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If a, b, and c are elements of a ring, does the equation

Contemporary Abstract Algebra | 8th Edition | ISBN: 9781133599708 | Authors: Joseph Gallian ISBN: 9781133599708 52

Solution for problem 52E Chapter 12

Contemporary Abstract Algebra | 8th Edition

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Contemporary Abstract Algebra | 8th Edition | ISBN: 9781133599708 | Authors: Joseph Gallian

Contemporary Abstract Algebra | 8th Edition

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Problem 52E

If a, b, and c are elements of a ring, does the equation ax + b = c always have a solution x? If it does, must the solution be unique? Answer the same questions given that a is a unit.

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4/42016 Bio 123 – Comparative Virology Lecture 4 – Laboratory Diagnosis of Viral Infections  Virus encodes, disassembles and exposes its nucleic acid depending on the virus  Can exploit each of the steps of the virus life cycle o Physicians want to identify what type of virus they have, so they take a sample from some specific tissue o In the case of HIV, the virus goes to blood, so you could take a blood sample  To identify the type of virus that is infecting you: o Screen blood for virus o Before HIV the blood screening was not that vigorous o Now blood screening is very vigorous o Now it is mandatory that everybody giving blood has an HIV test performed o It is possible there could be different HIV strains in different countries o Diagnosis is very important to prevent spread of viruses  Koch’s Postulates o Pathogen has to be isolated and it should be put back into the same host, and the host should show the same symptoms that they originally showed o Then you isolate the pathogen again  Viral Diagnostics in the Clinical Lab o Some specimens are very fragile, they can spoil very quickly  that is why they need to be isolated and transported in certain conditions so that the tests can be done properly  Storage and Collection of Biological Collections 1 o Identify what kind of pathogen is associated with what symptoms o Must get proper samples from proper tissues/parts of the body to send to the lab  Specimen Info o Not necessarily every respiratory infection is caused by Influenza  This is why it is very important to properly identify which disease is causing which symptoms o The same kind of symptoms can be created by more than one virus – very important concept  Lab Safety o Viruses are obligate parasites – they need a living host in order to survive or replicate o Viruses can be grown in animals, embryonic eggs, or tissue cultures o Some viruses must have very strict laboratory conditions o BSL-1 (minimum contaminant)  No pathogens present  Chemistry labs at UCR known as BSL-1, no pathogenic chemicals o BSL-2  Restricted access to labs  The people who are permitted to enter are prepared for it o BSL-3  Potentially lethal diseases present  HIV, etc.  Very strict conditions and rules 2  The lab needs to be given position from CDC, or someone else, it must be certified to handle the dangerous pathogens and procedures  UCR is trying to get a BSL-3 facility because of the Medical school  Work requires PPE (Personal Protective Equipment)– covered head to toe  Two closing doors, instead of just one  As you enter you must first step on mats to prevent bringing contaminants into the lab, and then again when you leave to prevent bringing pathogens into the outside environment o BSL-4  Pathogens pose a high risk  Ebola, Zika virus  Also used for completely unknown/unstudied/new viruses because they don’t know yet how serious the virus is and if it escapes they don’t know how rapidly it would spread  Anyone working in this lab has to go through rigorous training  How many people enter is monitored – record of time entry  Put glove inside and wrap apron around so that skin is not exposed  because some pathogens can enter through the skin  Person showers and rinses off while wearing protective suit, before leaving the lab  Diagnostic methods o Direct Examination (study what these viruses look like)  Antigen detection – viruses consist of both proteins and nucleic acids, so you can use antigen detection as a devise for diagnosis  They take a virus and put it in all different types of animals, and when the virus reacts it produces antibodies, then they collect the serum (blood) and they test it 3  For routine tests they use this serology test (blood tests that search for the presence of antibodies)  There are some other tests available that can look at the virus itself  Viruses are extremely small, cannot detect them using light microscope  viruses can only be detected on electron microscope  Electron microscope it a very direct way of studying the viruses but it is very expensive and requires a highly trained professional  Nucleic acids can be detected, it is done most commonly by PCR  PCR can get a fragment of DNA you want to work within 2-3hrs  Because PCR is so sensitive it can give you a lot of false positives  The first technique that got a Nobel Prize was Sander sequencing  The second technique was PCR  PCR is often used for confirming HIV  PCR amplifies DNA using primers, so you must know the sequence you want to amplify in order to use PCR (because you need to know the primers)  Light Microscopy  Can be used determine histological appearance o Study the anatomy of cells or tissue  may be able to determine viral infection based on