Response curves representing the likelihood of developing MS in genetically susceptible <i>women</i> (black lines) and <i>men</i> (red lines) with an increasing probability of a “<i>sufficient</i>” environmental exposure–<i>see</i> Methods <i>#1B</i>.

The curves depicted are “strictly” proportional, meaning that the environmental threshold is the same for both men and women–i.e., under conditions in which: (λ = 0)–see Text. The blue lines represent the change in the (F:M) sex ratio (plotted at various scales, indicated in each Figure) with increasing exposure. The thin grey vertical lines represent the portion of the response curve that covers the change in the (F:M) sex ratio from 2.2 to 3.2 (i.e., the actual change observed in Canada [6] between Time Periods #1 & #2). The grey lines are omitted under circumstances either where these observed (F:M) sex ratios are not possible or where both (Zw > Zm) and an increasing (F:M) sex ratio are not possible. Response curves A and B reflect conditions in which (R > 1); whereas curves C and D reflect conditions in which (R R = 1), the blue line would be flat. Response curves A and C reflect conditions in which (c = d = 1); whereas curves B and D reflect those conditions in which (c d = 1). Under the conditions for curves A and B (R ≥ 1), there is no possibility that the (F:M) sex ratio will be observed to increase with increasing exposure. Under the conditions of curve C–i.e., (c = d = 1) and (R Zw = P(MS, E│G, F, ET) > P(MS, E│G, M, ET) = Zm. Thus, the only “strictly” proportional model that could possibly account for an increasing (F:M) sex ratio, and for the fact that: (Zw2 > Zm2), is a Model in which (c d ≤ 1) and (R D.</p

Response curves for the likelihood of developing MS in genetically susceptible <i>women</i> (black lines) and <i>men</i> (red lines) with an increasing probability of a “<i>sufficient</i>” environmental exposure–<i>see</i> Methods <i>#1B</i>.

Like Fig 1, the curves depicted are also proportional (R = Rapp), but, for these, the environmental threshold in women is greater than that it is in men–i.e., these are conditions in which: (λ > 0). Also, all these response curves represent actual solutions and reflect conditions in which (c = d = 1) and, as discussed in Methods #4C, are representative of all conditions in which c = d Rapp ≥ 1.3), which is the minimum value of (Rapp) for any solution–which is depicted in Fig A. The blue lines represent the change in the (F:M) sex ratio (plotted at various scales, indicated in each Figure) with increasing exposure. The thin grey vertical lines represent the portion of the response curve (for the depicted solution), which represents the actual change in the (F:M) sex ratio that occurred between Time Periods #1 & #2). To account for the observed increase in the (F:M) sex ratio, these curves require the Canadian observations [6] to have been made over a very small portion the response curve–i.e., for most of these response curve, the (F:M) sex ratio is decreasing. Also, for each of these response curves, including the maximum difference in the environmental threshold (i.e., λ ≤ 0.13) under conditions of (c = d = 1), which is depicted in Fig B, the ascending portion of the curve (which reflects and increasing F:M sex ratio) is very steep–a circumstance indicating that the portion of the response curve available for fitting the Canadian data [6] is quite narrow. Also, the intersection of the response curves does not occur as early as seems to be implied by an extension of the conditions of Panels C–B. Also, such a rapid transition from an MS that is “male-predominant” to an MS, which is “female-predominant” would seem to fit poorly with the gradual transition, which has taken place over the past two centuries [3, 6, 22–30, 40, 77, 78, 88].</p

Hypothetical relationship between exposure “<i>intensity</i>” and disease expression (<i>see Sections 6g & 8a</i>, <i>8b in</i> S1 File).

