Applications of Integration in Biomedical Science

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Applications of Integration in Biomedical Science

• by
• William T. Self
• UCF EXCEL Applications of Calculus

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Calculus Topic Defining area under the curve

Topic 1 Approximating rectangles One
possible method for estimating area under a given
curve (or function) is the use of approximating
rectangles This is a simple method, but has
limitations in its ability to accurately define
the area
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Calculus concept 1
Approximating Rectangles
Section 5.1 1 By reading values from the
given graph of f (shown on the next slide) use
three rectangles to find a lower estimate for the
area under the given graph of f from x0 to x6.
In each case sketch the rectangles that you use.
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Approximating rectangles
Reminder 3 rectangles Lower limit From x0 to x6
Answers A) 17 B) 19 C) 21 D) 20 E) 28
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Approximating rectangles

• The use of this technique is inadequate to
  determine the area under a curve since it can
  overestimate and underestimate this area
• This section of the applications course will
  introduce you to concepts and methods in
  biomedical science that rely on calculus to
  determine the quantity of compounds and
  macromolecules

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Applications of Integration in Biomedical Science

• Some of the future courses (that you may take)
  that this will be relevant
• MCB 3020 General Microbiology
• BSC 3403C Quantitative Biological Methods
• MCB 4414 Microbial Metabolism
• BCH 4053 Biochemistry I
• BCH 4054 Biochemistry II

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Life Its existence on Earth
Time Line for Planet Earth
Prokaryotes
Eukaryotes

• Prokaryotes
• involved in formation of the biosphere
• required for plant animal survival

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Life Cellular level
eukaryotic cell
prokaryotic cell
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What are cells made of (E.coli )?
CHNOPS Carbon Hydrogen Nitrogen Oxygen Phosphorus
Sulfur
Adenosine triphosphate - ATP
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Biological Macromolecules
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Trace Elements

• Human composition (complements of Dept. of
  Energy)
• Dry weight
• Carbon 61.7
• Nitrogen 11.0
• Oxygen 9.3
• Hydrogen 5.7
• Calcium 5.0
• Phosphorus 3.3
• Potassium 1.3
• Sulfur 1.0
• Chlorine 0.7
• Sodium 0.7
• Magnesium 0.3
• Trace amounts of B, F, Si, V, Cr, Mn, Fe, Co,
  Cu, Zn, Se, Mo, Sn, I.
• There are some arguments as to the importance of
  other trace elements

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Biological Cells Complex mixtures

• Basics
• DNA, RNA Polymers of nucleic acids encode
  proteins
• Proteins Polymers of amino acids can be
  structural or act as enzymes
• Lipids Polymers of carbon structural
  components of cell membranes

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Biological Cells Complex mixtures

• A given cell will have thousands of different
  proteins, RNA molecules and metabolites present
  under a particular growth condition
• How do we define the role of each individual
  protein (for example)?
• First we must purify this protein away from all
  other components, then study it in a test tube
  (in vitro)

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Protein Purification
Proteins are polymers of amino acids Protein
sequence defines the chemical composition Each
protein has unique size, charge and shape
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Chromatography separation of mixtures

• Chromatography in general is the separation of
  compounds from mixtures using a Solid phase and a
  mobile phase
• Typically the solid phase is stationary, and held
  in place in a column
• The mobile phase (usually aqueous) moves through
  the solid phase and carries the sample

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Chromatography separation of mixtures
Samples separate from each other on the column
due to differences in their unique
properties 1.) net charge 2.)
hydrophobicity 3.) size 4.) specific affinity
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Chromatography separation of mixtures

• Types of chromatography used in protein
  purification
• 1.) Ion Exchange
• 2.) Gel filtration
• 3.) Hydrophobic
• 4.) Affinity

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Types of chromatography Protein separations

• 1.) Ion exchange
• The solid phase has a strong or weak charged
  group (e.g. strong positive charge)
• If a protein has a net negative charge
  (anionic), it will bind to a column that has a
  cationic group (positive charge). Each protein
  will have a slightly different net charge and
  thus mixtures of proteins can be separated based
  on net charge

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Types of chromatography Protein separations

• 2.) Gel filtration
• Proteins will separate based on size, due to
  pores present in beads in the solid phase. The
  pores define the separation capabilities of the
  media (e.g. 30,000 MW to 3,000,000 MW)

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Types of chromatography Protein separations

• 3.) Hydrophobic Interaction Chromatography
• Based on binding of hydrophobic amino acids
  (such as leucine, isoleucine) that are usually
  buried but occasionally present on the surface
• Common groups on the stationary phase are phenyl
  groups or carbon chains

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Types of chromatography Protein separations

• 4.) Affinity Chromatography
• Generally, proteins can be engineered to
  contain tags at their ends that will bind to a
  certain group (e.g. metal). This tag is usually
  unique in the mixture and thus a tagged protein
  can be purified quite readily from a cell extract
  using this procedure.
• The use of protein tags has revolutionized the
  study of proteins in enzymes in the wake of the
  era of molecular biology and cloning.

