48x48 poster template

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A CHEMICAL KINETIC MODEL OF TRANSCRIPTIONAL
ELONGATION Richard Yamada and Charles S.
Peskin Center for Applied Mathematics, Cornell
University (Ithaca, NY) and The Courant Institute
of Mathematical Sciences, New York University
(New York, NY)
LOGO
MATHEMATICAL MODEL
ABSTRACT
PARAMETER ESTIMATION
CHART or PICTURE
CHART or PICTURE

• Once we have a mathematical model, the natural
  question to ask is how does one estimate the
  parameters that gives the best fit to the
  experimental data, given the simulations output?
  Unfortunately, fitting a stochastic (i.e.
  Gillespie) model to noisy data is very difficult.
  Results from these attempts have proved
  unsuccessful.
• We propose to find parameters by first developing
  an deterministic approach for our model, via a
  Master Equation Formalism. We then fit this
  deterministic model, using least squares, to the
  experimental data.
• To check the consistency and reliability of our
  approach we also proposed a control experiment,
  where we
• 1) Pick a set of parameters, including window
  size
• 2) Generate synthetic data from this parameter
  set
• 3) See if the parameter estimation method can
  recover our original set of parameters from a set
  of arbitrary parameters original parameters were
  recovered.

In this poster, a chemical kinetic model of the
transcriptional elongation dynamics of RNA
polymerase along a DNA sequence is introduced.
The proposed model governs the discrete movement
of the RNA polymerase along a DNA template, with
no consideration given to elastic effects. The
model's novel concept is a look-ahead''
feature, in which nucleotides bind reversibly to
the DNA prior to being incorporated covalently
into the nascent RNA chain. Analytical AND
computational results for the proposed model are
studied for specific DNA sequences used in actual
single-molecule experiments of RNA polymerase
along DNA. By replicating the data analysis
algorithm from the experimental procedure, the
computational model produces velocity histograms,
enabling direct comparison with these published
experimental results. Parameter estimation
techniques to find an optimal set of the model's
parameters, along with their interpretation, are
also discussed
 

• There are 3 Essential Parameters for Our
  Hypothesized Model
• (Kon)ij for reversible binding of ribonucleotide
  of type i (ATP, GTP CTP, or UTP) to
  deoxyribonucleoside of type j (A, G, C, T) within
  the window of activity
• (Koff)ij for reversible unbinding
• (Kforward)ij for covalent incorporation of
  ribonucleotide of type i into the nascent RNA
  chain, provided that there is a ribonucleotide of
  type i reversible bound to a deoxyribonucleoside
  of type j at the first site of the window of
  activity
• Computational Simulation was done using The
  Gillespie Algorithm
• Let tn be the time of the nth event.
• Immediately after the nth event, let the system
  be in a state such that mn different transitions
  are possible, and let the rate constants for
  those transitions be k1nkmn.
• Then random time intervals T1nTmn are chosen
  according to Tjn -log(Rn)/kjn, j1.m.
• Then the time of the next event is chosen as
  tn1tnTn, where TnminTjn, and the index Jn of
  the transition that occurs is chosen as the value
  j that achieves the minimum.
• We imitated the experimental algorithms to enable
  direct comparison to experimental data
• Velocity data were fit using a Gaussian weight
  function with Standard Deviation of 1 second (1
  Hz Gaussian low pass filter).
• The velocity is obtained from the slope and
  position of the linear fit by incrementing the
  simulated time by 30 ms per point

BIOLOGICAL INTRODUCTION AND MOTIVATION
CONCLUSIONS AND FUTURE WORK

• The deterministic look ahead model fits best to
  window sizes of 1 or 2 basepairs.
• To differentiate between the 2 window sizes, we
  predict a qualitative difference in the
  histograms of pause times between basepair
  incorporation into the nascent RNA chain.
• Parameter estimation using Bayesian methods (with
  Prof. Darren J. Wilkinson, Newcastle Univ) are
  currently being studied this method involves
  inferring parameters from a noisy model to noisy
  experimental data.

From Adelman et al, PNAS vol.99 13538, 2002
Image from http//www.faculty.uca.edu

• Transcription is a complex biological process
  that consists of 3 major steps Initiation,
  Elongation and Termination. Our poster focuses on
  a mathematical model of elongation. Major issues
  in transcriptional elongation include the
  following
• Elongation Mechanisms (force generation and
  coupling chemical/mechanical energy)
• Termination Mechanisms
• Pausing Mechanisms
• Editing Mechanisms
• Sequence Effects/Informatics
• Quantitative Simulation

ACKNOWLEDGEMENTS

• We would like to thank the following individuals
  and institutions who generously funded and
  provided helpful advice over the course of this
  project
• National Science Foundation Integrative Graduate
  Education and Research Traineeship
• Center for Applied Mathematics at Cornell
  University
• Arthur LaPorta and Lucy Bai (Cornell/LASSP)
• Chris Myers (Cornell Theory Center)
• Josh Griffin (Sandia Laboratory)

Why study this problem as modelers?

• Out of all the steps in transcription, elongation
  is most amenable to a quantitative/physical
  description
• New experimental tools, for example Single Force
  Microscopy, have recently enabled collection of
  data of elongation dynamics
• A relatively new field (since 1994)