Applications of Logarithmic and Exponential functions in Biomedical Science

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1 Antibiotics: Chemotherapeutic agent that inhibits growth (bacteriostatic) or kills (bacteriocidal) a bacterium (or fungus or protozoan). How do antibiotics work (bacteria)? Only a very few targets have been identified nearly all through the use of natural products

2 Natural Products: A chemical produced by a biological organism (such as a bacterium or a fungus), that can be used as a chemotherapeutic Natural products have been the backbone of the pharmaceutical industry since its inception Example: Lovastatin fungal natural product

3 Major targets of antimicrobials 1) Cell wall (Beta lactams) 2) Ribosomes (kanamycin, tetracycline) 3) Nucleic Acids (ciprofloxin, rifampin) 4) Cell membrane (ergosterol antifungal) 5) Antimetabolites (trimethoprim, sulfa drugs)

4 New targets for an emerging pathogen How do you define a good target 1.) Required for growth of bacterium 2.) Unique to bacteria (humans don t have this pathway) 3.) Little toxicity to human cells (tolerated)

5 Clostridium difficile Gram +, anaerobic, spore-forming bacillus Transmission: fecal/oral route Primarily nosocomial?? Risk factors: antibiotics, age (>65) underlying illness Symptoms: mild diarrhea to pseudomembranous colitis and death

6 Mediated by toxins (A and B) Uptake via receptor mediated endocytosis Cause actin depolymerization and cell rounding End result: inflammation fluid and mucus secretion damage to the intestinal mucosa Pseudomembranous colitis

7 Major outbreak in Quebec, Canada 16x more toxin A, 23x more toxin B Division of Healthcare Quality Promotion (DHQP) -

8 States with the Epidemic Strain NAP1 of C.difficile Confirmed by CDC (N=27) Updated 4/3/2007 DC AK HI PR

9 Radioisotope labeling confirms expression of both Glycine reductase and D-proline D Reductase A B C. Difficile 630 C. Difficile ATCC GrdB Glycine Reductase Large subunit PrdB Proline Reductase GrdA Glycine Reductase Small subunit Anti-GR selenoprotein A Selenoproteins were shown to be required for growth of this pathogen Good target? Jackson S, Calos M, Myers A, Self WT. J Bacteriol Dec;188(24):

10 Serendipity Always the key to true discovery! Percent Growth 120 Auranofin a drug used for Rheumatoid arthritis, acts as a potential antimicrobial against C. difficile NAPI/O Auranofin (um) Is it blocking GR or PR activity, or Se metabolism???

11 Auranofin inhibits synthesis of GR and PR in C. difficile Auranofin treated cells (mid- logarithmic growth) Clear decrease in selenium incorporation No difference in 35 S incorporation (in either C. difficile or E. coli)

12 Au-Se complex isolated in vitro and confirmed in culture medium P Au Se Au P Au P Mass spectrometry analysis reveals a Se containing derivative that is predominant (based on direct injection into MS)

13 Goals (lecture two): 1.) Understand the basic science behind radioisotopes 2.) Utilize and understand equations that are used to calculate half-life of radioisotopes, both in an experimental or clinical example 3.) Gain an appreciation for the use of isotopes for medicine, as well as our day to day exposure to radioisotopes

14 What is a Radioisotope? The atom is the smallest unit of matter that is capable of entering into a chemical reaction. Atoms are made of electrons, which circle the center of the atom, as well as protons and neutrons within the center of the atom. The number of protons in the nucleus defines the element (also called atomic number). The total number of neutrons and protons is called the mass number.

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16 Isotopes are atoms of the same element (same number of protons) but that carry different numbers of neutrons. A radioisotope is an atom that contains an unstable ratio of neutrons to protons. In order to gain stability a radioisotope can release energy or particles from its nucleus, and this defines the type of radioisotope.

17 An alpha particle is a Helium 4 nucleus (two protons and two neutrons). Common isotopes Radon, Radium, Uranium Because of their size and charge don t even penetrate paper or the outer layer of your skin!!! Image courtesy Stanford Linear Accelerator (SLAC)

18 A beta particle is an electron. Common isotopes: 32-P, 14-C, 35-S, 3-H Depending on the size and energy, Beta particles can penetrate the skin several mm, and thick plastic (e.g. 14-C not very well, 32-P more penetrating) Image courtesy Stanford Linear Accelerator (SLAC)

19 A gamma particle is a photon (of energy). Common isotopes: 60-Co, 137-Cs, 75-Se Gamma rays are similar to other electromagnetic radiation (such as microwaves, radio waves) except that gamma rays are of much higher energy Most damaging to biological cells (produce hydroxyl radical upon homolytic splitting of water molecules Image courtesy Stanford Linear Accelerator (SLAC)

20 Radioactive decay Defined as the rate of decay of the unstable material to the more stable form. The unit used is called the Curie (named after Marie Curie), and a Curie is equal to 3.7 x disintegrations per second.

