DNA Mapping in addition to Brute Force Algorithms Outline Molecular Scissors Discovering Restriction Enzymes Discovering Restriction Enzymes

DNA Mapping in addition to 		Brute Force Algorithms Outline Molecular Scissors Discovering Restriction Enzymes Discovering Restriction Enzymes www.phwiki.com

DNA Mapping in addition to Brute Force Algorithms Outline Molecular Scissors Discovering Restriction Enzymes Discovering Restriction Enzymes

Walker, Stephanie, Meteorologist has reference to this Academic Journal, PHwiki organized this Journal DNA Mapping in addition to Brute Force Algorithms Outline Restriction Enzymes Gel Electrophoresis Partial Digest Problem Brute Force Algorithm as long as Partial Digest Problem Branch in addition to Bound Algorithm as long as Partial Digest Problem Double Digest Problem Molecular Scissors Molecular Cell Biology, 4th edition

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Discovering Restriction Enzymes HindII – first restriction enzyme – was discovered accidentally in 1970 while studying how the bacterium Haemophilus influenzae takes up DNA from the virus Recognizes in addition to cuts DNA at sequences: GTGCAC GTTAAC Discovering Restriction Enzymes Werner Arber Daniel Nathans Hamilton Smith Werner Arber – discovered restriction enzymes Daniel Nathans – pioneered the application of restriction as long as the construction of genetic maps Hamilton Smith – showed that restriction enzyme cuts DNA in the middle of a specific sequence My father has discovered a servant who serves as a pair of scissors. If a as long as eign king invades a bacterium, this servant can cut him in small fragments, but he does not do any harm to his own king. Clever people use the servant with the scissors to find out the secrets of the kings. For this reason my father received the Nobel Prize as long as the discovery of the servant with the scissors”. Daniel Nathans’ daughter (from Nobel lecture) Recognition Sites of Restriction Enzymes Molecular Cell Biology, 4th edition

Uses of Restriction Enzymes Recombinant DNA technology Cloning cDNA/genomic library construction DNA mapping Restriction Maps A map showing positions of restriction sites in a DNA sequence If DNA sequence is known then construction of restriction map is a trivial exercise In early days of molecular biology DNA sequences were often unknown Biologists had to solve the problem of constructing restriction maps without knowing DNA sequences Full/Complete Restriction Digest Cutting DNA at each restriction site creates multiple restriction fragments: Is it possible to reconstruct the order of the fragments from the sizes of the fragments {3,5,5,9}

Complete Restriction Digest: Multiple Solutions Alternative ordering of restriction fragments: vs Measuring Length of Restriction Fragments Restriction enzymes break DNA into restriction fragments. Gel electrophoresis is a process as long as separating DNA by size in addition to measuring sizes of restriction fragments Can separate DNA fragments that differ in length by only 1 nucleotide as long as fragments up to 500 nucleotides long Gel Electrophoresis DNA fragments are injected into a gel positioned in an electric field DNA are negatively charged near neutral pH The ribose phosphate backbone of each nucleotide is acidic; DNA has an overall negative charge DNA molecules move towards the positive electrode

Gel Electrophoresis (cont’d) DNA fragments of different lengths are separated according to size Smaller molecules move through the gel matrix more readily than larger molecules The gel matrix restricts r in addition to om diffusion so molecules of different lengths separate into different b in addition to s Gel Electrophoresis: Example Direction of DNA movement Smaller fragments travel farther Molecular Cell Biology, 4th edition Detecting DNA: Autoradiography One way to visualize separated DNA b in addition to s on a gel is autoradiography: The DNA is radioactively labeled The gel is laid against a sheet of photographic film in the dark, exposing the film at the positions where the DNA is present.

Detecting DNA: Fluorescence Another way to visualize DNA b in addition to s in gel is fluorescence: The gel is incubated with a solution containing the fluorescent dye ethidium Ethidium binds to the DNA The DNA lights up when the gel is exposed to ultraviolet light. Partial Restriction Digest The sample of DNA is exposed to the restriction enzyme as long as only a limited amount of time to prevent it from being cut at all restriction sites Each DNA molecule is cut at most twice The experiment generates the set of all possible restriction fragments between every two (not necessarily consecutive) cuts, equally likely The set of fragment sizes is used to determine the positions of the restriction sites in the DNA sequence Partial Digest Example Partial Digest results in the following 10 restriction fragments:

Multiset of Restriction Fragments We assume that multiplicity of a fragment can be detected, i.e., the number of restriction fragments of the same length can be determined (e.g., by observing twice as much fluorescence intensity as long as a double fragment than as long as a single fragment) Multiset: {3, 5, 5, 8, 9, 14, 14, 17, 19, 22} Partial Digest Fundamentals the set of n integers representing the location of all cuts in the restriction map, including the start in addition to end the multiset of integers representing lengths of each of the C(n,2) fragments produced from a partial digest the total number of cuts X: n: DX: One More Partial Digest Example Representation of DX = {2, 2, 3, 3, 4, 5, 6, 7, 8, 10} as a two dimensional table, with elements of X = {0, 2, 4, 7, 10} along both the top in addition to left side. The element at (i, j) in the table is xj – xi as long as 1 i < j n. Partial Digest Problem: Formulation Goal: Given all pairwise distances between points on a line, reconstruct the positions of those points Input: The multiset of pairwise distances L, containing n(n-1)/2 integers Output: A set X, of n integers, such that DX = L Partial Digest: Multiple Solutions It is not always possible to uniquely reconstruct a set X based only on DX. For example, the set X = {0, 2, 5} in addition to (X + 10) = {10, 12, 15} both produce DX={2, 3, 5} as their partial digest set. The sets {0,1,2,5,7,9,12} in addition to {0,1,5,7,8,10,12} present a less trivial example of non-uniqueness. They both digest into: {1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 7, 7, 7, 8, 9, 10, 11, 12} Homometric Sets Walker, Stephanie WVTM-TV Meteorologist www.phwiki.com

Brute Force Algorithms Also known as exhaustive search algorithms; examine every possible variant to find a solution Efficient in rare cases; usually impractical Can be the basis as long as the design of other algorithms (e.g., branch- in addition to -bound) Partial Digest: Brute Force Find the restriction fragment of maximum length M. M is the length of the DNA sequence. For every possible set X={0, x2, ,xn-1, M} compute the corresponding DX If DX is equal to the experimental partial digest L, then X is output as the correct restriction map BruteForcePDP BruteForcePDP(L, n): M <- maximum element in L as long as every set of n – 2 integers 0 < x2 < xn-1 < M X <- {0,x2, ,xn-1,M} Form DX from X if DX = L return X output “no solution” Efficiency of BruteForcePDP BruteForcePDP takes O(M n-2) time since it must examine all possible sets of positions. One way to improve the algorithm is to limit the values of xi to only those values that occur in L. O-notation: an asymptotic upper bound f(n) = O(g(n)) iff there exist two positive constant c in addition to n0 such that 0 f(n) cg(n) as long as all n n0 For example, 5n + 108 = O(n) in addition to 2n = O(nlog n). How fast functions grow For large data sets, algorithms with a complexity greater than O(n log n) are often impractical! n function (Assume one million operations per second.) Multiple Complete Digest (MCD) Mapping – a way to map genomes

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