cell structure  Used to determine presence of inclusion bodies – such as the presence of viral capsid proteins  Viral Genome  RNA, DNA  Antibody detection  ELISA (Enzyme Linked Immuno-Sorbent Assay) 4  First put either antigen or antiserum on plate  Then you take the patient’s serum and add it to the plate  If antibodies are present they stick to the virus particle  Then you add another antibody  Results in a certain color, the color represents whether or not the virus is present  Don’t need highly trained person to perform this test and it is very cost effective  Usefulness of Serological results o Fast results o Inexpensive o Do not need highly trained individuals  Cell culture o Some viruses may exist in patient in very low concentrations o So you must take the patient’s virus culture and grow it more in cell culture o Method often used for research not diagnosis o Problems  Long time period – can take up to 4 weeks  Must provide certain mediums, but bacteria may grow well on that medium so it is susceptible to bacterial growth  Molecular methods o Southern Blot – detects DNA o Northern Blot – detects RNA o Western Blot – detects protein 5 o Mostly for research purposes  Nucleic Acid detection o Mostly from PCR  First denature the DNA  both strands separate  Then anneal primers  Then add the enzyme (very highly stable enzyme)  that enzyme copies the DNA  as a result you get fragments  Then you repeat the cycle again and again  Very intelligent way of amplifying the DNA  if you wanted to amplify only a certain region you can amplify it, all you need are primers  Each cycle takes about 2 minutes  Takes 30 seconds for denaturation, and 30 seconds for annealing  This has greatly simplified molecular biology studies  There are many variations of PCR as well  Microarrays o Chips are already prepared o Just take a sample put it on the chip, put it in the computer, and analyze it  Protein Array o Can put antibodies in chips and then put it in computer  Advantages and Disadvantages o Microscopic  Fastest way of identifying the virus  Problem: Microscopes are extremely expensive and need special training o Antigen detection 6  Simple, easy  Problem: Not all viruses are highly mutagenic o Serology  Simple, minimum skills required  Problem: cannot be applied to all viruses because not all viruses are mutagenic  Serum is any blood or bodily fluid; antiserum is something that contains antibodies that acts against specific antigens 7 4/6/2016 Bio 123 – Comparative Virology Lecture 5 – Viral Taxonomy and Nomenclature  Top 10 deadliest diseases o Before the vaccine was developed, the flu was extremely dangerous o Someone that has HIV can be killed easily by the flu o A lot of these viruses are mostly found in sub-tropical regions o Malaria is very common in sub-tropical regions and especially during rainy season because mosquitos carry the virus o Ebola is a zoonotic disease (transmitted from animals to humans) o Cholera common during rainy season o Smallpox was one of the most dangerous viruses and it is extremely difficult to survive after contracting smallpox o Polio often infects children, and is often transmitted through the fecal-oral course  Studying viruses in more detail and classifying nomenclature is important because 6 out of the 10 most deadliest disease are caused by viruses  Many viruses in geysers  they can survive such a high temperature o Important because since they survive in such extreme temperatures they must have enzymes that can withstand that high temperature without denaturing  Tobacco Mosaic Virus (TMV) can easily be transmitted by smoking o People who smoke cigarettes can transmit the virus to the PLANTS o Plant viruses are restricted ONLY to plants  they do NOT affect humans  Viruses are classified by: o Phenotype 1 o Morphology o Nucleic acid type o Mode of replication o Host organisms o Type of disease they cause  Biological properties should NOT be used for classification because different viruses can cause the same symptoms  International Committee on Taxonomy of Viruses (ICTV) o ICTV determines whether or not a virus falls into a certain category o Approves or denies a virus’ classification o The given name should be very descriptive and no proper nouns should be used (cannot be named after a person)  2 exceptions : Rous Sarcoma virus and Epstein-Barr virus o Publish once every 4 years o Essential principles:  Cannot duplicate a name, any name must be useful and clearly different from existent viruses  Baltimore proposed using nucleic acids as a means for classification o He classified viruses into 7 groups by nucleic acid types  Naked – means no envelope, only capsid is present  DNA is the genetic material, if it has to make RNA it must go to nucleus because RNA Pol is in nucleus o Exception is the Poxvirus  it can replicate in the cytoplasm  Nomenclature o TMV produces a mosaic pattern on the plant 2  If you find any new virus, once you classify it you send your results to ICTV and they review it, and you propose a name, and if they think it is logical then they will accept it 3 4/8/2016 Bio 123 – Comparative Virology Lecture 6 – Poliovirus  You don’t hear about poliovirus anymore but there are some pockets of infection in the United States  Pico means small (because compared to other viruses this is the smallest virus known)  Known as far back as 1500 B.C. o The foot in the hieroglyph represented a symptom of polio  It was a major problem in 1916 New York City  Sanitation is the best prevention