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How does this relate to Calculus???

• To find and determine the quantity of a given
  protein, or other molecule of interest, we follow
  the elution of these molecules using a detector.
  This pattern is essentially a continuous function
  from one time period to the next as follows

Samples eluting become a series of peaks that can
be followed and quantified by area under the curve
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Calculus concept 2
Limitations of approximating rectangles
Section 5.1 2 Use 4 rectangles to find
estimates of each type for the area under the
given graph of f from x 0 to x 6. Three
questions left and right endpoints and finally
midpoints
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Calculus Topic Defining area under the curve
Reminder Left endpoints 3 Answers A) B) C) D)
E)
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Calculus Topic Defining area under the curve
Reminder Right endpoints 3 Answers A) B) C) D)
E)
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Calculus Topic Defining area under the curve
Reminder Midpoints 3 Answers A) B) C) D) E)
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Calculus Topic Defining area under the curve

• Which of the three techniques is best?
• Why?
• Could there be a better way based on your current
  knowledge of calculus?

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Applications of Integration in Biomedical Science

• In addition to protein purification,
  chromatography (and area under the curve) has
  many other uses in biomedical science
• Some issues to discuss
• 1.) Arsenic (and other contaminants) in drinking
  water
• 2.) Drug testing (e.g. steroid use)
• 3.) Bioterrorism detection of explosives
• 4.) Pesticides in agriculture and consumer use

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Applications of chromatography

• How do we determine the presence of a pesticide
  present in a lake, river or stream?
• How do we quantify such a compound?
• Why does this quantization matter?

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Drug testing front lines

• Websites for discussion
• http//www.questdiagnostics.com/employersolutions/
  standard_urine_testing_es.html
• http//www.agilent.com/about/newsroom/lsca/backgro
  und/2007/bg_sports_drug_testing.pdf

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Drug testing front lines
Recent article in the journal Nature outlines
issues in drug testing for anabolic steroids
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Example of LC-MS analysis
Overview of typical HPLC setup
Detector is typically a mass spectrometer
that can predict the mass of eluting compounds
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Example of LC-MS analysis
Agilent Technologies example of LC profile of
steroids
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Gas chromatography (GC)

• Gas chromatography

• Similar to HPLC, with the exception that the
  mobile phase is a gas
• Sample is either a gas or is derivatized to a
  volatile form to allow for separation in a gas
  mobile phase
• Column has a liquid stationary phase which is
  bound to an inert support phase that is solid
• This form of chromatography is most common in
  analytical analysis of pesticides and lipid
  analysis.

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GC typical set up
Typical GC setup courtesy of Waters, Inc.
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Explosives GC-MS example

• Small amounts of explosives can be buried in
  compounds that mask their presence in samples
• GC-MS can uncover readily

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Calculus concept 3

• Fundamental theorem of calculus

The fundamental theorem of calculus states (Part
1) g(x) ? f (t )dt where f is a continuous
function on a,b and x varies between a and b.
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Fundamental Theorem of Calculus
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Fundamental Theorem of Calculus
Part 2 states If f is continuous on a,b
then ? f (x ) dx F (b ) F (a )

• Essentially, for purposes of defining area under
  the curve, the difference in the antiderivative
  of f between two points a,b on the curve
  (assuming a continuous function) is equal to the
  area of that curve to the x-axis
• This is the most critical application (in
  biological sciences) of the fundamental theorem

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Fundamental Theorem of Calculus
Insert clicker question Integration (Alvaro
figure)
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Fundamental Theorem of Calculus
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Biomedical Science - review
What are the three most abundant elements in the
human body (dry weight analysis)? A.) Hydrogen,
Nitrogen and Calcium B.) Carbon, Nitrogen and
Hydrogen C.) Magnesium, Carbon and Nitrogen D.)
Carbon, Oxygen and Hydrogen E.) Carbon, Selenium
and Magnesium
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Methods of detection in chromatography

