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## Introduction to Biological Mathematics: Meeting 1

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Title: Introduction to Biological Mathematics: Meeting 1

1
Introduction to Biological Mathematics Meeting 1
• March 31, 2004

2
Introduction
• Alex ShulmanE-mail shulmana_at_post.tau.ac.il
• Website
• http//www.cs.tau.ac.il/shulmana/

3
Overview
• What is BioMath?
• Main Fields of Research
• Biological Goals and Motivation
• Computational Aspects
• Biological Background
• Molecular and Cellular Biology

4
Mathematical biology
• Mathematical biology or biomathematics is an
interdisciplinary field of academic study which
aims at modelling natural, biological processes
using mathematical techniques and tools. It has
both practical and theoretical applications in
biological research.

5
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6
Main Fields of Research
• Molecular and Cellular Biology
• Genomics and Proteomics
• Simulations and Drug Design
• Bio-Inspired Materials.
• Neurosciences.
• Biotechnology, Medical Imaging, Signal
Processing and Equipment.
• Ecology, Evolutionary Biology, Epidemiology.

7
Genomics
• The Human Genome Project (HGP) was the
international research program whose goal was the
complete mapping and understanding of all the
genes of human beings. All our genes together are
known as our "genome.
• The HGP has revealed that there are probably
somewhere between 30,000 and 40,000 human genes.

8
The Genome
• Human genes occupy a tiny fraction of the genome.
Less then 2 percent codes for proteins.
• They are divided into coding regions (exons) and
noncoding regions (introns).
• Apparently humans do more with their genes than
do other animals. It is thought that most human
genes can produce about three different proteins
as compared to about one protein per gene for
most other species.
• One way this occurs is through alternative
splicing in which a single RNA transcript (called
a premRNA) gives rise to more than one mRNA.

9
Computational Aspects
• Significant work is required to develop data
management systems to make these data not just
retrievable, but usable as input to computations
and amenable to complex, ad hoc queries across
multiple data types.
• Significant work is also required on techniques
for integrating data obtained for multiple
observables, at different scales, with different
uncertainties (data fusion) and for formulating
meaningful queries against such heterogeneous
data (data mining).

10
Proteomics
• The proteome is the complete set of biologically
active proteins in a cell.
• Individual proteins are characterized by specific
structural domains.
• A given protein domain can play different roles
in different proteins.
• In humans old protein domains can be
rearrangedin new ways to produce larger
proteomes.

11
Structural Genomics
• Structural genomics is a worldwide initiative
aimed at determining a large number of protein
structures in a high throughput mode.
• Functional annotation of the newly determined
proteins is another interesting field of
research.

12
Simulations
• The Goal
• To reproduce and predict structure, dynamics and
thermodynamics.
• Computational representations that range from
simple lattice models to full quantum mechanical
wave functions of nuclei and electrons.
• Computational Aspects
• Developments of both hardware and software for
parallel computing.
• Developing simplified but realistic computational
models that will reduce the running time.

13
Drug Design
An infection (bacterium, virus)? A mutant protein?
Classifications, comparisons and statistical
analysis.
Understanding the biological nature of the
disease.
Given a candidate can you test it?
Lab equipment
Developing an essay (wet lab).
Predict and analyze its structure.
Identify the target, usually a protein.
Known substrate?
Alignment, docking and DB searches. Statistical
analysis.
What molecules bind to the target?
Statistical evaluation.Structural analysis.
Preclinical testing (in vitro and animals)
Clinical Trials (Phases I-IV)
14
Drug Design
The binding sites of receptor protein tyrosine
kinase c-Kit (1pkg, purple) and c-ABL
tyrosine kinase (1iep, green) aligned by the
SiteEngine method.
15
Immunology and Virology
• Mathematical modeling has had a major impact on
research in immunology and virology.
• Mathematical modeling combined with analysis of
data obtained during drug clinical trials
established for the first time that HIV is
rapidly cleared from the body and that
approximately 10 billion virus particles are
produced daily.
• Challenges remain in studying such issues as how
rapidly viruses mutate and become drug resistant
under different therapeutic regimes needs to be
considered, which is also relevant to the
development of antibiotic resistance.

