Computational and experimental analysis of DNA shuffling : Supporting text N. Maheshri and D. V. Schaffer PNAS, vol. 100, no. 6, Summarized by Shin, Soo-Yong

© 2003, SNU BioIntelligence Lab, Length Distribution Comparison Experimental and simulation data cannot be directly compared due to an agarose gel.  Fragments migrate due to both the external electric field and molecular diffusion  The intensity of fragments is related to both their concentration and size Solution: Gaussian distribution  Fitting to each band by mean and standard deviation

© 2003, SNU BioIntelligence Lab, Length Distribution Comparison Gaussian transformation function can be limited in accuracy for large fragments (> 2kb)  because of retarded mobility Gaussian transformation function can be limited for small fragments (< 200 bp) because of difficulties with detection  Small fragments bind less dye and diffusion significantly disperses them

© 2003, SNU BioIntelligence Lab, Length Distribution Comparison Detection can be improved by loading a greater amount of DNA  Overloading a gel results in retarded mobility of the fragments: DNA steaking

© 2003, SNU BioIntelligence Lab,

Deviation of annealing probabilities Two fragments will anneal with at least some minimum overlap (7 bp)  The effects of mismatched annealing are also included. The free energy of hybridization at any temperature T 0 0

© 2003, SNU BioIntelligence Lab, Deviation of annealing probabilities The equilibrium constant, K The equilibrium concentration in terns of an equilibrium conversion, X S1 and S2 are equal in concentration All DNA initially is in the ssDNA state The fraction of the reaction that has occurred

© 2003, SNU BioIntelligence Lab, Deviation of annealing probabilities X = 0 implies no reactants have converted to products. X = 1 implies all reactants have converted to products. The equilibrium conversion Two distinct sequence : 4 Self-complementary : 1

© 2003, SNU BioIntelligence Lab, Deviation of annealing probabilities Total number of ways, N, that S 1 and S 2 can anneal, given fragment lengths l 1 and l 2, and a minimum overlap v  No gap or bulges  Two ssDNAs stretched out  With dangling ends

© 2003, SNU BioIntelligence Lab, Deviation of annealing probabilities The reaction is modeled as a Markov chain

© 2003, SNU BioIntelligence Lab, Deviation of annealing probabilities To calculate the equilibrium probability for each state Transition probability from state X to state Y Probability in state X

© 2003, SNU BioIntelligence Lab, Deviation of annealing probabilities This equations are used to choose are final state when two ssDNA collide

© 2003, SNU BioIntelligence Lab, Effects of concentration and temperature on hybridization stringency Changing temperature alters annealing probabilities in a strongly sequence- dependent fashion Changes in concentration alter them in a more nonspecific manner

© 2003, SNU BioIntelligence Lab, Kinetics of DNA hybridization On collision, a few base pairs of two complementary ssDNA strands form a nucleation site, after which they rapidly zipper into a single dsDNA strand. A mixture of ssDNA fragments hybridizes at a rate described by 2 nd -order kinetics Nucleation rate constant Length of the shorter fragment involved Complexity of the mixture or the number of unique sequences of ssDNA in the mixture

© 2003, SNU BioIntelligence Lab, Kinetics of DNA hybridization Estimate the rate constant by using the length of the gene, L G, divided by the initial average fragment size, L F0, for the complexity, and the current average fragment size for L F can be calculated

© 2003, SNU BioIntelligence Lab, Estimating collision frequency of ssDNA in dilute solution The collision frequency can be estimated by finding the average velocity for the ensemble of ssDNA molecules and then using the kinetic theory of gases  based on Zimm’s rederivation of the bead-spring model of a polymer in dilute solution to include hydrodynamic effects Number of nucleotides Length between nucleotides Viscosity of the solvent temperature Boltzmann’s constant

© 2003, SNU BioIntelligence Lab, Estimating collision frequency of ssDNA in dilute solution Average velocity of each particle and the mean free path, λ, between the particles, assuming the gas particle are ideal (neither interact nor take up volume) and spherical, Number of particles per unit volume Mean free path Average radius of each particle

© 2003, SNU BioIntelligence Lab, Estimating collision frequency of ssDNA in dilute solution We can estimate the radius of a DNA molecule by its radius of gyration For an aqueous solution of ssDNA molecules at 0.3 μM (corresponding to approximately 1 μg of digested fragments with an average fragment size of 100 bp in a 50 μl volume) at a temperature of 60°C  an estimated collision frequency of ≈25 collisions per second per molecule.