The Min Sys­tem: All the Places You'll Go!

by Veron­ica W. Rowlett

Most bac­te­ria di­vide quite pre­cisely and their daugh­ter cells are of­ten the same size. The rea­son for this ac­cu­racy is not re­ally known, but it must be im­por­tant be­cause it is such a fre­quent phe­nom­e­non. This re­quires good mea­sur­ing sticks, sys­tems that cal­cu­late dis­tance from the ends and re­strict the for­ma­tion of the di­vi­sion site to the mid­dle of a di­vid­ing cell. In Es­cherichia coli, two sys­tems are known to help con­tribute to mid­cell po­si­tion­ing of the di­vi­sion ma­chin­ery: nu­cleoid oc­clu­sion, which pre­vents the scaf­fold pro­tein FtsZ from form­ing rings over nu­cleoids, and the Min sys­tem. Even with the help of these mech­a­nisms, the ques­tion of how a bac­terium finds its cen­ter so pre­cisely is still enig­matic.

Fig­ure 1. Min os­cil­la­tion in E. coli. The nu­cleoid is shown as a blue oval. Source

The os­cil­lat­ing Min sys­tem of Es­cherichia coli

The Min sys­tem is named for the phe­no­type of cells when it is dis­rupted. In cells that lack Min pro­teins, FtsZ forms rings at all nu­cleoid free re­gions in the cell, in­clud­ing at the cell poles. This re­sults in di­vi­sions oc­cur­ring ei­ther at mid­cell or at cell poles, cre­at­ing "minicells" that lack nu­cleoids and longer, nu­cle­ated cells. E. coli con­tains an ar­ray of three Min pro­teins, MinC, MinD, and MinE that self-or­ga­nize to os­cil­late back and forth be­tween the ends of the cells to pre­vent FtsZ from form­ing rings at cell poles. This is how it works: MinC in­hibits the as­sem­bly of FtsZ into rings. MinC is re­cruited to the mem­brane by MinD, which it­self binds the mem­brane as an ATP-con­tain­ing dimer. Fur­ther, MinE forms a mem­brane-bound ring that moves to­ward com­plexes of MinC-MinD and in the process dis­places MinC from MinD. It also stim­u­lates the AT­Pase ac­tiv­ity of MinD, causes it to dis­so­ci­ate from the mem­brane, and to move to­ward the op­po­site pole. MinE can re­main on the mem­brane to re­move ad­di­tional com­plexes, or dis­so­ci­ate from the mem­brane along with MinD to cy­cle to the op­po­site pole. The os­cil­la­tion of this sys­tem keeps the con­cen­tra­tion of MinC high­est at cell poles and low­est at mid­cell, al­low­ing FtsZ ring for­ma­tion at their nor­mal site at mid­cell. Over the years, sev­eral pat­terns of Min os­cil­la­tion have been ob­served that dif­fer from the nor­mal pole-to-pole pat­tern of wild-type cells. These pat­terns emerge in short, long, and even branched cells and have in­spired the de­vel­op­ment of com­pu­ta­tional mod­els to pre­dict the pat­tern of Min sys­tem os­cil­la­tion un­der var­i­ous con­di­tions.

Com­pu­ta­tional mod­els of os­cil­la­tion

Fig­ure 2. E. coli mini­cells in a ∆min strain. Photo: William Mar­golin

Sev­eral com­pu­ta­tional mod­els have been pro­duced over the past decade to bet­ter un­der­stand the dy­namic Min sys­tem. These mod­els are based on ex­per­i­men­tal data and al­low es­ti­ma­tion of how the sys­tem would change un­der a va­ri­ety of con­di­tions. They can then be con­firmed by fur­ther ex­per­i­ments. As in other fields, two types of mod­els can of­ten be cre­ated in bi­ol­ogy: de­ter­min­is­tic and stochastic.In de­ter­min­is­tic mod­els, the state of the sys­tem is de­fined by the den­sity of pro­teins and their change over time.  In sto­chas­tic mod­els the state of the sys­tem is de­fined by the po­si­tion of in­di­vid­ual mol­e­cules and the lo­ca­tion of these mol­e­cules is de­ter­mined prob­a­bilis­ti­cally. Pre­vi­ous mod­els have in­cor­po­rated the idea that Min pro­tein os­cil­la­tion oc­curs due to dy­namic in­sta­bil­ity, mean­ing that a ho­mo­ge­neous cel­lu­lar dis­tri­b­u­tion of Min pro­teins is un­sta­ble. These mod­els have con­sid­ered the co­op­er­a­tive mem­brane bind­ing of MinD and the ac­tiv­ity of MinE to re­move MinD from the mem­brane.

