First Passage Time Boxed Molecular DynamicsBoris Fackovec
The document summarizes the First Passage Time Boxed Molecular Dynamics (FPT-BXD) method for calculating rate constants from molecular dynamics simulations. FPT-BXD enhances sampling by running many short simulations between defined boxes in configuration space. It connects to the master equation approach and allows determining rate constants by fitting the decay of state populations to exponentials. The method was tested on a Lennard-Jones cluster system, showing good agreement with transition path sampling results. Limitations and potential future extensions are discussed.
Rate constants: from Sinai billiards to protein foldingBoris Fackovec
The document summarizes a presentation about calculating rate constants from rare molecular events using discretised relaxation path sampling (DRPS). DRPS allows calculating rate constants for processes that span a large range of timescales, from molecular vibrations occurring in femtoseconds to protein folding taking milliseconds. Examples discussed include the rate of particle diffusion in Sinai billiards, polymer reversal and translocation, peptide dynamics, and biomolecular folding. DRPS estimates rate constants based on calculating the probability of relaxation from a transition state to equilibrium populations.
This document is a Beamer theme presentation for USM titled "Gelugor" created by Lim Lian Tze on September 30, 2014. It contains sections on introduction, text blocks, frames with bullet points and definitions. The presentation demonstrates different elements that can be included in a Beamer theme such as text, frames, definitions, theorems and concludes with a thank you.
The DICOM Image Viewer is freeware that allows viewing of ophthalmic DICOM images and associated tags, performing caliper measurements on images, and validating DICOM tags. It supports DICOM formats for fundus photographs, optical coherence tomography scans, and generic reports.
The document discusses LaTeX and beamer. It begins with an introduction to LaTeX as a document markup language and preparation system. It then covers features of beamer like overlays, customization, and using the same source for articles and presentations. The basic structure of a beamer presentation is also demonstrated.
Gradient Dynamical Systems, Bifurcation Theory, Numerical Methods and Applica...Boris Fackovec
This document is a presentation on gradient dynamical systems, bifurcation theory, numerical methods, and applications. It discusses dynamical systems, phase portraits, linear and nonlinear systems of ordinary differential equations, bifurcations, bifurcation diagrams, numerical methods for constructing bifurcation diagrams, and two examples - a chemical reactor system and a cluster of three charged atoms.
Este documento describe las funciones básicas de Beamer para crear presentaciones y posters en LaTeX. Explica cómo configurar la cabecera con el título, autor y otros metadatos. También cubre la estructura básica de las diapositivas o "frames", incluidas opciones como añadir pausas o permitir que un frame ocupe varias páginas. Por último, introduce algunos efectos como bloques, columnas y otras herramientas para crear presentaciones de manera profesional con Beamer en LaTeX.
This document discusses how to create a domain-specific language (DSL) using Ruby. It begins with an introduction to DSLs and examples of external and internal DSLs. It then demonstrates how to build a DSL for configuring Meetup groups by parsing a configuration file using Ruby's instance_eval method. Key points are that instance_eval interprets a string as Ruby code in the context of an object, and using it with a block changes the default receiver inside the block. The document provides sample code for loading the configuration and implementing setter methods to configure the Meetup object.
First Passage Time Boxed Molecular DynamicsBoris Fackovec
The document summarizes the First Passage Time Boxed Molecular Dynamics (FPT-BXD) method for calculating rate constants from molecular dynamics simulations. FPT-BXD enhances sampling by running many short simulations between defined boxes in configuration space. It connects to the master equation approach and allows determining rate constants by fitting the decay of state populations to exponentials. The method was tested on a Lennard-Jones cluster system, showing good agreement with transition path sampling results. Limitations and potential future extensions are discussed.