16
Targeted Medicine
A better understanding of the genetic root cause
of disease is the key to improved diagnosis and
treatment of many complex chronic diseases.
17
Bio-Inspired Materials
Developing new high-performance engineering
materials based on ideas inferred from Nature.
Proteins derived from spider silk serve as the
inspiration for high-strength fibers.
18
Nanotubes
19
Neurosciences
Understanding how behavior emerges from
properties of neurons and networks of neurons.
Mathematical analysis is needed to interpret the
results of massive computations, and to
incorporate the insights into network models.
20
Medical Signal Processing
21
Medical Imaging and Image Processing
22
Ecology, Evolutionary Biology, Epidemiology
To what extent is the organization of the
biological world are predictable and unique?
What are the rules governing its evolution?
23
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24
The Cell
25
BackgroundThe Central Dogma
RNA is an information carrier from DNA to Protein
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From Genes to Proteins
28
DNA
29
Building Blocks of DNA
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The Watson-Crick model
32
Gene - encodes for protein
body cells
nucleus
DNA - The fundamental chemical unit of life ACTG
33
Splicing
• DNA encoding a gene's precursor mRNA (pre-mRNA)
is organised into regions called exons (EXpressed
sequences) which may be spread across thousands
of nucleotide base pairs (bp).
• The areas between exons ina gene are called
introns (INtervening sequences).

34
Splicing and Spliceosome
• Most introns start (5') with the sequence GU and
end (3') with an AG which are referred to as the
splice donor and splice acceptor sites.
• Another important sequence is the branch site
located 20-50 base pairs upstream (5') of the
splice acceptor site and containing a conserved
A.
• Five small nuclear RNA molecules (snRNA) and
their proteins form a complex called the
spliceosome. Through an enzymatic process the
intron is then removed and the exons joined
together.

35
Alternative Splicing
• Another form of intron removal involving a
spliceosome is called alternative splicing and is
shown below.
• This process can produce more than one protein
due to different ways of splicing the same mRNA.

36
RNA
37
The RNA World Model
• Messenger RNA (mRNA) carries the information
recorded in DNA from the nucleus to the cytoplasm
of the cell.
• Ribosomal RNA (rRNA) form complexes with protein
to form ribosomes, the site of protein synthesis
wihtin the cytoplasm of the cell.
• Small nuclear RNA (snRNA) is involved in pre-mRNA
splicing.
• Heterogenous nuclear RNA (hnRNA) is the primary
transcript from the eukaryotic enzyme, RNA
polymerase II. hnRNA is the precursor of all mRNA
often called "pre-mRNA", prior to the removal of
introns.
• Transfer RNA (tRNA) carries amino acids to
nascent polypeptide chains synthesised on the
ribosomes.
• Small nucleolar RNA (snoRNA) is found in the
cell's nucleolus where it processes and
methylates rRNA.

38
Different Types of RNA
• Involved in translation mRNA, rRNA, tRNA
• Other non-coding RNAs

39
Nucleotide Bases
• Also called Nitrogen bases
• Aromatic bases
• Planar molecules

Pyrimidines
Purines
40
RNA Structure
Secondary Structure
Primary Structure
Tertiary Structure
A
A
C
C
41
Secondary Structure
Primary Structure
Secondary Structure
Base Pairing- Mainly Watson-Crick A-U (2
H-bonds) G-C (3 H-bonds)
A
A
C
C
42
Secondary Structure Elements
43
Tertiary Structure
tRNA-Phe from yeast
44
• Binding divalent metals in coaxial stacking

The role of Mg in the P4-P6 structure
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46
• The Nobel Prize in Chemistry 2004, Avram Hershko,
Aaron Ciechanover and Irvin Rose - for the
discovery of ubiquitin-mediated protein

47
Computational Aspects
• Sequence
• Alignment between DNA sequences
• Recognition of genes and classification
• Prediction of binding and function
• Sequence assembly
• Prediction of the location of genes, exons,
introns and splicing sites.
• Gene Expression Data Analysis
• Structure
• Prediction of structure
• Similarity of structures and prediction of
function
• Prediction of binding and drug design

48
Thank You!