Journal of Theoretical Biology (1998) 192, 489-504 [With the permission of the copyright holder, Academic Press]

Summary

Introduction

Relative Roles of Base Composition and Base Order

Randomization to Assess the Role of Base Composition

Importance of the Product of C and G

Fold Analysis of G0S2

Single Linear Regression Correlations

Correlations with Other Base Composition-Derived Parameters

Multiple Linear Regression

Conflict between base order and base composition

Identification of genes in uncharted sequences

1. Introduction

Opportunities for the single strands of duplex DNA molecules to form stem-loop structures may arise both during replication, and when the duplex is supercoiled (Murchie et al., 1992). The former has been invoked to explain expansions and contractions of simple sequence repeats (Wells, 1996). The latter may be involved in the initiation of recombination by way of the "kissing" of the tips of single strand loops (Kleckner & Weiner, 1993; Kleckner, 1997). This self/not-self homology search would appear to be a fundamental part of various long-range intra- and inter-chromosomal homology-dependent phenomena (Lewis, 1954; Wu, 1993), and its progressive impairment could lead to speciation (Radman et al., 1993; Forsdyke, 1996a). The stem-loop potential of a DNA sequence is unlikely to be just a passive and indirect consequence of the action of various evolutionary pressures on DNA; there appear to be powerful genome-wide pressures which actively confer or inhibit the potential to form stem-loops (Forsdyke, 1995a,b).

    Improved knowledge of the energetics of base stacking and loop formation has facilitated the development of computer programs to predict the most likely secondary structures (stem-loops) in nucleic acids using the energy-minimization approach (Zuker, 1994). The programs work well with single stranded RNA and, with minor adaptations, can be applied to single stranded DNA (Gacy et al., 1995; Nielsen et al., 1995). Although the chemistry and thermodynamics of stem-loop formation are very important, nucleic acids can be considered more simply as informational macromolecules with three fundamental characteristics: length, base composition and base order (Forsdyke, 1995c). If windows of constant length are chosen, the properties of stem-loop structures can be analysed just in terms of base composition and base order. The total potential of a window in a sequence to form stem-loop structures can be decomposed into the base composition-dependent stem-loop potential, and the base order-dependent stem-loop potential (Forsdyke, 1995d;1996b).

   Studies using this approach led to the proposal that, because of a role in recombination, stem-loops once dominated the sequences of the "replicators" in the early "RNA world". Protein-encoding potential was subsequently imposed, and the pressure on base order to encode stem-loops had to accommodate to the pressure on base order to encode proteins (Forsdyke, 1995a). This suggested that a region of DNA might have a high base order-determined stem-loop potential if accommodation was possible, or zero base order-determined stem-loop potential if protein-encoding potential dominated. Computer analyses of the secondary structure of natural DNA sequences showed some agreement with this model, except that base order-determined stem-loop potential was often observed to be significantly less than zero. This was particularly evident in protein-coding regions, but was also found in non-protein-coding regions. I here extend the original model to deal with this, and demonstrate application of this way of thinking about stem-loops to the analysis of the contribution of various base composition-dependent parameters to the potential secondary structure of the human G0S2 gene. The results draw attention to the importance of base products, particularly CxG, and suggest a new approach to the detection of genes in the uncharted genomic sequences currently accumulating in databases.

2. Relative Roles of Base Composition and Base Order

    The role of base order in determining the secondary structure of a nucleic acid is evident from the demonstrated importance of dinucleotide nearest-neighbour stacking interactions in calculating secondary structure (Borer et al., 1974; Breslauer et al., 1986). This may relate, in some way, to the observation that dinucleotide frequencies, rather than higher oligonucleotide frequencies, are a fundamental distinguishing feature of biological species (Nussinov, 1981; Forsdyke, 1995c). Calculation of secondary structure using the energy minimization approach requires accurate knowledge of the enthalpy and entropy changes involved in the formation of stems (which tend to stabilize secondary structure), and of various types of loops (which tend to destabilize the structure; Turner et al., 1988; Fontana et al., 1993; Sinden, 1994). The important process of assigning and refining energy values for formation of various structural elements is ongoing (Shen et al., 1995; SantaLucia et al., 1996), but there is growing confidence that the calculated secondary structures are biologically relevant, at least in the case of RNA (Zuker et al., 1991). The complexities in the calculations are ignored in the first part of the present work, and the energetics of nucleic acid folding are considered simply in terms of base composition and base order. Following Tinoco et al., (1971), "stability numbers" of 1 and 2 are assigned to A-T and C-G base pairs, respectively.

