Modeling hybridization kinetics Jian-Ying Wang, Karl Drlica Mathematical Biosciences 183 (2003) 37-47

Introduction (1) DNA-RNA & RNA-RNA hybridization are important : nucleic acid (n.a.) func’n, detection of n.a., alteration its exp’n Two parameters that characterize the hyb. Equilibrium yield (main concern when incubation time is unlimited, e.g. Southern hyb.) Annealing rate (when hyb. is involved in the inhibition of gene exp’n)

Introduction (2) Effective antisense oligont. for hyb. to target RNA Previous efforts at computational identification 1.Predictions of RNA 2° structure ( identify regions likely to be single stranded & presumably accessible for hyb. ) -> correlation w/ antisense oligodeoxynt. (ODN) hyb. Shows considerable scatter. ( ss regions don’t correspond to regions that hybridize most readily) 2.Calculate overall E gain due to hybrid formation & relate to inhibition of gene exp’n -> do not always correlates with experimental data. -> more problematic is the inability of E gain calculations to explain the large (up to 1000 fold ) difference in hyb. rate Necessary to use experimental methods to determine favorable sites for antisense attack of RNA

Introduction (3) Important factors in determining accessibility for hyb. : melting E & E (free E) gain develop a computational description for hyb. of short complementary regions within large n.a. calculate a rate factor (that is proportional to the rate at which oligont. hybridize to sites in RNA under quasi st-st conditions) rate factor model

Results

Theoretical Considerations A : antisense oligonucleotide S : target RNA AS : antisense-target RNA hybrid P : products of the second step The second step may be : an enzymatic cleavage (e.g. antisense-DNA mediated RNase H cleavage rxn ) : structural change ( e.g. annealing of long antisense-target RNA hyb. )

E advantage

by kinetic approach of quasi st-st conditions, d[AS]/dt=0 thus, the 2 nd order association constant : for the initial rate of a single-tube assay, total antisense is conserved, [A 0 ]=[A]+[AS] (at beginning, [P]~0) thus, the 2 nd order association constant : Estimation of K m enables us to compare relative rxn rates for different sites in a given RNA ( if, k 2 ~constant )

to estimate K m, first consider eq. constant for hybrid dissociation from Boltzmann distribution, the occupancy of the activated state is proportional to k 1 * : forward rate constant for the binding of the activated antisense oligont to the activated target site : related to assay conditions, independent of RNA structure k 2 /k 1 * can be considered constant 1

1 Can be used for compare different sites in RNA for antisense ODN hyb. For this, define a rate factor, x=k/k 2 for comparing relative hyb. rate at st-st for estimation of initial hyb. rate (pre-equil.)

Correlations bt’n rate factor & experimental antisense- mRNA hyb. determined w/ oligonucleotide libraries As a test for 기존 실험 결과와 비교. hyb. in the presence of RNase H. the most readily hyb. regions -> degraded by RNase H and revealed by gel electrophoresis

12/13 arrows align with peaks in the trace

Correlation bt’n maximal rate factor and initial hyb. rate For oligont. longer than 15 nt. by considering all 15 nt region, & using, calculate maximum rate factor. The maximal rate factor shows good correlation w/ the 2 nd order binding rxn rate constant. ( Accessibility score is based on a statistical consideration of single- strandedness. )

Discussion An expression was derived that relates nucleic acid secondary structure to the steady-state rate of oligont.–RNA hyb. The assumption of the model : hyb. of nucleic acids occurs through an intermediate state The central feature of the rate factor model is that it uses both melting energy and energy gain to identify favorable sites for hyb. Since dynamic processes are more likely to be relevant than eq. processes for inhibition of gene expression with antisense oligonucleotides, the st-st model should be more suitable than eq. models for identifying favorable hyb. sites.

Materials and methods G 0 anti and G 0target were obtained from the output files of the GCG RNA folding program FoldRNA (GCG Package Version 10-Unix, Genetics Computer Group, University of Wisconsin, Madison, WI)

extra discussion… DNA / RNA hyb. rate constant data 는 많은데, DNA / DNA 는 잘 못찾겠음 … DNA / DNA hyb. rate constant 에 대한 experimental data 가 있으면, modeling 한 equation 으로 각 strand fragment 의 concentration 추이를 알아볼 수 있다. But 3 strand 이상의 것에 대해서는 새로운 experimental data 가 필요할지도 … 우리의 model 에 대해 (1) 식을 적용하는 것이 타당할까 ? quasi st-st 의 적용은 타당할까 ?