A Microscopic model for Microtubules

An important class of force generating mechanisms in living cells involves the controlled polymerization and depolymerization of biological macromolecules, such as Microtubules. There has been much activity in trying to understand the mechanism by which a microtubule alternates between polymerization and depolymerization. While several interesting hypotheses have been made over the last decade or so, progress has been slow due to the absence of a microscopic model which can properly explain the various observed properties of the microtubule. In this thesis we try to constuct a microscopic model for the microtubule which can reproduce the experimentally observed structures. The basic subunit of our model is the tubulin heterodimer, and we construct the microtubule by arranging 13 protofilaments in a cylindrical lattice. Each subunit of the microtubule lattice is connected to its four nearest neighbours by springs, and the energetics penalises deviations from the equilibrium bond length or the equilibrium bond angle both in the horizontal and vertical directions. There is also an energy cost for deviations from the perfect square topology between the bonds. In addition, we incorporate a self-avoiding energy term for the lateral and longitudinal bonds. Having defined our model, firstly we study the elastic response of our model to small deformations. Specifically, we determine the torsional and tilt moduli of our model microtubule. We also study the equilibrium structures generated by MonteCarlo and Brownian Dynamics simulations in different regimes of the parameters of our model both at zero and at finite temperatures. Finally, we try to provide a future direction for further work that needs to be done within the scope of the model. ilLtU1oCill&C[TIT-QPru&CTn. J)J&51TIm &L(b1UU(b1~~UULL UIT6U1illrftCCfCf ~LD, ~UIT6U1illrftCCfCf~LD ilLtU1oQCfru&51TIm ~[J[)ru ilL@lruIT&@LD umTl&51TIru @&@llJU Ur5.J&IT[J! J)J@m[)6\IT. mill&C[TIT(b1U1ll.jru 61Ji>~ ru~@m[)tU1ru, UIT6U1illrftCCfCfm, ~UIT6U1illrftCCfCfm 61m[) @@I illIT! J)JULL @m[)&m611, Cill[JQ&IT6TI@[)~ 61mUm~U UW ~m5)llJ U6\l ~li.J6l. j&6TI Cill[JQ&IT6TI611UUL(b16TI6116\IT. QCfm[) U$b$bIT~(b1&51TIru uruCru! J)J &@I$b~ ~&r5.J&6TI @~~m[)tU1ru QCfITru6\lUULLIT~LD @rD1UU1L~$b&& @mC6\IT[J[)LD 61~6l.jLD @rum6\l. mill&C[TIT(b1U1ll.j6U1m ~mmillmllJ ru1611&&~~@Ji>~ J91~illIT~rft @ru6\lIT~C~ @~[J@ @&@llJ &IT[TmTLD ~@LD. @Ji>~ ~li.Jru1ru, CCfIT~m6\ITtU1ru &ITmTUULL &LLmillUmu~ ~[T&CTn.~llJ mill&C[TIT(b1U1ll.j6U1m @millIT~rfttU1m6\ITU QU[) @llJru@C[)ITLD. ~ill~ illIT~rfttU1m ~~uumL~ ~mmT ~6\l@ (b1U1ll.j6U1m-W~C[TITmLillo~@LD. 13 LjQ[)ITLCLITU1611 Qill~(b1&m611 ilL@lm611ru ~ru C6\l~ conS1ruru ~ru millu U ~ m QP6\lLD ~ ITLD mill & C [TIT(b1U1ll.jm6\lu Q U ! J)JCru ITLD. mill & C[TIT(b1U1ll.jru C6\l~ conS1 m gru Qru IT@I~ ~ m6lJl5T ~6\l@LD ~~m LEl& ~@I@ru ilL6TI611~ITm@ ~m6lJl5T ~6\l@&~Lm CJi-@l6TI&LDU1&611ITru @m6lJl5T&&u U L (b16TI 611~ . 616\IToW~&rorU @mLillLL ill[J! J)JLD QCfr5.J@~ ~~mCf &51TIru $1m6\lu U (b1~ ~ U U L L U1m6lJl5TuU1m $1611LD ill[J! J)JLD C&IT6lJl5Till IT! J)JU IT(b1&6TIQu [)U U (b1@[)~ . @Ji>~ illIT! J)JUIT(b1&@b&&IT6\IT~[J[)ru @WULj Cf~[T CLITUIT6\lW Q&IT~(b1 ~rD1llJuu(b1@[)~. ~[T ill[J! J)JLD ilLllJ[T U1m6lJl5TuLj&@b&&IT6\IT $bITm -~ru1oU Lj ~[J[)ru @6lJl5T&LDQu [)U U (b1@[)~ . CJi~ ill[J! J)JLD 61Ji>~ g@l @rD1u U1L L Qru U U $1mrutU1~ LD ~ ill~ illIT~rfttU1m Cfill$1m6\lU U L L &LLmillUmu illIT~CL-&ITo-C6\lIT, LjC[TIT6M1llJm @LUr5.J@ru1LUru~ illIT~rftmLU& Q&IT~(b1 Cill[JQ&IT6TI611&CTn.~LU CfIT~ ~llJillIT 6\IT U mTl&m611U U WLU ru m[T ru1m6\ITU Qu ! J)J@C[)ITLD.