Rate constants: from Sinai billiards to protein foldingBoris Fackovec
The document summarizes a presentation about calculating rate constants from rare molecular events using discretised relaxation path sampling (DRPS). DRPS allows calculating rate constants for processes that span a large range of timescales, from molecular vibrations occurring in femtoseconds to protein folding taking milliseconds. Examples discussed include the rate of particle diffusion in Sinai billiards, polymer reversal and translocation, peptide dynamics, and biomolecular folding. DRPS estimates rate constants based on calculating the probability of relaxation from a transition state to equilibrium populations.
This document is a Beamer theme presentation for USM titled "Gelugor" created by Lim Lian Tze on September 30, 2014. It contains sections on introduction, text blocks, frames with bullet points and definitions. The presentation demonstrates different elements that can be included in a Beamer theme such as text, frames, definitions, theorems and concludes with a thank you.
The DICOM Image Viewer is freeware that allows viewing of ophthalmic DICOM images and associated tags, performing caliper measurements on images, and validating DICOM tags. It supports DICOM formats for fundus photographs, optical coherence tomography scans, and generic reports.
The document discusses LaTeX and beamer. It begins with an introduction to LaTeX as a document markup language and preparation system. It then covers features of beamer like overlays, customization, and using the same source for articles and presentations. The basic structure of a beamer presentation is also demonstrated.
Gradient Dynamical Systems, Bifurcation Theory, Numerical Methods and Applica...Boris Fackovec
This document is a presentation on gradient dynamical systems, bifurcation theory, numerical methods, and applications. It discusses dynamical systems, phase portraits, linear and nonlinear systems of ordinary differential equations, bifurcations, bifurcation diagrams, numerical methods for constructing bifurcation diagrams, and two examples - a chemical reactor system and a cluster of three charged atoms.
Este documento describe las funciones básicas de Beamer para crear presentaciones y posters en LaTeX. Explica cómo configurar la cabecera con el título, autor y otros metadatos. También cubre la estructura básica de las diapositivas o "frames", incluidas opciones como añadir pausas o permitir que un frame ocupe varias páginas. Por último, introduce algunos efectos como bloques, columnas y otras herramientas para crear presentaciones de manera profesional con Beamer en LaTeX.
This document discusses how to create a domain-specific language (DSL) using Ruby. It begins with an introduction to DSLs and examples of external and internal DSLs. It then demonstrates how to build a DSL for configuring Meetup groups by parsing a configuration file using Ruby's instance_eval method. Key points are that instance_eval interprets a string as Ruby code in the context of an object, and using it with a block changes the default receiver inside the block. The document provides sample code for loading the configuration and implementing setter methods to configure the Meetup object.
Chemical dynamics and rare events in soft matter physicsBoris Fackovec
Talk for the Trinity Math Society Symposium. First summarises the approximations leading from Dirac equation to molecular description and then the synthesis towards non-equilibrium statistical mechanics. The relaxation approach to projection of a molecular system to a Markov jump process is discussed.
Simulating dynamics of rare events using discretised relaxation path samplingBoris Fackovec
This document summarizes the discretised relaxation path sampling (DRPS) method for simulating rare events. DRPS partitions configuration space into cells and propagates response functions describing the relaxation between cells to obtain rate constants. The method was tested on Sinai billiards and a cluster of Lennard-Jones disks, obtaining good agreement with other methods. Future applications discussed include polymer reversal in nanopores and biomolecular folding.
Universal Stability Model for Globular ProteinsBoris Fackovec
The document presents a universal stability model for globular proteins. The model decomposes the folding free energy into three components: solvent accessible surface area terms, interresidual two-body interaction terms, and solvation of individual amino acids. Scaling factors for these components were optimized using a genetic algorithm to fit calculated interaction energy matrices from 1287 protein structures. The model achieved a fitting accuracy of around 3% and provides insights into the contributions of different interactions to protein stability.
