Identification of the most significant amphipathic helix with application to HIV and MHV envelope proteins

Abstract Amphipathic helices, which play important roles in protein structure, occur in a wide variety of lengths. Yet existing methods employ fixed window lengths. We present a hierarchical procedure that identifies the Q most significant amphipathic helices regardless of length. Since the observed hydrophobicities are not normally distributed, test statistics usually employed for least-squares regression are inappropriate for assessing statistical significance of amphipathic helices. We show that an adjusted F statistic provides a good test. An application to the envelope protein of HIV finds an unexpected long amphipathic helix in gp41.


Introduction
In an amphipathic structure hydrophobic residues tend to cluster on one side with hydrophilic residues on the opposite side. An amphipathic a-helix is a structure that exhibits periodicity in hydrophobicity of -3.6 residues per turn. Amphipathic helices are important elements of protein structure. They can have functional roles as in the case of the spikes in viral envelope protein (Wilson et al, 1981;Skehel et al., 1982;de Groot et al., 1987), and they can participate in T cell receptor binding (DeLisi and Berzofsky, 1985) and in signal transport functions (Heijne, 1986).
The two basic methods for detecting periodicity in hydrophobicity compare the sequence to a harmonic sequence (Cornette et al., 1987). The first method uses the discrete Fourier transform to compute the so-called power spectrum or correlation function of the observed numerical sequence and a harmonic sequence. This approach has been widely used to detect amphipathic helices as illustrated by Eisenberg et al. (1984) for hydrophobic moments and by DeLisi and Berzofsky's (1985) procedure to detect T cell antigenic sites. The second method uses least-squares estimation. Cornette et al. (1987) have shown that these two approaches are closely related, and have discussed the advantages of each.
In native proteins, helices come in a wide range of lengths. For example, in influenza hemagglutinin HA2 there is a long helix of 60 residues, a shorter helix of 30 residues (Wilson et Laboratory of Biometrics, PO Box 509, Wadsworth Center for Laboratories and Research, New York State Department of Health. Albany. NY 12201, USA "To whom reprint requests should be sent al., 1981) and an amphipathic signal peptide of 10 residues (Auger and Lawrence, 1989). Existing methods employ windows with lengths set at fixed values, usually in the range of 7-20 residues. This restriction to fixed-length windows stems from the legitimate concern that existing measures of amphipathicity may not be length invariant. As we shall show, this is indeed the case since high amphipathic moments are more likely to arise by chance alone in short segments. This incompatibility of the available analytic techniques with the variability in length of natural helices has lead to considerable difficulty in sequence analysis (Heijne, 1986).
Below we examine the role of chance variation on measures of amphipathicity, develop an amphipathic measure that is length unbiased and present a method for identification of the Q most significant amphipathic helices. We illustrate the application of this method to an envelope protein of mouse hepatitis virus (MHV), a coronavirus, and to the envelope protein of human immunodeficiency virus (HIV).

