Distribution of UniProt-derived TM segments in the complexity/hydrophobicity plot. 181132 transmembrane helices from single and multi-spanning membrane proteins were extracted based on the keyword FT_TRANSMEM described in the UniProt annotation file (dated 16-09-2010). The three-dimensional histogram (Figure 1A) shows a fin-shaped distribution across the diagonals of the complexity and hydrophobicity space. The cross-section of the histogram (Figure 1B) shows a tear-shaped pattern. Furthermore, the medians of 15 sets of spanning membrane proteins (containing 1 to 15 TM helices respectively) were computed and denoted by the black circles. The medians were connected in ascending order, starting from the single-spanning set. The trace of the complexity and hydrophobicity from the single-spanning set to the four-TM spanning set indicates a progressive shift towards high complexity and low hydrophobicity. The medians converge to almost a singular cloud beyond the five-transmembrane-spanning set. The three-dimensional surface plot (Figure 1C) shows the hybrid distributions of the single-spanning and those with at least five membrane-spanning TM helices. The single-spanning ones appear more 'simple' while, as a trend, the others seem more 'complex'. The two to four-spanning helices are excluded as they were considered to be 'in-betweeners'. Two distinct peaks (in red) can be seen in the surface plot, denoting 'simple' and 'complex' populations respectively. The contour plot (Figure 1D) emphasizes on the two peaks.

Definition of the z-score with regard to the set of functional TMs. Figure 3A shows the normalized sequence complexity/hydrophobicity measures of the membrane anchors (in blue), functional TM-helices (UniProt-derived; in red) and functional α-helices (in green). The univariate z-score is given by the squared sums of two normalized measures. The expectation of the z-scores for the functional TM-helices set is zero. The regression line (ρ = -0.436) for the functional TM set and its normal are indicated. The negative halve of the functional TM helices' z-scores is given by the inequality (3) while z-scores failing to satisfy the inequality makes up the positive halve. It is apparent that the majority of the membrane anchors have negative z-scores while the functional α-helices have positive z-scores. Figure 3B depicts the distributions of the membrane anchors (in blue) as simple TM helices and the functional TM-helices (in red) as complex TM helices. For illustrative purpose, the membrane anchors are approximated by the Gumbel distribution given its long left tail while the functional TM-helices are fitted to the normal distribution. For a given z-score threshold, the complex TM helices are partitioned into true-positives (TP) and false-negatives (FN) while the simple helices are divided into the true negatives (TN) and false-positives (FP). Consequently, the false-positive and false-negative rates can be determined for a given z-score threshold defined by equation (4).

Z-score histograms of the functional α-helices, functional TM-helices (SCOP/UniProt-derived), membrane anchors and signal anchors. The z-score histograms for the functional TM-helices (SCOP-derived; Figure 5A and UniProt-derived; Figure 5B), membrane anchors (Figure 5C) and signal anchors (Figure 5D) are shown. The functional TM-helix sets have a characteristics long-tailed, symmetrical and unimodal shape histogram. On the other hand, the histograms of the membrane and signal anchor sets have a left-skewed long-tailed non-unimodality shape. This is suggestive of multiple populations. The two vertical dotted lines define a twilight zone between the functional TM-helices and the anchors based on the z-score thresholds of -7.84 and -3.29 that are calculated from f = 1.980 and f = 1.282 respectively via equation (4).

Rate of occurrences and expected number of simple TM helices with increasing number of TM helices in membrane proteins. Figure 7A shows the general trend that the rate of occurrences (in terms of ratio of simple TM helices) decreases exponentially as the number of TM helices increases in the protein. The ratios stabilize beyond 6 TM helices. Note that the trend is independent of the z-score thresholds of f = 1.282 (false-negative rate of 10%; see red lines) and f = 1.645 (false-negative rate of 5%; see blue lines). On the other hand, Figure 7B shows that the expected total numbers of simple helices do not plateau with increasing TM helices. Generally, the number of expected simple helices sh is about proportional to the number of TM helices nTM in the protein. The relationship between these two values is sh = 0.218nTM (goodness of fit is R² = 0.93) for f = 1.282 and sh = 0.112nTM (goodness of fit is R² = 0.82) for f = 1.645.