General Trends of Intramolecular Interactions in Globular ProteinsBoris Fackovec
The document discusses analyzing protein structures through calculating interaction energies between fragments of amino acid residues. It examines how residue interaction energy (RIE) distributions vary based on secondary structure content and protein size. The analysis finds that secondary structure does not strongly influence RIE distributions except for backbone-backbone interactions. It also determines that nonpolar-nonpolar average RIE dependence can be used to estimate protein domain size, and that backbone and polar side chain interactions are coupled. The goal is to gain physical insights into intramolecular interactions in globular proteins.
Intramolecular Interactions in Globular ProteinsBoris Fackovec
This document summarizes Boris Fačkovec's thesis on intramolecular interactions in globular proteins. It discusses the development of methods to study protein structure and energetics over time, from early theories to modern computational techniques. The thesis aims to characterize interaction energies within proteins using an interaction energy matrix approach. It analyzes distributions of interaction energies between different residue types and defines optimal cutoffs for determining inter-residue contacts. The results provide insight into factors influencing protein domain size and stability.
Chemical dynamics and rare events in soft matter physicsBoris Fackovec
Talk for the Trinity Math Society Symposium. First summarises the approximations leading from Dirac equation to molecular description and then the synthesis towards non-equilibrium statistical mechanics. The relaxation approach to projection of a molecular system to a Markov jump process is discussed.
Simulating dynamics of rare events using discretised relaxation path samplingBoris Fackovec
This document summarizes the discretised relaxation path sampling (DRPS) method for simulating rare events. DRPS partitions configuration space into cells and propagates response functions describing the relaxation between cells to obtain rate constants. The method was tested on Sinai billiards and a cluster of Lennard-Jones disks, obtaining good agreement with other methods. Future applications discussed include polymer reversal in nanopores and biomolecular folding.
Universal Stability Model for Globular ProteinsBoris Fackovec
The document presents a universal stability model for globular proteins. The model decomposes the folding free energy into three components: solvent accessible surface area terms, interresidual two-body interaction terms, and solvation of individual amino acids. Scaling factors for these components were optimized using a genetic algorithm to fit calculated interaction energy matrices from 1287 protein structures. The model achieved a fitting accuracy of around 3% and provides insights into the contributions of different interactions to protein stability.
General Trends of Intramolecular Interactions in Globular ProteinsBoris Fackovec
The document discusses analyzing protein structures through calculating interaction energies between fragments of amino acid residues. It examines how residue interaction energy (RIE) distributions vary based on secondary structure content and protein size. The analysis finds that secondary structure does not strongly influence RIE distributions except for backbone-backbone interactions. It also determines that nonpolar-nonpolar average RIE dependence can be used to estimate protein domain size, and that backbone and polar side chain interactions are coupled. The goal is to gain physical insights into intramolecular interactions in globular proteins.
Intramolecular Interactions in Globular ProteinsBoris Fackovec
This document summarizes Boris Fačkovec's thesis on intramolecular interactions in globular proteins. It discusses the development of methods to study protein structure and energetics over time, from early theories to modern computational techniques. The thesis aims to characterize interaction energies within proteins using an interaction energy matrix approach. It analyzes distributions of interaction energies between different residue types and defines optimal cutoffs for determining inter-residue contacts. The results provide insight into factors influencing protein domain size and stability.
1. Úvod do štatistickej mechaniky I: úvod do
termodynamiky a neinteragujúce castice
Boris Fackovec
David Wales group
Department of Chemistry
University of Cambridge
Jarná škola FX
17. Apríl 2014
1 / 13 Boris Fackovec (bf269@cam.ac.uk) StatPhys Jastrabie, 17th April 2014
2. O com to chce byt
štatistická fyzika, štatistická mechanika, štatistická
termodynamika, chemická kinetika, fyzikálna kinetika,
chemická dynamika??
popis priemerných vlastností velkého poctu (> 1020)
castíc
jednoduché pravidlá pre 1 casticu ! zložité správanie
množstva (emergent property, many-body problem)
2 / 13 Boris Fackovec (bf269@cam.ac.uk) StatPhys Jastrabie, 17th April 2014
3. Aby sme si rozumeli
zopár užitocných pojmov (extenzívne/intenzívne,
stavové/procesové veliciny, vektorové/skalárne)
zopár užitocných velicín
hybnost p
všeobecná koordináta q
sila f
objem V
látkové množstvo n
energia E
teplota T
tlak p
zoznam doplníme . . .