Methods
A segment of observed hydrophobicities H k , k = p, . . ., p + d exhibits amphipathic periodicity that can be described as: where /3 0 is a constant, /3 h is the amplitude of the periodicity in hydrophobicity, 0 is the phase, co is 2n73.6 and e k is the error, i.e. the difference between the observed hydrophobicity (H k ) and the one predicted (H k ) by the sine model. Leastsquares estimates of the unknown parameters of equation (1) are obtained as follows by minimizing The effect of chance variation on these estimators can be assessed when the distribution of the estimators is known under the null model, H o : /3 h = 0. That is, the sequence shows just chance variation around a constant hydrophobicity, H k = /3 0 + 6*. If the errors e^ were normally distributed, then it can be easily demonstrated that the parameter estimators A and fi would be normally distributed, and the corresponding Fstatistic: is F distributed with 2, n -3 degrees of freedom (Draper and Smith, 1966).
This approach is one step beyond the hydrophobic moment (Eisenberg et al., 1984) and the least-square power spectrum (LSPS) (Cornette et al., 1987) in that it assesses the statistical significance of having observed such an amphipathic helix. We could similarly assess the statistical significance of LSPS since LSPS/a 2 is x 2 distributed with three degrees of freedom if the errors are A^CCT 2 ) (Draper and Smith, 1966). This would test whether all regression parameters are different from zero, but this is useful only when a 2 is known.
The assumption of normality of the errors is clearly not justified in this setting since the hydrophobicities assume 20 discrete values. It is well known that in some circumstances the F statistic is very intolerant to departures from normality of the dependent variable. In a classic paper, Box and Watson (1962) show that the robustness of the F statistic to departures from normality depends on the distributional form of the independent variables. They further show that, under the assumption that the errors under the null are independently distributed with some common distribution, not necessarily normal, then the F statistic is approximately distributed aŝ .Urf. where v\ and v 2 are the nominal number of degrees of freedom. In this application v, = 2, v 2 -n -3. Also, we have: where k 2 and fc, are the sample cumulants for the n values of Y and Cx is a multivariate analogue of kjk\.
To examine the effects of the non-normality and the utility of the above approximation in this setting, we generated 100 000 random residue sequences with sizes m = 10, 15, 20, 30, 40, 50, 75 and 100. The amino acid frequencies used are those of Dayhoff et al. (1978). Since we are interested in the most significant ones, we compare in Table I the p values for both the unadjusted and adjusted F distributions with the observed ones at significance levels in the right tail, 0.05, 0.01, 0.005 and 0.001. Notice that the departures from normality have a substantial and segment-length-dependent bias in the Fstatistic. For example, at a nominal value of 0.005 the unadjusted F statistic is nearly twice the nominal value for segments of length 10 and gradually approaches the nominal value as the segment length increases. On the other hand, the adjusted results provide uniformly good agreement and are consistently superior to the unadjusted distribution. Thus, the unadjusted distribution has a substantial length bias, while the approximation shows little if any bias. To evaluate the validity of the approximation in the extreme right tail of the distribution, we have examined the distribution of the smallest p values. We generated 1000 replicates of the smallest p value of a segment of length 20 in a sequence of length 200. We find that these p values from the adjusted F statistic follow the expected extremel distribution (Galambos, 1978) while the unadjusted do not.
We also investigated the utility of this approximation for other fixed frequencies. These include a periodicity of 3.5 as suggested for heptad patterns in coiled coil helices (McLachlan and Stewart, 1975), a periodicity of 3.7 as suggested by Cornette et al. (1987) and periodicities of 2 and 2.3 which are commonly used for /3-strands. In all cases, simulation results were comparable with those described above for period 3.6. Furthermore, simulations using alternate hydrophobicity scales (Cornette et al.'s PRIFT, 1987;Sweet and Eisenberg, 1983;Eisenberg and McLachlan, 1986) also confirmed the utility of the Box and Watson adjustments. The only exception was Hopp and Wood's scale (1981) where there was no need for an adjustment.
In the next section we illustrate how these results can be employed to identify the Q most significant non-overlapping amphipathic helices.

Algorithm
To find the most significant amphipathic helix, we select the segments whose consonance with the model, equation (1), is least likely to arise by chance alone, as follows. For any given segment, starting at any residue p and continuing an arbitrary number of residues d, the probability of type I error is the probability of falsely rejecting the null hypothesis H o , when it is true in favor of the alternative. As shown in the previous section, this probability is well approximated by evaluating the test F ratio against the F distribution with an adjusted number of degrees of freedom as follows: Since a(i,i + d) applies for arbitrary / and d, the most significant amphipathic helix is the segment with smallest probability of type I error, i.e.
where 5 is the set of starting points and lengths of interest. For example, to search an entire polypeptide of length n for amphipathic helices of length between 8 and 150 residues, S is the set, 7 5 d ^ 149, /' = 1, 2, . . ., n -d.
The algorithm shown in Figure 1 will identify the Q most significant non-overlapping segments.
The above algorithm first computes the least-squares estimates of model (1)  techniques such as regression updating using Givens or Householder transformations (Seber, 1977), or by using the method of provisional means to compute the means, sum of squares and sum of cross-products (Herraman, 1968).
The above algorithm is hierarchical. As such, all segments included in previous steps remain in the solution. It may be the case that the top Q segments identified by this approach are not the best Q when they are considered in combination. We have previously described an algorithm that will yield the best Q segments regardless of order of entry (Auger and Lawrence, 1989). We need not repeat the algorithm here, since all that is required is the use of the p values from the adjusted F statistic in the objective function of the algorithm.
Under the null, the random variable p ilg is the smallest of a set of uniform random variables a(i,i + d). There are Oin 2 ) of these uniform random variables. Many of these are observed from overlapping segments, since any segments within d residues of one another use common data. Thus, p s \ g follows the distribution of the first-order statistic from a set of independent uniform random variables. This situation is common in sequence analysis problems. Two types of methods have been developed for finding the critical values for such order statistics. The analytic approach employs asymptotic extremal theory (Karlin and Ghandour, 1985). The second set of methods employs random permutations (Karlin and Ghandour, 1985). In the applications presented below we employ the latter.

Applications
Many animal viruses obtain a lipid-containing membrane during maturation through a 'budding' process. These viruses direct the insertion of their own surface glycoproteins into the membrane envelope. Influenza haemagglutinin is the most well studied of these viral envelope proteins. This protein is composed of a fibrous stem section anchored into the membrane by a hydrophobic membrane-spanning region, and a globular domain distal to the membrane (Wilson et al., 1981). The stem domain is composed of two amphipathic helices of 30 and 60 residues. The fibrous stem is formed by a coiled-coil interaction of these helices into a trimer. There is substantial evidence that many other viral envelope proteins exhibit a similar structure (Wiley, 1985). These proteins are frequently called spike proteins due to their appearance on electron micrographs. Thus, a search for amphipathic helices of variable length in the sequences of viral surface glycoproteins appears promising.

