Introduction to Biological Mathematics: Meeting 1

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Introduction to Biological Mathematics Meeting 1

• March 31, 2004

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Introduction

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

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Overview

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

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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.

http//www.answers.com/topic/mathematical-biology
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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.

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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.

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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.

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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).

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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.

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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.

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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.

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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?
Lead Identification and optimization.
Statistical evaluation.Structural analysis.
Preclinical testing (in vitro and animals)
Clinical Trials (Phases I-IV)
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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.
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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.

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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.
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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.
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Nanotubes
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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.
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Medical Signal Processing
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Medical Imaging and Image Processing
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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?
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The Cell
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BackgroundThe Central Dogma
RNA is an information carrier from DNA to Protein
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From Genes to Proteins
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DNA
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Building Blocks of DNA
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The Watson-Crick model
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Gene - encodes for protein
body cells
nucleus
DNA - The fundamental chemical unit of life ACTG
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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).

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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.

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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.

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RNA
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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.

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Different Types of RNA

• Involved in translation mRNA, rRNA, tRNA

• Other non-coding RNAs

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Nucleotide Bases

• Also called Nitrogen bases
• Aromatic bases
• Planar molecules

Pyrimidines
Purines
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RNA Structure
Secondary Structure
Primary Structure
Tertiary Structure
A
A
C
C
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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
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Secondary Structure Elements
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Tertiary Structure
tRNA-Phe from yeast
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• Binding divalent metals in coaxial stacking

The role of Mg in the P4-P6 structure
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Protein Degradation

• The Nobel Prize in Chemistry 2004, Avram Hershko,
  Aaron Ciechanover and Irvin Rose - for the
  discovery of ubiquitin-mediated protein
  degradation (animation).

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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

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Thank You!