21 Examples of half-life of isotopes: Hydrogen-3 Carbon-14 Phosphorus-32 Phosphorus-33 Sulfur-35 Selenium years 5730 years 14.3 days 25.3 days 87.6 days 117 days

22 Radioisotopes Use in scientific research Because a radioactive isotope behaves in a biological system just as the more stable isotope, it can be used effectively to trace the material. The conversion of the carbon from sugars into metabolic intermediates and cellular biomass was primarily followed using 14 C-labeled glucose. This allowed for isolation of each of the enzymes that acts on carbon in the cell. Likewise the metabolism of nitrogen, phosphorus and trace metals can easily be followed by radiolabeling your compound of interest and introducing it into a living cell model.

23 Radioisotopes used to map metabolic pathways This is not even all inclusive! Normally a large wall chart

24 Radioisotopes used to map metabolic pathways General overview Note: glucose is at the top of the metabolic chart

25 Calculation of half-life of radioisotopes Radioisotope half life can be calculated using the following equations: A = A 0 e -λt λ= 0.693/t 1/2 Where: A = Current amount of radioactivity A 0 = Original amount of radioactivity e = base natural log (approximately 2.718) λ= the decay constant = 0.693/t 1/2 (where t 1/2 = half-life) t = the amount of time elapsed from A 0 to A

26 Sample calculation: We have a test tube with Selenium-75 with a known activity of 10 μci on October 31st. However some time has elapsed and you are now planning to do an experiment to label Yersinia pestis (causative agent of the plague!) to determine whether it makes selenoproteins. Your experiment will be done on December 20th, 50 days later. The half-life of Selenium-75 is 144 days.

27 Sample calculation (continued): A = A 0 e -λt λ= 0.693/t 1/2 A will be activity that will remain on Dec. 20 (to be found as the answer) The A o will represent the original activity (10 μci ) T will represent the elapsed time, 50 days. First, calculate the decay constant λ. λ= days or days.

28 Sample calculation (continued): A = A 0 e -λt λ= 0.693/t 1/2 Next, determine how much 75Se remains in the test tube on the day of the experiment A = A 0 e -λt A = 10 e -(0.0048)50 A = 10 e A = 10 (0.7866) = 7.86 μci remains on Dec. 20th

29 Radioisotope exposure everyday! We are exposed to radioisotopes everyday (Iclicker) On average, what is the most significant source of radiation exposure? A.) Environment (natural geological source) B.) Sun s radiation (gamma rays) C.) Eating bananas D.) Smoking E.) I am not exposed to radiation

30 Let s try a test to see what my exposure is:

31 This is based on the average US citizen living in the continental US (and not in Denver!!!) Source: US Nuclear Regulatory Commission On a person to person basis these values would vary to a significant extent

32 Calculations from exposure around the world Note: Radon is primary source

33 Radioactivity of some natural and other materials 1 adult human (100 Bq/kg) 7000 Bq 1 kg of coffee 1000 Bq 1 kg superphosphate fertiliser 5000 Bq The air in a 100 sq metre Australian home (radon) 3000 Bq The air in many 100 sq metre European homes (radon) Bq 1 household smoke detector (with americium) Bq Radioisotope for medical diagnosis 70 million Bq Radioisotope source for medical therapy million Bq 1 kg 50-year old vitrified high-level nuclear waste million Bq 1 luminous Exit sign (1970s) million Bq 1 kg uranium 25 million Bq 1 kg uranium ore (Canadian, 15%) 25 million Bq 1 kg uranium ore (Australian, 0.3%) Bq 1 kg low level radioactive waste 1 million Bq 1 kg of coal ash 2000 Bq 1 kg of granite 1000 Bq

34 Radioisotopes in Medicine In addition to their valuable use in research, radioisotopes also play a critical role in the clinic. The half-life of isotopes varies depending on the rate of decay of the energy, so very short-lived isotopes can be used safely to allow for imaging of internal organs.

35 Nuclear medicine uses Determine functionality of organs Check whether blood flow to heart is adequate Detect early stage cancer Assess response of cancer to chemotherapy Detect unusual areas of the brain and other organs that are not functioning properly Determine whether or not kidneys are functioning normally and whether the stomach is emptying properly Assess lung function and bone density

36 Nuclear Stress test (one example): Isotopes used: thallium-201, technetium-99m How administered: Patient is injected with radioisotopes in a chemical form that facilitates labeling of the heart and imaging of the blood flow to and around the heart

37 Nuclear Stress test (one example, continued): The heart is imaged at both rest (no stress) and after running for a period of about 5-10 minutes, in order to raise the heart rate to a certain percentage of the maximum heart rate The differential imaging will indicate whether there is any coronary artery disease, or evidence of a past heart attack This tool in quite valuable to the cardiologist as it allows a noninvasive procedure to find any signs or CAD, or assess ongoing problems with CAD for a patient