Application to a coronavirus
We have previously analyzed influenza hemagglutinin using another method (Auger and Lawrence, 1989). Since the substantive results of the two analyses are quite similar, we do not present them here. Instead, we first present an analysis of another well-defined viral surface glycoprotein. Mouse hepatitis virus (MHV-A59) is a coronavirus. Coronaviruses are positivestranded, RNA-enveloped viruses. They infect human and domestic animals. An unusually large (-200 A) spike protein (E2) projects from the virion surface. This spike protein mediates binding of the virion to cell surface receptors and is involved in host cell fusion. E2 is also the main target of the host immune response. A post-translational cleavage of the protein between residues 717 and 718 divides this protein into two halves, 90B and 90A. Cleavage is required for fusion activity (Sturman et al., 1985). By analogy with influenza hemagglutinin the carboxyl half (90A), which contains the apparent transmembrane anchor segment, is generally acknowledged to constitute the stem portion. As an internal control we also applied the algorithm to the other structural proteins of MHV, El and N. None of these are expected to have long amphipathic helices.
Using an analysis focusing on heptad repeat patterns, de Groot et al. (1987) have proposed that there are two helices that combine together in a coiled coil to form the fibrous stem structure. Their model proposes that these helices form a dimer with a coiled coil in a manner similar to that of influenza hemagglutinin.
The most signifiant amphipathic helices for 90A and 90B are give in Table D along with the critical values derived from 100 random shufflings of the sequence. The most significant amphipathic helix is composed of 64 residues (971 -1034). As indicated in Table n, this result is unlikely to have resulted from chance alone. The longer helix (948-1056) suggested by de Groot et al. covers this region. The second most significant helix (799-843) is also long. However, only the first amphipathic helix is statistically significant. The second helical structure (1209-1267) indicated by de Groot et al. (1987) is very close to the transmembrane region near the carboxyl terminus of the molecule. As indicated in Table n, we find no long helix in this region. The fourth most significant helix (1235 -1248) is within the region, but is only 14 residues long. Application to the two other structural proteins of MHV (data not shown) showed no other significant amphipathic helices. Thus, we also find evidence to support the proposal that 90A has a helical fibrous structure. Furthermore, we find no significant amphipathic structures in 90B, the reputed globular half of the spike protein, or in any of the internal controls, structural proteins El and N.

