduced with permission from ref. (copyright 1989), with permission from Elsevier.]

Fig. 2.

The statechart of the AC. Rectangles represent states, and arrows represent transitions. A short arrow exiting a small circle marks the initial state of the object. The circled C denotes a condition between two states. A transition from a condition is taken if the guard is true.

Fig. 3.

The statechart of the VPC. (A) The high-level statechart of the VPC. Areas separated by dashed lines are orthogonal components; i.e., the VPC is present in all these components simultaneously. (B) The VulNotMutated substate. A zoom into the VulNotMutated state shows the various states and actions present within this state.

Fig. 4.

Additional mechanism governing the lateral specification. Experimental results were compared with simulation results of Muv mutation in the presence (A) and absence (B) of AC.

Fig. 5.

Timing of events that occur in response to the different levels of inductive signal. This sequence diagram specifies a proposed order of events leading to VPC fate specification. Time flows from top to bottom. Two events on the same vertical line are ordered according to the time flow. The horizontal dashed lines synchronize the different vertical lines. All events above a synchronization line occur before an event below the synchronization line. The time order between two events on parallel vertical lines without a synchronization line is unknown. The drawing is not to scale; i.e., a longer distance between two events does not necessarily mean that the time elapsed between them is longer. The left time line starts with a high inductive signal, the middle time line starts with a medium inductive signal, and the right time line starts with no inductive signal. Events shown in black represent wild-type behavior. The event shown in gray (“reduce ability to respond to lateral signal”) would occur in an isolated VPC (i.e., if the lateral signal is not received and does not trigger LIN-12 activation). In the abstraction level used, an event occurs when the system reaches a threshold that triggers an effective response.