mariel vazquez- analyzing dna topology with mathematical and computational methods

8/3/2019 Mariel Vazquez- Analyzing DNA topology with Mathematical and Computational Methods

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February 2nd, 2010 Mariel Vazquez - Math414-714: Lecture 3 1

Math 414-714: Analyzing DNAtopology with Mathematical and

Computational Methods

Mariel [email protected]

Mathematics Department, SFSU


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2. Action of enzymes on DNA

Substrate Products

(DNA knots or links)

recombination


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Knots are spies

Substrate Products

(DNA knots or links)

recombination?

Goal: characterize the products experimentally;use Mathematics to elucidate the enzymatic mechanism.


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Experimental data

Substrate Products(knots or links)

recombination



Tangle Model (Ernst and Sumners, 91)

Enzyme = ball .

Enzyme+bound DNA

2-string tangle 3-string tangle



One round of enzymatic action is translated

into a system of two tangle equations

N(O+P) = substrate

N(O+R) = product

recombination

Where O, P and R are 2-string tangles



(i) Substrate = N(O+P) = = = = b(1,1)

(ii) Product = N(O+R) = = = = b(4,3)

Solve for O and R.

Tangle Equations

Xer recombination

(i) Substrate = unknotted DNA molecule

(ii) Product = 4-crossing torus link

Experimental Data (Collomset al.

, 1997)

Xer



ResultsAssuming P=(0)

O = (-3,0) = and R= (-1) =

O = (-5,0) = and R= (+1) =

O = (-4,0)= and R=(0,0) =

Note: O is shown, mathematically, to be a rational tangle



Xer synapse: molecular model

M. Vazquez, S.D. Colloms, D.W. Sumners, J. Mol Biol (2005) 346: 493-504



Computer implementation:TangleSolve

Java applet + Graphical user interface

Location: http://bio.math.berkeley.edu/TangleSolve

Saka Y. and Vazquez M., TangleSolve: topological analysis of site-specific recombination, Bioinformatics (2002) 18:1011-1012


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BaMBA meetings: Biology and

Mathematics in the Bay Area

BaMBA I: SFSU BaMBA II: MSRI Berkeley

BaMBA III: San Jose State University BaMBA IV UC Davis

BaMBA V: UC Santa Cruz

BaMBA VI: November, 2010Stanford University


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Other Activities

Chromatin research group and Journal Club:http://online.sfsu.edu/~pasion/cjc.html

Math Biology Seminars, Math Department

Center for Computing in the Life Sciences


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February 2nd, 2010 Mariel Vazquez - Math 414/714: Lecture 3 15

Chapter I: Atomic and Molecular

Structure of DNA

Objective: Describe the DNA molecule at theatomic level


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Section 1. Atomic interactions and Energy

minimization

Today:1.1 Basic facts about atomic structure

1.2 Atomic interactions and bond formation


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ATOMOS An atom was defined by the greek as the smallest indivisibleparticle of matter.

An atom consists of a nucleus surrounded by a cloud of electrons:

nucleus : protons (+ charge); neutrons (neutral ch.)electron cloud: electrons (- charge)

Def: If the number of protons in an atom equals the number ofelectrons then the atom is neutral; otherwise the atom is called anion.

Note: an accurate description of an electron and other atomic particlesfalls within the field of quantum mechanics, which is beyond thescope of our course.

Intuitive Description


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ScalesLength: 1 nm =10=10-9 m

Weight: 1 Dalton = 1.67 x 10-24 g = 1.67 x 10-27 kg

Notation: 1 Dalton = 1Da = 1DParticle weight

1 e- 9.11x 10-28

g1 proton 1.6929 x 10-24 g ~ 1D

Approximation:1 atom (#protons + #neutrons) x 1.6929 x 10-24 g

~ (#protons + #neutrons) D


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Scales in Molecular Biology Length: (1 nm) =10A=10-9 m

Weight: (1 Dalton): 1.67 x 10-24 g

Water molecule 0.3 nm 18D

Bacteriophage 25nm 4,700,000D

Escherichia coli

(E. coli)

2,000nm=2m

icrons

2pg

Liver cell: 20microns 8 ng


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The Periodic Table (Mendeleev 1869)

IA

IIA IIIA IVA VA VIAVIIA

VIIIA

Atomic number = Number of protons in the nucleusPeriod = horizontal rowGroup = vertical column

Question: H has 1 proton, no neutrons, what is its mass?

mariel vazquez- analyzing dna topology with mathematical and computational methods

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