This report analyzes the theoretical limits of DNA sequence discrimination by linked …

• Abstract
• Introduction
• Methods
• Results and Discussion
• References
• Figures

Biology Articles » Biophysics » The theoretical limits of DNA sequence discrimination by linked polyamides » Methods

Methods

- The theoretical limits of DNA sequence discrimination by linked polyamides

Linked polyamides bind in the minor groove of DNA such that each ring contacts primarily a single base. Each base pair is thus contacted by two polyamide rings, one from each of the two side-by-side polyamide chains (see Fig. 1). An individual ring will be denoted as R_N with the subscript denoting the particular specificity of the ring, such as R_A for an adenine-specific ring. It will be assumed that these rings bind strongly to their target base, and equally poorly to the three nontarget bases, with the difference in binding free energy denoted as d_N, where N again denotes the specific base. Thus, for an adenine-specific ring R_A:

[ 1 ]

where DG_N is the free energy of binding of a given ring to base N. The notation R_NR_N will refer to a pair of rings that bind side-by-side in the minor groove to a given base pair; for instance, R_AR_T is a pair of rings that bind preferentially to an AT bp. The representation (R_N1,...,R_Nm) will refer to an entire polyamide composed of a given set of m base-specific rings; for instance, an (R_G, R_A) polyamide is composed of two types of ring, one specific for G and one specific for A.

The sequence discriminatory ability of each polyamide will be evaluated using three assumptions. First, the binding free energy will be approximated as a linear sum of binding energies for each individual ring with a single DNA base. This approximation has worked well in a study of experimentally determined binding constants of polyamides with pyrrole and imidazole rings (16). In long pyrrole-imidazole polyamides, however, a slight mismatch between the contour length of the polyamide and the contour length of the DNA minor groove causes the rings to get "out of phase," and binding does not improve for polyamides with greater than »5 units (17). This issue has been addressed previously in connection with polyamide design (18), and methods have been reported to restore proper phasing by incorporating spacers into long polyamides (19). Hence, the effects of phasing mismatch will be neglected in this work. Second, any interference from competitive binding of overlapping binding sites will be neglected. Third, all sequences will be assumed present with equal frequency in the genome.

Given these assumptions, the fractional occupancy of the i^th n-bp DNA site (q_i,n, where i ranges from 1 to 4ⁿ and i = 1 corresponds to the target sequence) is calculated with the following Hill equation:

[ 2 ]

where K_i,n is the binding constant and [P_n] is the concentration of polyamide with length n. (Note: polyamides are denoted by the length of DNA contacted by the rings; a P_n polyamide is comprised of 2n rings that bind to n consecutive base pairs. As seen in Fig. 1, the charged tails and linkers, which are not addressed in the current work, will recognize an additional AT bp at each end of the linked polyamide.). The binding fraction Y_n, the ratio of the occupancy of the target site relative to that of all possible n-bp sites, is calculated as:

[ 3 ]

where a_i,n = K_1,n/K_i,n = exp[(DG_1,n  DG_i,n)/RT] and DG_i,n is the free energy of binding of the polyamide to the i^th n-bp site. The parameter a_i,n is a function of the relative number of mismatches between the polyamide with the target sequence compared with the number of mismatches with the i^th nontarget sequence and is a function of the energetic cost (d_N) of each of these mismatches. The binding fraction Y_n ranges between 0 and 1 and larger values indicate more specific binding to the target sequence relative to the nontarget sequences.

In cases where the target sequence is bound at least as favorably as all other sequences, two limits on the binding fraction may be evaluated. As the ligand concentration increases, Y_n decreases monotonically to a value of 1/4ⁿ, and all of the DNA sequences become equally saturated. Conversely, at low polyamide concentrations, the binding fraction approaches the upper limit:

 

[ 4 ]