CISC 203 Lecture Notes - Lecture 1: Recurrence Relation, Fibronectin

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raspberryserval319

25 Sep 2017

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A and b: assume a prime p p is irrational. 5 + 2 + 2 + 2 fn = 5 + (n 1)*2. Let"s use the example above: claim: f1 = 5 and fn = fn-1 + 2 is equivalent to fn = 5 + (n 1)*2, base case: let n = 1, 5 = 5 + (1-1)*2 = 5. Inductive step: assume for some k, k 1, fk = 5 + (k 1)*2: consider fk+1 fk+1 = fk + 2. Question: f1 = 1 and fn = 2*fn-1 + 1. 1: claim: f1 = 1 and fn = 2*fn-1 + 1 is equivalent to fn = 2n - 1, base case: let n = 1, 1 = 21 1 = 1. Inductive step: assume for some k, k 1, fk = 2k - 1: consider fk+1 fk+1 = 2*fk + 1.

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5. (18 pts) Circle True if the statement is ALWAYS true; circle False otherwise. No explanations are required. Let f be a one-to-one function and f its inverse. (a) If the point (2, 5) lies on the graph off, then the point (5,2) lies on the graph of f. True False f (2) = 5 f-1 (5) = 2 (b) sin-1 (T) = 0 True False Since >1, ris not in the domain of sin-?; | or sin-1 (7) #0, since sin (0) = 0 # Iff and g are two functions defined on (-1, 1), and if (c) limg (x) = 0, then it must be true that lim[ f(x) g (x)] = 0. True False Let f (x) = 1 / x, if x #0, and f (0) = 4 and g(x) = x. Then lim g (x) = lim (x) = 0, but Lim ( f (x) g(x)] = lim [() x] = 18 0. Iffis continuous on (-1, 1), and if f (0) = 10 and lim g (x) = 2, (a) True False then lin (= 5. Because lim : (*) - Limx-of (*) .f(0) = 20 = 5 If f is continuous on [1, 3], and if f(1) = 0 and f(3) = 4, then the equation f(x) = (e) has a solution in (1, 3). True False Since f continuous on [1, 3), f(1) = 0 < < 4 = f (3), by the Intermidiate Value Theorem there exists a cin (1, 3) such that f (c) = . (f) Let f be a positive function with vertical asymptote x = 5. Then lim f (x) = +0. True False Let f (x) = 1, if x < 5, and f (x) ==, ifx>5. Then lim f (x) = +00, and therefore, X = 5 is a vertical asymptote. 5 - X So, f is a positive function with vertical asymptote x = 5 but lim f (x) + +co, since lim f (x) = + 0 + lim f (x) = 1, which means that lim f (x) does not exist.

ey table is seen below xeecions tor Chapter 1 12, Fori, b â¬ Î.el * b-aa (0 (D 14 ForVEQ r the operation defined in Example 1 on the wr John Sue Henry. P iDFor 15ine if is ass ociative by determining if the final six engu defined ang property (ii)of Theorem 1 . So no element i if the operntion debined in Example 1 of Emle if each element has an inverse Section 1.3 Groups iw comutatityn ild Chapter 3 where the Funda the exercises that follow etermining why they are not Write out the Cayley table for the gru(o)nud lensify thee element the 10 elements of the group Z 18 its operation uses ts in the first coordinnte and +2 in the secotu Ldessity the Zn and write out the Cayley table. Reeall th of each element does Theorem 1.14 tell us aont the entries in the Cayley table ol s xrewp that is set with exactly one element. A {n), will always form group since there 19. What nly one way to define an operation on the set. Be sure to shhow that the properi combination of the usual notice what set the rule is be of a group all hold. 21. We can create even create groupe with games! Consider four cups placed in a ssare patter table. If we have a penny in one of the cups there are four ways we can move it to t cup: Horizontally, Vertically, Diagonally, or Stay nehere it is. We will p, S. To define nn operation, consider two movements in a row, v.e.,m ove the penny as r tells us to, then after that move the penny as y instruets. the set of integers the set of real numbers n the set of positive integers. e set of positive integers. n the set of positive integers. on the set of integers e set of negative integers. we ple, HV D since if we first move it horizontally and then vertically nltogether e moved it diagonally. Create the Cayley table for this group, identify the identity and the inverse of cach element 22. Prove that the set A 0 under matrix multiplication. Is it abelian? 23. Verify that 3(R) is a group using the addition of funetions as defined in Example 13 e set of nonzero rational n he set of nonzero real num n on the set R (-1 Section 1.4 Basic Algebra in Groups 24. Prove the Cancellation Law (Theorem 1.20). Do not use any theorems that occur after it in the text ssociative, commutative, has roof or counterexample fo 25. Assume G is a group and a e G. Consider a fixed integer k and use PMI (Theorem 0.3) to prove that for all nEN, a aYou will need to consider cases here since k can be positive, negative, or o 26. Prove Theorem 1.23 (ii) for the case of n > 0 and m

