Biochemistry Examples

[paulflang]

This PR adds examples from

• https://github.com/ToposInstitute/sys-bio-collab/pull/15
• https://github.com/ToposInstitute/sys-bio-collab/blob/main/notes/examples/Incremental%20Examples.md

After merging this PR and #1 , it might make sense to create a separate file to store all example models.

The following lists a few characteristics, learnings and TODOs (not for this PR) about each example:

toy_model_species_granularity

is inspired by examples 1 and 3 here. It tests:

• describing a model with only a single agent (of a terminal type ReMonomer)
• morphisms with nontrivial domain (i.e. other than [])
• composite morphisms
• customizing species granularity (i.e. ReB vs. ReB1 and ReB2)

Learnings:

• We can already reuse one and the same model description for both cases. The only difference is how we define the Signature.
• This example also makes heavy use of PatTm::Tensors, which we cannot restrict via PatTm::res, IIUC. Instead, we use the .subst method to replace a partial restriction with a "longer" composite restriction.
• When we define variables for later use in the rules, we need to work with .clone. This is a bit unergonomic, but will be obsolete once models can be parsed from bare text.

toy_model_emergent_agent

• illustrates emergent behavior: C-binding is only possible (in the sense of reachable) after A to B dimerization. Neither A nor B alone can bind C.
• trimerization (implemented as nested PatTm::Let)

Open questions:

• I see one way in which the rule R_dimerization can be restricted. R_trimerization already lives in []. Yet, there are weird nameless transitions like this one generated, that also contain R_dimerization. Why is that?

toy_model_directionality

• implements monomers with head and tail sites; written, such that rules are agnostic if the monomer is free or at the end of a long chain; reachable states should be identical to the previous example (except maybe for asymmetry in C).

Personal learnings on notation:

• It seems to be more convenient to reuse the variables for agent sites in let/bond expressions (rather than replacing with generic s1 and s2)
• Identities appear as variables of the rules. To facilitate readability of more complex rules. To facilitate readability of complex rules, it makes sense to prefix them with "id_" or "1". This helps to distinguish them from (non-trivial) restrictions.

TODO:

• Look at the transitions after the open question from the previous example is clarified.
• R_AtoB_dimerization is of type [head, Site_C, Site_C, tail]. Starting from only monomers, this should lead to the same reachable states as if the type were [head, tail], since there is no rule producing AC and BC dimers (remark: this is just for experimentation. In practice, rules should not rely on reachability assumptions and be specified in the most restrictive way possible, to minimize unintended side-effects (esp. when knowledge from different authors is combined) and computational complexity). Test if this is true, once we can restrict to reachable states.

toy_model_phospho_tyrosine

tests:

• morphisms with nontrivial domain (i.e. other than [])
• composite morphisms
• indexing category with parallel morphisms out of objects other than [].

Learnings

• Parallel restriction morphisms would split up (i.e. have different domains) in a preorder setting. This will require handling different types on LHS and RHS of rules.

[paulflang]

I think we need emergent sites for this, as described here: https://github.com/ToposInstitute/sys-bio-collab/pull/15

This would make sure that C-binding ability emerges from A-to-B dimerization.

[paulflang]

I think the problem is that (M [iota_B], M [iota_SiteA [0.0]]) is not indecomposable. To generate indecomposable agents from monomers, we'd need something like emergent sites and species, as described here: https://github.com/ToposInstitute/sys-bio-collab/pull/15

[paulflang]

@epatters any thoughts on the last two comments? Otherwise I believe this is ready to merge.