Math­e­mat­i­cal Model

Dif­fer­ent mod­els have pre­vi­ously been devel­oped to describe the propul­sion of pathogens, but with­out knowl­edge of the orga­ni­za­tion of the fil­a­ments involved in push­ing. In a new mod­el­ling approach we sought to sim­u­late the struc­ture of actin comets dri­ving bac­ulovirus obtained by elec­tron tomog­ra­phy as well as the paths fol­lowed by bac­ulovirus in host cell cyto­plasm. For details of the math­e­mat­i­cal model, see Mueller et al., 2014 (Text S1).

Three sce­nar­ios of fil­a­ment inter­ac­tions with the sur­face of the virus were con­sid­ered: (A), con­tin­u­ous teth­er­ing of fil­a­ments dur­ing push­ing; (B), teth­er­ing only dur­ing the ini­ti­a­tion of a branch at the filament-virus inter­face; and ©, no teth­er­ing dur­ing push­ing.

The video shows math­e­mat­i­cal sim­u­la­tions of bac­ulovirus propul­sion gen­er­ated accord­ing to two of the sce­nar­ios above: Con­tin­u­ously teth­ered and unteth­ered fil­a­ments. The case for fil­a­ments teth­ered only dur­ing branch­ing resem­bled closely the case for unteth­ered fil­a­ments (Mueller et al., 2014).

An impor­tant fea­ture of the model was the require­ment of inter­mit­tent nucle­ation (or cap­ture) of fil­a­ments at the virus sur­face to cor­rect for a sto­chas­tic paucity of fil­a­ment ends engaged in push­ing. With­out this fea­ture motion was irreg­u­lar. An addi­tional con­se­quence of this fea­ture was the gen­er­a­tion of fil­a­ment sub­sets, whose exis­tence was sug­gested from fil­a­ment track­ing in the tomo­grams.

Related Pub­li­ca­tions

  • Mueller J, Pfanzel­ter J, Win­kler C, Narita A, Le Clainche C, Nemethova M, Car­lier MF, Maeda Y, Welch MD, Ohkawa T, Schmeiser C, Resch GP, Small JV. Elec­tron tomog­ra­phy and sim­u­la­tion of bac­ulovirus actin comet tails sup­port a teth­ered fil­a­ment model of pathogen propul­sion. PLoS Biol. 2014 Jan;12(1):e1001765. PDF NCBI PubMed