Re­cently, Bonny et al. pro­posed and tested an up­dated model that ac­counts for the abil­ity of MinE to form com­plexes with MinD, bind the mem­brane, and ei­ther leave the mem­brane with MinD or re­main bound. This model does not in­clude MinC, which, for this con­sid­er­a­tion, is sim­ply along for the ride. It also only con­sid­ers MinD dimers, dimer­iza­tion be­ing re­quired for mem­brane bind­ing. For this model, equa­tions rep­re­sent­ing re­ac­tion schemes that con­sider pro­tein con­cen­tra­tion, dif­fu­sion rates, and mem­brane binding/dissociation of MinD and MinE were solved for a cylin­dri­cal do­main with hemi­spher­i­cal caps, a proxy for the shape of an E. coli cell.

These com­pu­ta­tional mod­els con­firm pat­terns that were pre­vi­ously ob­served both in vivo and in vitro and ac­cu­rately pre­dict two ad­di­tional pat­terns. Sim­u­la­tions for a typ­i­cal sized E. coli cell are shown in Fig­ure 3. Both the de­ter­min­is­tic and sto­chas­tic mod­els show a stand­ing wave pat­tern of Min os­cil­la­tion con­sis­tent with pre­vi­ous ob­ser­va­tions. This pat­tern de­scribes Min pro­teins that bind the mem­brane at one pole, are re­moved, and travel through the cy­to­plasm to bind the mem­brane at the op­po­site pole. This stand­ing wave pat­tern, also com­monly re­ferred to as pole-to-pole os­cil­la­tion, will oc­cur in cells that are less than or equal to 5 mi­crom­e­ters in length, roughly the size of a typ­i­cal E. coli cell. How does the Min sys­tem be­have when cells are elon­gated and/or the Min pro­tein con­cen­tra­tion in­creases?

Fig­ure 3. Com­pu­ta­tional mod­els of Min os­cil­la­tion in a cell of nor­mal length (3.8 µm). The top model is a de­ter­ministic sys­tem and the bot­tom model is a sto­chas­tic sys­tem. Be­low are ky­mo­graphs cor­re­spond­ing to the po­si­tion of the pro­teins over time. Source

To an­swer this ques­tion, the au­thors present a phase di­a­gram (Fig. 4) that shows how the com­po­nents of the Min sys­tem vary as a func­tion of to­tal MinD con­cen­tra­tion and cell length, while keep­ing a con­stant MinD:MinE ra­tio. In this di­a­gram, red tri­an­gles rep­re­sent pole-to-pole os­cil­la­tions ob­served in cells of nor­mal length. Green cir­cles rep­re­sent trav­el­ing waves that have been ob­served in longer cells and with in­creas­ing MinD con­cen­tra­tion. In a trav­el­ing wave state, Min pro­teins as­sem­ble at one pole and travel through the mem­brane to the op­po­site pole where they de­tach from the mem­brane and travel through the cy­to­plasm back to the orig­i­nal pole. Both of these os­cil­la­tion pat­terns con­tain one node (the cen­ter of the os­cil­lat­ing wave). Light blue squares rep­re­sent stand­ing waves with two nodes. This pat­tern is ob­served when a cell is elon­gated prior to di­vi­sion and a sin­gle Min os­cil­la­tion (one node) be­comes two Min os­cil­la­tions (two nodes), one in each daugh­ter cell. Yel­low pen­tagons rep­re­sent spa­tially het­ero­ge­neous steady states ob­served in short cells. In short cells with higher MinD con­cen­tra­tions, Min pro­teins do not os­cil­late, but in­stead switch sto­chas­ti­cally from pole to pole. Dark blue di­a­monds and pur­ple tri­an­gles rep­re­sent stand­ing waves with three and four nodes, re­spec­tively. These ad­di­tional nodes ap­pear as the cell length in­creases when the con­cen­tra­tion of MinD is low.

Over­all, as the length of cells in­crease when the con­cen­tra­tion of MinD is low, a sin­gle Min os­cil­la­tion will be­come mul­ti­ple Min os­cil­la­tions (one to four nodes). As the con­cen­tra­tion of MinD is in­creased, cells of nor­mal length re­tain pole-to-pole os­cil­la­tion, longer cells mostly ex­hibit a trav­el­ing wave pat­tern, and short cells lose an os­cil­la­tion pat­tern. Min pro­teins have been shown to self-or­ga­nize into a wave pat­tern in vitro on sup­ported lipid bi­lay­ers and this pat­tern was also pre­dicted us­ing the com­pu­ta­tional model.