• After separation (HPLC, GC, etc.) we must
  identify and quantify a molecule of interest
• Some of the commons ways to find and quantify
  molecules
• 1.) UV-visible spectroscopy
• 2.) Mass spectrometry
• 3.) Flame ionization (FID)
• 4.) Thermal conductivity (TCD)

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Methods of detection in chromatography

• These abbreviations lead to the multitude of
  common analytical techniques
• LC-MS (Liquid chromatography detection by mass
  spectrometry
• GC-MS, etc.
• All are still based on the fundamental concepts
  of chromatography, and all can use integration of
  peak area to determine the quantity of an eluted
  sample

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Methods of detection in chromatography
1.) UV-visible spectroscopy

• Functional groups in a molecule can absorb light
  at a given wavelength
• Aromatics and metal-complex ligands are common
  groups in biological samples that absorb light in
  UV or visible range

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Methods of detection in chromatography
DNA absorbs light at approximately 260 nanometers
Courtesy Biocompare
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Methods of detection in chromatography
Proteins absorb light at approximately 280
nanometers Due to tryptophan and tyrosine
residues
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Methods of detection in chromatography
HPLC analysis of purines A purine metabolizing
enzyme was tested for its substrate specificity
(which compounds it acts on) using HPLC
analysis Each substrate and product elutes at a
different time from reverse phase HPLC
(hydrophobic stationary phase) Purines followed
by UV-vis
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Methods of detection in chromatography
2.) Mass spectrometry Mass spectrometry
determines the overall predicted molecular weight
of a molecule based weighing its charge to mass
ratio Molecules are charged in an ion source,
then accelerated to a high speed. They are then
passed through a magnetic field and their
trajectory is altered by this field, dependent on
their charge to mass ratio
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Methods of detection in chromatography
The particles are then detected and their
composition can be predicted based on this charge
to mass ratio Other information on the sample is
generally needed to be able to identify and
confirm the molecule of interest
Image courtesy of USGS
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Methods of detection in chromatography
3.) Flame Ionization Detection (FID) FID is
commonly used in GC applications, and is based on
burning of the sample FID is very good at
detecting hydrocarbons and other carbon
containing molecules 4.) Thermal Conductivity
Detection (TCD) TCD is commonly used to detect
gases (hydrogen) when carried in an inert gas
(argon) TCD is based on changes in thermal
conductivity useful since it can detect nearly
any compound
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Use of calculus in Biomedical Science - Review
What characteristic of proteins is useful in gel
filtration chromatography? A.) Affinity for
ligands B.) Net charge C.) Hydrophobicity D.)
Size E.) Sequence
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Proteomics cutting edge use of chromatography
Cancer diagnosis Current techniques Example
Breast cancer Mammogram Ultrasound Biopsy Gene
tic screening Expensive, labor intensive and
usually only detect cancer at later stages (not
when first forming)
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Proteomics cutting edge use of chromatography
Proteomics The proteome is defined as the set of
proteins present in the cell under a given growth
condition The complement of proteins changes in
different cell types (tissues) and under
different conditions (stress, infection,
disease) Genetic variability also is displayed in
the proteome
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Proteomics cutting edge use of chromatography
Proteomics in Cancer diagnosis Using reverse
phase chromatography to follow the proteome of
a clinical sample (e.g. serum), one can obtain a
profile of the peptides that are present in a
patient Analysis of hundreds of patients, both
ill and healthy, allow for patterns to emerge in
this analysis
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Proteomics cutting edge use of chromatography
Above is a sample chromatogram of the peptides in
serum of an ovarian cancer patient Biomarkers of
Ovarian Cancer, Gynecologic Oncology 88, S25S28
(2003) doi10.1006/gyno.2002.6679
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Proteomics cutting edge use of chromatography
Proteomic analysis to diagnose cancer In a
study published in 2002 using a blinded set of
samples, the proteomic pattern correctly
predicted 36 (95, 95 confidence interval CI
82 to 99) of 38 patients with prostate cancer,
while 177 (78, 95 CI 72 to 83) of 228
patients were correctly classified as having
benign conditions. Serum proteomic patterns for
detection of prostate cancer. J Natl Cancer Inst.
2002 Oct 1694(20)1576-8.