Application to HIV
The viral surface glycoprotein of human immunodeficiency virus (HIV) is synthesized as a gpl60 precursor protein, and is subsequently cleaved into the exterior gpl20 and integral membrane gp41 proteins. Given the importance of this virus for public health, it is not surprising that this sequence has been the subject of intensive analysis (Alizon et al., 1986;Cease et al. ,1987;Modrow et al., 1987). We have analyzed both gpl20 and gp41. Table HJ shows the five most significant helices in gpl20 of the BH10 variant. Cease et al. (1987) used the AMPHI algorithm (DeLisi and Berzofsky, 1985;Margalit etal., 1987;Spouge et al., 1987) to identify antigenic sites in gpl20. They found five potential antigenic sites, and they chose to study those from more conserved regions. The two most favorable sites are env T2 (residues 112-124) and env Tl (residues 428-443). They found that helper T cell immunity can be induced with short peptides for both of these. From Table III we find that the first and third most significant regions are 420-435 and 99-129. Thus, env Tl clearly overlaps with our most significant region, and env T2 is contained in the third most significant region. Random shuffling indicates that these regions are not statistically significant.
Our most surprising result is found in the analysis of gp41. As indicated in Table IV for the BH10 variant, we find a long amphipathic helix covering a long stretch between residues 785 to 854 near the carboxyl terminus of gp41. We found significant long amphipathic helices in several other variants of HTV-1, but this is expected since gp41 is highly conserved across the HTV-1 variants. Given this high degree of conservation, more notable is the finding of a somewhat different pattern for variants BRU, HXB2 and HXB3. As illustrated for BRU in Table IV, we found two long, significant amphipathic helices near the carboxyl terminus of these variants. We also find a long amphipathic helix for HIV2's ROD variant (see Table IV). Given the 44.8% level of conservation (Guyader et al., 1987) in the gp41 region between HIV-1 (BRU isolate) and HTV-2 (ROD isolate), this result is notable. As we have discussed above, such long amphipathic helices are observed in the stem portion of viral envelope glycoproteins.
The membrane-associated polypeptide gp41 has three possible membrane-spanning regions (Modrow et al., 1987) (see Figure  2). In the following paragraph the residue numbers of the BH10 variant are used for illustrative purposes. The first two candidate membrane spanning regions, TM1 and TM2, follow directly after the cleavage site in a 70 residue segment (511-580), interrupted by a stretch of 10 hydrophilic residues. The third candidate region, TM3, is a segment of 26 hydrophobic amino acids (670-695), followed 26 residues downstream by a hydrophilic segment (722 -745). Thus gp41 may cross the membrane once, twice or three times. Consequently, it is not clear whether the segment in which the long amphipathic helices are located, carboxyl to TM3, is inside or outside the membrane. There is experimental evidence for both locations.
Within the TM1 sequence is a peptide that shows sequence similarity to the paramyxovirus fusion peptides. It has been shown that deletion mutants that lack this segment interfere with membrane fusion (Kowalski et al., 1987). On the other hand, the carboxyl terminus of gp41 does not appear to be necessary for fusion in that deletions in this region do not affect syncytium formation (Kowalski et al., 1987). However, such deletions result in a poorly replicating virus (Terwilliger et al., 1986). HIV replicates by budding at the cell surface. While the sequence of events is not fully understood, evidence indicates that the budding process involves the interaction of the cytoplasmic domain of viral surface glycoproteins and components of the virus in the cytoplasm (Wiley, 1985). Thus, the carboxyl end of gp41 may be involved in the budding process, and thus be at the interior. On the other hand, it has been observed that monoclonal antisera against the hydrophilic sequence (735-752) give cell surface labeling and are neutralizing. This suggests that the segment carboxyl to TM3 (695-856) is on the exterior, where a role as a fibrous spike is more plausible.
Viral surface glycoproteins are anchored in the membrane by a transmembrane hydrophobic peptide, which is terminated by a cytoplasmic domain. In most of these proteins the cytoplasmic domain is short. HTV and other related lentiviruses are unusual in that they have a large peptide in the region that appears to be a cytoplasmic domain. The structure and function of these large domains is poorly understood. Our finding that a large proportion of this domain contains a significant amphipathic helix may be taken either as supporting evidence that this domain is on the exterior, as indicated by antibody studies, or that this peptide functions in budding activity.

Discussion
Amphipathic helices play an important role in protein structure. These structures are known to occur in a wide range of lengths, yet existing methods are centered on the use of fixed window lengths. We have presented a method that identifies the most significant amphipathic helix, regardless of length.
A number of other features have been suggested as indicative of helices, such as the capping pattern at their termini (Presta and Rose, 1988;Richardson and Richardson, 1988). The method developed here can be extended to incorporate such additional features by adding terms to the regression model. Since this avenue provides a means to the simultaneous incorporation of multiple effects, it is an important area for further research.
A key to the development of the method we presented was our finding that the F distribution, with suitable adjustment for the non-normality of the data, provided a good approximation to the distribution of the test F statistic. This produces a good estimate of the probability of type I error. It is important to point out that the usefulness of the adjusted F distribution of Box and Watson is dependent on the distributional characteristics of the independent variables. However, as reported above, our simulation results show that this approximation is useful for many commonly used frequencies and hydrophobicity scales.
Under the null hypothesis, we assume that the hydro- phobicities of the residues are independent. In the case of DNA sequences, it is well known that dinucleotide frequencies deviate from the expected under independence. Markov chain models have been used to describe this departure. The order of the Markov chain depends on the sequence (Fuchs, 1980;Blaisdell, 1986), and it has been observed to be from 1 to 4. The literature on Markov effects for proteins is limited. However, there is one directly germane report. Lipman and Pastor (1987) examined the correlation between the hydrophobicity of a residue and its neighbors 1 -4 positions apart, and found no correlation in hydrophobicity when the full-length proteins were considered. However, when a sample is composed exclusively of a-helices of proteins with known structure, they found a correlation in the hydrophobicity of residues spaced four apart. This is the effect that we have exploited above.
As the HIV example illustrates, it is not always necessary to show statistical significance. In those cases where there is prior evidence that there are or should be important amphipathic helices, as in the case of gpl20, the experimentalist needs help in identifying the best candidate sequences for further study. In such circumstances, the statistical significance of the identified sequence is of only marginal relevance to the pursuit of amphipathic helices. On the other hand, when there is no such a priori basis for the existence of amphipathic helices, as in the case of gp41, then statistical significance is crucial. In this case, without such a result there is little reason to pursue the finding experimentally.
Our applications to date have shown the ability of the algorithm to identify long amphipathic helices in the stem portions of viral spike proteins, where they are widely suspected of playing a major functional role. We have also illustrated the ability of the method to identify such a structure where none was suspected previously, in spite of extensive analysis.