Fig­ure 4. Phase di­a­gram of Min pro­tein pat­terns for var­ied MinD con­cen­tra­tions and cell length. Source

The model con­cludes that the mem­brane bind­ing of MinE is an es­sen­tial com­po­nent when de­scrib­ing dif­fer­ent Min pat­terns formed based on pro­tein con­cen­tra­tion and cell mor­phol­ogy. This model com­pre­hen­sively de­scribes Min pat­terns ob­served in vivo and in vitro and brings us closer to bet­ter un­der­stand­ing the be­hav­ior of Min pro­teins, which should emerge from ad­di­tional stud­ies of the mol­e­c­u­lar de­tails of the Min pro­teins. The ad­di­tion of the mem­brane dy­nam­ics of MinE to com­pu­ta­tional mod­els is in­deed "MinD" bog­gling as new pat­terns of lo­cal­iza­tion emerge, high­light­ing the com­plex­ity of the Min sys­tem. This model can be used to de­sign new in vivo or in vitro ex­per­i­ments. Also, this work can con­tribute to the field of syn­thetic bi­ol­ogy in pur­suit of syn­the­siz­ing what is min­i­mally re­quired for a bac­te­r­ial cell. Ad­di­tional ex­per­i­men­ta­tion is nec­es­sary to fur­ther re­fine the model of Min os­cil­la­tion, but it is ex­cit­ing to see that com­pu­ta­tional mod­els have ac­cu­rately pre­dicted pat­terns of Min lo­cal­iza­tion that oc­cur in vivo and in vitro on sup­ported lipid bi­lay­ers.

Min sys­tems and other reg­u­la­tors of FtsZ in di­verse bac­te­r­ial species

Sev­eral species of bac­te­ria con­tain ho­mologs of Min pro­teins, but some bac­te­r­ial Min sys­tems be­have dif­fer­ently from that of E. coli. For ex­am­ple, the well-stud­ied Gram-pos­i­tive bac­terium Bacil­lus sub­tilis has ho­mologs to MinC and MinD, but lacks MinE. In this sys­tem, MinC and MinD are teth­ered to both cell poles to pre­vent FtsZ ring for­ma­tion at newly formed cell poles with­out the need for os­cil­la­tions. The Gram-neg­a­tive bac­terium He­li­cobac­ter py­lori con­tains ho­mologs of MinD and MinE, but lacks MinC and has less pre­cise FtsZ ring place­ment than E. coli, in­di­cat­ing that Min pro­teins likely have a dif­fer­ent func­tion in this species.

Other species such as My­cobac­terium tu­ber­cu­lo­sis lack Min ho­mologs. M. tu­ber­cu­lo­sis has a very slow dou­bling time when com­pared with E. coli (~15 hours vs. 20 min­utes), di­vides asym­met­ri­cally, and sis­ter cells dif­fer in length. Caulobac­ter cres­cen­tus lacks Min ho­mologs, but con­tains a neg­a­tive reg­u­la­tor of FtsZ, MipZ, which forms a gra­di­ent to re­strict FtsZ ring for­ma­tion to mid­cell. In other species there are also pos­i­tive reg­u­la­tors of FtsZ ring for­ma­tion that lo­cal­ize to mid­cell and re­cruit FtsZ to that site. These in­clude SsgA and SsgB of Strep­to­myces coeli­color and PomZ of Myx­o­coc­cus xan­thus.

Why do dif­fer­ent species have dif­fer­ent sys­tems to reg­u­late FtsZ ring for­ma­tion? It is likely that bac­te­ria use sys­tems that are "good enough" for them to thrive in their re­spec­tive en­vi­ron­ments. Since E. coli is found in the nu­tri­ent rich colon, it may be that it can af­ford to use more en­ergy for this ex­pen­sive os­cil­lat­ing sys­tem. How­ever, there may be more vari­a­tions on these themes. In ad­di­tion to the known pos­i­tive and neg­a­tive reg­u­la­tors of FtsZ, it is likely that ad­di­tional fac­tors have yet to be iden­ti­fied. As the model of Min sys­tem os­cil­la­tion and other reg­u­la­tors of FtsZ ring place­ment con­tinue to be re­fined and in­ves­ti­gated, we should bet­ter un­der­stand how bac­te­ria iden­tify their cell cen­ter for di­vi­sion. And you thought this was a sim­ple ques­tion...

 

Ref­er­ence

Bonny M, Fis­cher-Friedrich E, Loose M, Schwille P, Kruse K (2013). Mem­brane bind­ing of MinE al­lows for a com­pre­hen­sive de­scrip­tion of Min-pro­tein pat­tern for­ma­tion. PLoS com­pu­ta­tional bi­ol­ogy, 9 (12). PMID 24339757

 

Veron­ica is a Ph.D. can­di­date in the Mi­cro­bi­ol­ogy and Mol­e­c­u­lar Ge­net­ics pro­gram at The Uni­ver­sity of Texas Health Sci­ence Cen­ter at Hous­ton. She is a mem­ber of William Margolin's lab.