of any disease  It is a very rare disease these days  1979 – last cases, however some cases have been reported in 2005 o Polio was a major concern  Children are more susceptible to polio virus, but it can infect adults as well o As you grow old you develop resistance to polio, but if you don’t develop resistance you will get polio  Naked – has no envelope, it just has a capsid protein, and within the capsid nucleic acid  Virus is extremely small, and extremely stable o Some acids can be inactivated by acid o Polio virus cannot be inactivated by acid  Polio virus uses a receptor called CD155  it is a very specific receptor  that is what it uses to attach to cells  Nucleic acid is a single stranded +RNA 1 o So it can be directly translated  Polio virus is very unusual – it does not have a 5’ cap o It does have a 3’ tail though o How does this virus translate if it doesn’t have a 5’ cap  Very long non-coding region that forms into different structures and directs translation  Entire non-coding region – IRES – functions in place of 5’cap  this is a very unusual feature of polio virus RNA  It has one long Open Reading Frame  The cell’s mRNA can only translate one protein even though the coding region codes for 11 proteins  it translates one large polyprotein o The polyprotein has proteolytic cleavage sites o The polyprotein gets cleaved into multiple proteins o The virus knows when to cleave at these sites o The entire process doesn’t take that long  it is extremely rapid o Within one hour or so the virus can replicate o It makes a polyprotein and then the polyprotein gets cleaved by proteases to make multiple proteins  Viruses use host translational machinery  Trans-acting means that the host protein is doing the cleaving  Cis- acting means the virus is cleaving itself  Virus goes directly from RNA to more RNA o RNA serves as a template for making more RNA o Nothing happens in the nucleus, everything happens in the cytoplasm 2  All these viruses exploit the cellular structures – most of them use ER (endoplasmic reticulum) as a site of replication, some use nucleus, some use mitochondria  Minus strands themselves are not infectious because they cannot replicate, so minus strands make plus strands  as a result you end up with hundreds of plus strand RNAs  All the viruses encode their own polymerases  their polymerase will only copy the virus RNA  The polymerase in the host cell cannot copy the viral RNA efficiently  Mouth is the portal of entry  Regularly present in throat or stool  can get samples for diagnosis from throat, stool, or sometimes blood  Once the virus enters the blood it can go anywhere in the body  95% of infections are asymptomatic (they do not show any symptoms)  it all depends on the immunity level of the person o Adults have higher immunity than children  In the laboratory they swab the throat or get the virus from the stool because it goes through the intestines  virus is kept frozen and then transported to the lab where it is cultured in human or monkey cells  then they can categorize what type of strain it is  “Paired serum specimens” means that sample is collected today and then a sample is collected again one week later  Passive immunity – mother to child o When mothers breastfeed o But immune mothers can pass antibodies/resistance to child as well  Once a person is exposed to the virus they will develop antibodies  All age groups are susceptible to the disease  Humans are the only known reservoir for the disease  the virus cannot survive in any other host besides humans 3  Edward Jenner took live cowpox virus and injected it into his son o Same concept used for poliovirus  Live-virus is inactivated via UV rays, so the virus cannot replicate therefore it cannot infect you  your body recognizes the virus and develops antibodies and you develop immunity o This is more successful in producing immunity because it replicates slowly over a long time and thus antibodies are being produced over a long time, and booster shots are not necessary  In rare cases some vaccines are associated with other viruses  Because poliovirus affects the limbs Sister Kenny started doing physical therapy with patients  Vaccine-related poliovirus  The inactivation was inadequate  as a result some people were getting polio from the vaccines  Sabin designed live, attenuated virus  it can replicated in the body but it cannot be replicated at the same speed  it replicates very slowly  How can we tell if the vaccine is efficient o Screening is done, people are tested for the virus  15 million Russians vaccinated  They stopped using oral vaccine now they use IPV  Polio reduced from 125 to 6 countries  tremendous success  Roosevelt was a victim of polio 4 Quiz Questions (all False): 1. All means it includes plants  plant viruses cannot cross into humans 2. The meaning of virus is poison 3. Tb is a bacterial disease not a virus (it is one of the top 10 diseases though) 4. TMV is not icosahedral 5. Father of Virology is Beijerinck 6. They discovered that DNA is the genetic material 7. 80% of viruses are RNA viruses not DNA, very few DNA viruses 8. No virus can carry its own translational machinery 9. 80% of the plants are RNA viruses 10. Jenner vaccinated for smallpox, not rabies 5

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Textbook: Contemporary Abstract Algebra
Edition: 8
Author: Joseph Gallian
ISBN: 9781133599708

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If a, b, and c are elements of a ring, does the equation