Trends of complexity and hydrophobicity as a function of the number of TMs per protein in UniProt. The boxplots of complexity (Figure 2A) and hydrophobicity (Figure 2B) of the single-spanning to 15-transmembrane and beyond spanning sets are shown. The medians of the complexity and hydrophobicity measures increase with the number of spanning TM helices found in each set. Interestingly, the complexity boxplots highlighted an excess of outliers on the lower part of the complexity axis (suggestive of low-complexity sequence segments) while the hydrophobicity boxplots emphasized the excess of outliers on the bottom part of the hydrophobicity axis (towards charged composition). This is independent of the size of the membrane-spanning proteins. Taken together, this is somewhat contrary to the expectation that TM helices are simple and purely hydrophobic. Therefore, it raises the notion that some TM helices are 'simple' and others are 'complex' regardless of the number of TMs in a protein.

Sequence complexity/hydrophobicity plot for membrane and signal anchors against functional TM-helices. Figure 4A shows the sequence complexity/hydrophobicity plot of the membrane anchors (blue) against the functional α-helices (green), functional TM-helices (UniProt-derived; red) and low-complexity segments (SEG25/3.0/3.3-detected; gray). The dotted lines are defined by x_Φ = μ_Φ + 1.282σ_Φ and x_c = μ_c -1.282σ_c where (μ_Φ,σ_Φ)and (μ_c, σ_c) are the summary statistic calculated from the UniProt-derived functional TM-helix set. This corresponds to a false-negative rate of 10% (at f = 1.282). Based on the plot, there is some overlap between the functional α- and TM-helices which justifies for the extension of the sequence homology concept for these cases. 55.8% (169 out of the 303) of the membrane anchors occupy the upper left quadrant, suggestive of simple TM helices. Figure 4B shows the complexity and hydrophobicity plot of signal anchors (blue) against the functional α-helices (green), functional TM-helices (UniProt-derived; red) and signal peptides (cyan). Similarly, the dotted lines define the boundaries at the false-negative rate of 10%. 30.1% of the signal anchors (531 out of the 1767) occupy the upper left quadrant, suggestive of simple TM helices.

Effects on the homology searches for TCDB with the removal of simple and complex TM helices. The performance of the homology searches for 2202 TCDB entries between their original and masked sequences are shown for the z-score thresholds of f = 0.840, 1.000, 1.282, 1.645 and 1.980 respectively. The corresponding false-negative rates are 20%, 16%, 10%, 5% and 2.5% respectively. Figure 6A shows the masked ratios (m = number of masked TMs over total TMs) of the 2202 TCDB entries. The median mask ratios of the TCDB entries are 0.41, 0.33, 0.18, 0.08 and 0.00 for f = 0.840, f = 1.000, f = 1.282, f = 1.645 and f = 1.980 respectively. The non-zero mask ratio means that some TM helices in the multi-spanning entries are considered simple. The corresponding total number of entries (where 0 < m < 1) are 1747, 1705, 1533, 1071 and 680 respectively. On average, each masked TCDB entry has about 9 to 10 TM helices. Therefore, most TCDB entries are multi-spanning. Figure 6B shows that the false-discovery rates of the searches for the masked sequences are at least equal or less than that of their corresponding full sequences at a comparable sensitivity. This means that the masking of simple TMs can improve the false-discovery rates of the searches. This trend is independent of the different z-score thresholds that influence the level of masking (most masking at false-negative rate of 20% and least masking at false-negative rate of 2.5%). Figures 6C and 6D show the sensitivity plots of the searches for the 2202 TCDB sequences. The red, blue and black lines represent the sensitivities of the original, masked and control sequences respectively. The sensitivity of the original (red) and masked (blue) sequences are comparable at 1.0 for most of the sequences. At a sensitivity of 1, the number of false-negatives is zero. On the other hand, the sensitivity of the search for the control sequences (where the complex TMs are masked) deviates greatly from the sensitivity of 1. This implies that the masking of complex TMs has a detrimental effect on the TCDB classification.