   A series of hypothetical stem-loop structures are shown in Figure 1. For present purposes, only a single stem is allowed, and no sliding of strands relative to each other is permitted. Furthermore, the role of the loop is ignored. The first stem consists of a series of 16 A residues, which do not complement each other. Thus, if this were part of a natural DNA sequence, either the sequence would remain unextruded from duplex DNA, or a large loop (rather than a stem), would form. In the second stem a quarter of the bases are T residues.

    The third stem consists of equal proportions of As and Ts. The total possible number of A-T base pairs (8) is formed. The number of A-T pairs which would be formed if 8 As and 8 Ts were randomly mixed would be 4. Thus, the contribution to the score attributable to base composition alone is 4. By subtraction we can determine that the base order-dependent component of the score is 4. The fourth stem has the same base composition as stem 3, so that the potential base composition-dependent contribution to the stability remains at 4. However, the distribution of As and Ts is such that no A-T base pairs form. Thus, the total score is zero, and by subtraction we determine that the contribution of base order is minus 4. The bases are ordered so as to oppose the random tendency for a sequence of 8 As and 8 Ts to form 4 A-T intrastrand base pairs. Stem-loop extrusion from duplex DNA is opposed. Alternatively, if associated with an extruded structure, the order of bases would favour loop, rather than stem, formation.

    The fifth and sixth stems contain equal proportions of all four bases. In the fifth stem only four complementary pairs are present. These are C-G pairs, to each of which we assign the score of 2, for a total score of 8. The relative contributions of base composition and base order are 3 and 5, respectively (as will be shown below). The sixth stem has no base pairing. The potential contribution of base composition remains at 3, so that the contribution of base order is minus 3.

   Figure 1 shows that the correct bases may be present in the correct proportions, but if base order is inappropriate there may be no stem (zero total score). Stem stability depends on base composition in two ways.

• Complementary bases must be present in equal proportions, and
  
  

• the more C-G pairs there are, the higher will be the stability.

3. Randomization to Assess the Role of Base Composition

    If the fifth stem in Figure 1 were a natural sequence, then we could call the total score (8) the "folding of natural sequence" (FONS) value. How do we calculate the contributions of base composition and base order to that score? The stem has a unique characteristic, its base order, and two other characteristics which it shares with large sets of other possible DNA sequences, its length and base composition. The natural sequence is but one member of a hypothetical set of sequences which share length and base composition. Any average characteristic of this set must be a function of the latter two parameters. By keeping length constant, we can focus on the role of base composition. If the order of bases is randomized (shuffled), keeping the length constant, then members of the set which differ only in base order, are obtained. The sixth stem in Figure 1 is one member of the set. Figure 2 shows 10 other members of the set. These happened to be those generated first by consecutively shuffling base order in the fifth stem in Figure 1. Associated with each member is a total score. Each score is a "folding of randomized sequence" (FORS) value for the fifth stem in Figure 1.

    It is seen that most members score less than the natural sequence. The mean score of the set of 10 is 3.3±0.7 (standard error), which closely approximates to 3. This is the "folding of randomized sequence mean" (FORS-M) value, which is an average characteristic of the set, and thus should be base order-independent. The value provides a measure of the contribution of base composition to the FONS value for the 5th stem of Figure 1. By subtraction, the contribution of base order is found to be 5. This is the "folding of randomized sequence difference" (FORS-D) value, which provides a measure of the contribution of the primary sequence (base order) to the stability of stem-loop structures in a natural sequence of given length. In this case, the FORS-D value is positive, and is significantly different from zero (P<0.01). This makes it likely that the sequence of the fifth stem in Figure 1 (if it were a real sequence) had accepted mutations which form complementary base pairs, thus enhancing its stem potential. FORS-D values can provide a measure of what Le & Maizel (1989) have termed "statistically significant" stem-loop potential. However, statistical significance may not be the same as functional significance (Karlin & Brendel, 1992). Le and coworkers (1991) have shown for retroviruses that "statistically significant" stem-loop potential is functionally relevant.