; ; d; @
stavová rovnica
3 / 13 Boris Fackovec (bf269@cam.ac.uk) StatPhys Jastrabie, 17th April 2014
4. A ešte trochu metafyziky
systém (otvorený, uzavretý, izolovaný)
mikrostav - detajlný popis - len zriedka zaujímavý
makrostav - popis pomocou malého poctu stavových
velicín - prakticky zaujímavý
termodynamická limita
rovnováha
definovaná vágne - separácia caskových škál
ergodická hypotéza
reálne nás zaujíma casový priemer všetky mikrostavy sú
rovnako pravdepodobné
zákon zachovania energie (1. zákon tdn)
4 / 13 Boris Fackovec (bf269@cam.ac.uk) StatPhys Jastrabie, 17th April 2014
5. Pocet mikrostavov
(E) - bezrozmerná velicina (ako aj Q; )
pre reálne systémy je závislá na viac premenných
(N; V;E)
popisuje “mikrokanonický súbor” mikrostavov
všetky stavy sú rovnako pravdepodobné
pre nezávislé (neinteragujúce) stavy
(N1+N2; V1+V2;E1+E2) =
(N1; V1;E1)
(N2; V2;E2)
“superastronomicky velké hodnoty” - užitocné používat
log
S = kBlog
kB je v rovnici z historických dôvodov
5 / 13 Boris Fackovec (bf269@cam.ac.uk) StatPhys Jastrabie, 17th April 2014
6. Druhý zákon termodynamiky
Entropia uzavretého systému je v rovnováhe vo svojom
maxime.
Nemožno dosiahnut teplotu 0 K.
Pohyb casu je jednosmerný.
snaha zostrojit perpetuum mobile 2. druhu na základe
známych fyzikálnych zákonov
6 / 13 Boris Fackovec (bf269@cam.ac.uk) StatPhys Jastrabie, 17th April 2014
7. Teplota
0. zákon termodynamiky: “Existuje teplomer” (teplota
existuje a je stavovou velicinou)
uzavretý systém (miesto izolovaného)
majme systémov, ktoré si môžu vymienat hmotu
v rovnováhe
@
(N; V;E;E1)
@E1
N;V;E
= 0
13. = 1=kBT
zákony termodynamiky
1 existuje teplomer
2 energia sa zachováva
3 entropia s casom rastie
4 entropia je absolútna
pocet mikrostavov
(N; V;E)
S = kB log
(N; V;E)
9 / 13 Boris Fackovec (bf269@cam.ac.uk) StatPhys Jastrabie, 17th April 2014
14. Použitie termodynamiky na jednoduché deje
príklady: vratné deje s ideálnym plynom
izobarický
izotermický
izochorický
adiabtický
10 / 13 Boris Fackovec (bf269@cam.ac.uk) StatPhys Jastrabie, 17th April 2014
15. Kanonická particná funkcia I
Q(N; V; T)
systém si môže vymienat s okolím teplo, nie však castice
zovšeobecnenie - pravdepodobnost mikrostavov nie je
rovnaká
log
(E i) = log
i
d log
dE
+ O(1=E)
pravdepodobnost
P(i) =
P
(E i)
j
(E j)
=
e
20. i
vztah s fenomenologickou termodynamikou
A = kBT logQ(N; V; T)
zmiešavacia a informacná entropia
S =
X
i
pilogpi
12 / 13 Boris Fackovec (bf269@cam.ac.uk) StatPhys Jastrabie, 17th April 2014
21. Výmena castíc a chemický potenciál
chemický potenciál = práca 1 castice
particná suma pre všetky možnosti
X
(; V; T) =
N
e