10 AM Tue 13-Feb Genomics, Computing, Economics Harvard Biophysics 101 (MIT-OCW Health Sciences & Technology 508)MIT-OCW Health Sciences & Technology 508

Binomial, Poisson, Normal

p and q  p  q  q = 1 – p two types of object or event. Factorials 0! = 1 n! = n(n-1)! Combinatorics (C= # subsets of size X are possible from a set of total size of n) n! X!(n-X)!  C(n,X) B(X) = C(n, X) p X q n-X  np  2  npq (p+q) n =  B(X) = 1 Binomial frequency distribution as a function of X  {int  n} B(X: 350, n: 700, p: 0.1) = × = PDF[ BinomialDistribution[700, 0.1], 350] Mathematica ~= 0.00 = BINOMDIST(350,700,0.1,0) Excel

P(X) = P(X-1)  X =  x e -   X!  2  n large & p small  P(X)  B(X)  np For example, estimating the expected number of positives in a given sized library of cDNAs, genomic clones, combinatorial chemistry, etc. X= # of hits. Zero hit term = e -  Poisson frequency distribution as a function of X  {int  }

Z= (X-  Normalized (standardized) variables N(X) = exp(-  2 /2) / (2  ) 1/2 probability density function npq large  N(X)  B(X) Normal frequency distribution as a function of X  {-  }

Expectation E (rth moment) of random variables X for any distribution f(X) First moment= Mean  variance  2 and standard deviation  E(X r ) =  X r f(X)  E(X)  2  E[(X-  2 ] Pearson correlation coefficient C= cov(X,Y) =  X-  X )  Y-  Y )]/(  X  Y ) Independent X,Y implies C  but C  0 does not imply independent X,Y. (e.g. Y=X 2 ) P = TDIST(C*sqrt((N-2)/(1-C 2 )) with dof= N-2 and two tails. where N is the sample size. Mean, variance, & linear correlation coefficient

One form of HIV-1 Resistance

Association test for CCR-5 & HIV resistance Samson et al. Nature :722-5Nature :722-5

Association test for CCR-5 & HIV resistance Samson et al. Nature :722-5Nature :722-5

But what if we test more than one locus? The future of genetic studies of complex human diseases. RefRef (Note above graphs are active spreadsheets -- just click) GRR = Genotypic relative risk

Class outline (1) Topic priorities for homework since last class (2) Quantitative exercises so far: psycho-statistics, combinatorials, exponential/logistic, bits, association & multi-hypotheses (3) Project level presentation & discussion (4) Discuss communication/presentation tools Spontaneous chalkboard discussions of t-test, genetic code, non-coding RNAs & predicting deleteriousness of various mutation types.