    It will be noted that four of the stems derived by randomization (Fig. 2), have lower total scores than 3. An extreme example of this is the sixth stem in Figure 1. To generate by chance a stem with no base pairs would usually required more randomizations than the ten used to generate Figure 2. Thus the sixth stem of Figure 1 is relatively improbable. If the sixth stem were part of a real natural sequence, then the low FORS-D value would imply that base order had been working strongly against base composition in determining the total score. We return to this in section 9.

4. Importance of the Product of C and G

   Of the various factors likely to contribute to the FORS-M value of a sequence window of a given length, the four simplest are the quantities of the four bases. Two slightly more complex factors are the bases of each potential base pair which are present in lowest amounts. Thus if the quantities of A, T, C and G in a 200 nt window are 60, 40, 70 and 30, respectively, then the "AT_min" would be 40 and the "CG_min" would be 30. These numbers would reflect the upper limit on the number of base pairs which could form stems, and might be expected to correlate positively with the base composition-dependent component of the stem-loop potential (FORS-M values).

    Conversely, the excess of bases (in the example A - T = 20 and C - G = 40) might provide an indication of the minimum number of bases available to form loops. Since loops tend to destabilize stem-loop structures, these "Chargaff difference" values (Smithies et al., 1981; Bell & Forsdyke, 1999a, b), might be expected to correlate negatively with the base composition-dependent component of the stem-loop potential.

    However, in section 2 above, FORS-M values were considered as if the result of random interactions between free bases in solution. This predicts that the two products of the quantities of pairing bases should be important (60 x 40, and 70 x 30, in the above example). The products would be maximal when pairing bases were in equal proportions (i.e. [50 x 50] > [60 x 40] > [70 x 30]). Thus the products provide an index both of the absolute quantities of the members of a Watson-Crick base pair, and of their relative proportions.

    In an attempt to derive formulae permitting the prediction of FORS-M values directly from the proportions of the four bases, Chen and coworkers (1990) demonstrated the relative importance of eight of the above factors; (they referred to FORS-M values as "energy_random" = "e_r" values). The factors were A, C, G, T, AT_min, CG_min, A x T, and C x G, where A, C, G, and T refer to the quantities of each particular base in a sequence window. Multiple least-squares linear regression analysis of data obtained by folding nucleic acid using the energy minimization approach (e.g. Zuker, 1994), produced coefficients for each of the factors which provided an index of relative importance. The products of the quantities of the Watson-Crick pairing bases (A x T, and C x G) were found to be of major importance, with the coefficients of C x G (the strongly interacting S bases), exceeding those of A x T (the weakly interacting W bases). Less important were AT_min and CG_min and the quantities of the four bases. The following case-study of the G0S2 gene supports these findings, and thus the line of reasoning presented in sections 2 and 3. The influence of the pairing of mismatched bases will not be considered here.

   If a major determinant of base composition-dependent stem-loop potential is the C x G product (see Section 4), then the high negative FORS-M values in the region of the CpG island could reflect the high (C+G)% of the region (Fig. 3a), but the relative proportions of C and G would have to be balanced. This implies a high CG_min. Conversely, the difference between the number of Cs and Gs ("Chargaff difference") should be low.

   The significances of various correlations, some of which are noted by direct inspection of Figure 3, were investigated using the least-squares linear regression approach. Correlations with base composition expressed as (C+G)% are shown in Figure 4. Points corresponding to the CpG island form a cluster (larger symbols) at the right of the graphs. Linear regressions for all points (continuous dark lines) are shown with linear regressions both for points corresponding to the CpG island, and for the points remaining after excluding the CpG island (dashed blue lines). Some parameters of the lines (3 sets of 3 numbers) are shown, with the uppermost set of numbers referring to the linear regression for all points. The 3 numbers refer to the slope (Sl), the coefficient of determination (r²), and the probability (P) that the slope of the line is not significantly different from zero. The influence of base composition on FONS values (Fig. 4a) reflects the summation of the dual influences on FORS-M values (Fig. 4b), and on FORS-D values (Fig. 4c).

As the proportion of the S bases increases (and the proportion of the W bases reciprocally decreases), the base composition-dependent stem-loop potential increases (Fig. 4b). This emphasizes the positive role of the S bases. Points corresponding to the CpG island make a major contribution, and when these points are removed the dependence of FORS-M values on base composition is much less evident (r² = 0.084), although still significant (P = 0.001). This emphasises the point that base composition tends to be a non-local, genome or genome-sector, characteristic, and tends to have a large local impact only under unusual circumstances (presence of a CpG island).