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Author:Mökkönen, Harri
Title:Numerical simulation approaches to dynamics of polymer escape
Polymeerin pako-ongelman numeeriset simulaatiot
Publication type:Master's thesis
Publication year:2012
Pages:51 s. + liitt. 15      Language:   eng
Department/School:Teknillisen fysiikan laitos
Main subject:Fysiikka (laskennallinen fysiikka)   (Tfy-105)
Supervisor:Ala-Nissilä, Tapio
Instructor:Ikonen, Timo
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Location:P1 Ark Aalto  237   | Archive
Keywords:polymer
polymer escape
Kramers
path integral hyperdynamics
transition state theory
PIHD
TST
FENE
DNA
polymeeri
pako-ongelma
Kramers
polkuintegraali
hyperdynamiikka
PIHD
transitiotilateoria
TST
FENE
DNA
Abstract (eng): Polymer escape is an event occurring in numerous processes in the nature.
Modern DNA sequencing methods as well as some novel medical treatments and drugs are based on this phenomenon.
In this Master's Thesis polymer escape from a metastable external potential well by thermal activation was studied.
Problem setting corresponded to the Kramers' problem generalised for polymers.
Dynamics was obtained by the Langevin equation and the polymer was modelled with the bead-spring model having monomers connected by finite extension nonlinear elastic (FENE) springs and Lennard-Jones (LJ) potential giving excluded volume interactions.

To obtain the crossing rate of the escape, the path integral hyperdynamics (PIHD) method was used to enhance the direct simulations of the crossing events.
The external potential with perpendicular confinement was introduced and its effects on crossing rate were compared with the original potential.
The crossing rate was also calculated by sampling the energy landscapes of the escape event and applying the Kramers' formula and the transition state theory (TST) to these energy landscapes.
For the new external potential, a set of PIHD biases was designed and tested.
An increase in the crossing rate for longer polymers was found in the new potential.
The polymer was also found out to favour escaping in a stretched conformation thus having a strong analogy to the quantum tunnelling of one particle.
The Kramers' formula and TST predicted qualitative behaviour of the crossing rate correctly but their quantitative values differed.
Abstract (fin): Polymeerin pako-ongelma esiintyy luonnossa monissa biologisissa prosesseissa.
Muun muassa monet modernit DNA:n sekvenssointimenetelmät, lääketieteelliset hoidot sekä lääkkeet hyödyntävät tätä ilmiötä.
Tässä diplomityössä tutkittiin termisen aktivaation aiheuttamaa polymeerin pakenemista metastabiilista ulkoisesta potentiaalikuopasta.
Ongelman asettelu vastaa kuuluisaa Kramersin ongelmaa yleistettynä polymeereille.
Dynamiikka saadaan Langevinin yhtälöstä ja polymeeriä kuvataan helmi-jousi-mallilla, jossa polymeetin monomeerejä yhdistävät epälineaariset FENE-jouset sekä Lennard-Jones potentiaalista saatava äärellinen tilavuus.

Pakotaajuus selvitettiin ilmiön numeerisilla simulaatioilla, joita nopeutetaan polkuintegraalihyperdynamiikalla (PIHD).
Ylimääräisen kaarevuuden sisältävää uutta ulkoista potentiaalia tutkittiin ja polymeerin käyttäytymistä siinä verrattiin vanhaan potentiaaliin.
Pakotaajuus laskettiin myös mallintamalla numeerisesti pakenemisen aikaisia energiapintoja ja soveltamalla Kramersin teoriaa sekä transitiotilateoriaa (TST) näihin pintoihin.
Uudelle potentiaalille suunniteltiin neljä ajavaa PIHD-voimaa ja näitä voimia testattiin.

Tulosten perusteella pakotaajuus kasvaa pidemmillä polymeereillä uudessa potentiaalissa selkeästi.
Polymeeri myös näyttää suosivan venynyttä tilaa paetessaan potentiaalikuopasta.
Tämä ilmiö vihjaa analogiasta yhden hiukkasen kvanttitunnelointiongelmaan.
Kramersin teorian ja TST:n ennusteet pakotaajuuksille käyttäytyvät kvalitatiivisesti oikein, mutta lukuarvot poikkeavat.
ED:2012-12-19
INSSI record number: 45726
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