1. You have the following prokaryotic DNA sequence: 5â²-GGACTAGACAATAGGGACCTAGAGATTCCGAAA-3â² 3â²-CCTGATCTGTTATCCCTGGATCTCTAAGGCTTT-5â² If the top strand is the template strand which sequence below is the correct mRNA transcript? A. 5â²-GGACUAGACAAUAGGGACCUAGAGAUUCCGAAAâ3â² B. 5'-UUUCGGAAUCUCUAGGUCCCUAUUGUCUAGUCC-3' C. 5'-CCUGAUCUGUUAUCCCUGGAUCUCUAAGGCUUU-3' D. None of the above are correct

2.Starting in the cytoplasm with a fully mature mRNA explain the process of translation initiation and then elongation and termination to me.

3.Prior to export from the nucleus, pre-mRNA must be processed. What specifically does this entail?

4.The biosynthetic pathway for the two amino acids E and H is shown schematically in the figure. You are able to show experimentally that E inhibits enzyme V, and H inhibits enzyme X. The most logical hypothesis regarding the regulation of Enzyme T would be that it is most likely subject to feedback inhibition by E alone. True or False?

5. A. kinase B. ligase C. polymerase D. oxido-reductase E. Phosphatase F. protease G. nuclease H. ATPase 1. Removes a phosphate group from a molecule 2. Hydrolyzes ATP 3. Hydrolyzes bonds between nucleotides 4. Adds phosphate groups to molecules 5. Catalyzes reactions in which one molecule is oxidized and another is reduced 6. Hydrolyzes peptide bonds 7. Joins two ends of DNA together 8. Catalyzes the synthesis of polymers such as RNA and DNA

6. Looking at the figure showing the change in reaction rate for two different enzymes that both utilize the same substrate, answer the following questions. a. What is the approximate Vmax for enzyme B ? b. What is the approximate Vmax for enzyme A ? c. What is the approximate Km for the enzyme which has a higher affinity for the substrate uM.

7. Answer the following question either yes or no (spell out the word, do not abbreviate as y or n). Looking at the following coupled reaction: Luciferase luciferin + O 2 ==========> oxyluciferin + light âG = + + Mg2+ ATP <=> AMP + PPi âG = - - - a. Based on your knowledge of free energy change and reactions would this coupled reaction occur ? b. Would changing the second step from ATP<=> AMP + PPi âG = - - - to ATP <=> ADP + Pi âG = - change your answer

7.Spontaneous reactions by definition will happen instantaneously. Why false?

8. Each of the following questions apply to the image of the channel protein. The purple sphere is a charged ion. Type your response to each question in the blank provided. a. Based you on what you know about cells and ions, what does the tri-lobed red and white molecule represent (although there aren't anywhere near enough of them shown) ? b. Since the question stated the purple sphere was a charged particle, using what you know about the tri-lobed red and white molecule what is the charge of the purples sphere c. On the extracellular space, on the right side of the purple sphere, there are two tri-lobed red and white molecules in close proximity to one another. The red of one appears to be attracted to the white of the other. What type of bond is this ? d. Based on your knowledge of proteins that interact with the membrane and the properties of the membrane, to what family of amino acids would the amino acid marked by A. most likely belong? ?

CISC 203 Lecture Notes - Lecture 1: Recurrence Relation, Fibronectin

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