Plotted on the x-axis is the level (or “intensity”) of exposure in units of the log-transformed exposure–log(a). Plotted on the y-axis is the proportion of the susceptible population (G) who experience an exposure “sufficient” to cause MS in them. The solid black lines represent the distribution of “actual” level of exposure experienced by the susceptible population. The dotted lines (red for women and blue for men) represent the distributions of these “critical exposure intensity” (or “threshold”) levels for susceptible men and women. These “threshold” levels for each individual are defined as that exposure level, at (or above) which, the exposure becomes “sufficient” to cause MS in that person. These threshold distributions have been plotted, arbitrarily, for conditions of (p = 0.5). Because (a) is the odds of exposure, the distribution of these “threshold” levels are expressed in units log(a), because this transformation will generally normalize the variance [39]–see also Section 8a, 8b in S1 File. In these Figures, the exposure level of: {log(a) = 0}, has been chosen as the point where the average odds of a “critical exposure intensity” level is equal to (1). No other units are provided because these are undefined other than as they relate to the variance of these “threshold” distributions in susceptible men and women ( and ), respectively. The circumstances depicted are those, in which men and women have the same variance but men have a lower mean compared to women (i.e., ). In any case, however, because (λ > 0), men must disproportionately (or exclusively) experience a “sufficient” exposure at low exposure “intensities”. In these examples, the blue shading represents those individuals who receive a “sufficient” exposure as the level of population exposure increases progressively–i.e., Fig 5A depicts the circumstance, in which the population exposure is such that no one experiences a “sufficient” exposure; Fig 5B and 5C depict circumstances, in which some (but not all) individuals experience a “sufficient” exposure; and Fig 5D depicts the circumstance where the population exposure has increased to the point where it exceeds the “critical exposure intensity” level for everyone.</p

Response curves for the likelihood of developing MS in genetically susceptible <i>women</i> (black lines) and <i>men</i> (red lines) with an increasing probability of a “<i>sufficient</i>” environmental exposure–<i>see</i> Methods <i>#1B</i>.

Like Fig 1, the curves depicted are also proportional although here the environmental threshold is greater for men than for women–i.e., under conditions in which: (λ see Text. The blue lines represent the change in the (F:M) sex ratio (plotted at various scales, indicated in each Figure) with increasing exposure. The thin grey vertical lines represent the portion of the response curve that covers the change in the (F:M) sex ratio from 2.2 to 3.2 (i.e., the actual change observed in Canada [6] between Time Periods #1 & #2). The grey lines are omitted under circumstances where these observed (F:M) sex ratios are not possible. Response curves A reflects conditions in which (c = d = 1) & (R > 1); Response curves B reflects conditions in which (c = d = 1), (R p ≥ p′); curves C reflect conditions in which (c d = 1) and (R D reflects those conditions in which (c d = 1) and (R F:M) sex ratio, curves D (compared to curves C) requires a small enough value of (R) so that the (F:M) sex ratio curve dips below 2.2 and, also, a small enough value of (c) so that the curve rises above 3.2. For all points in curves A after the intersection, and for all points in curves B, (Zm > Zw), which is not possible. Curves C never even approach the (F:M) sex ratio of 2.2. By contrast, for curves D, both an appropriate increase in the (F:M) sex ratio and (Zw > Zm), can be observed.</p

Principal parameter abbreviations^†.

ObjectiveTo explore and describe the basis and implications of genetic and environmental susceptibility to multiple sclerosis (MS) using the Canadian population-based data.BackgroundCertain parameters of MS-epidemiology are directly observable (e.g., the recurrence-risk of MS in siblings and twins, the proportion of women among MS patients, the population-prevalence of MS, and the time-dependent changes in the sex-ratio). By contrast, other parameters can only be inferred from the observed parameters (e.g., the proportion of the population that is “genetically susceptible”, the proportion of women among susceptible individuals, the probability that a susceptible individual will experience an environment “sufficient” to cause MS, and if they do, the probability that they will develop the disease).Design/methodsThe “genetically susceptible” subset (G) of the population (Z) is defined to include everyone with any non-zero life-time chance of developing MS under some environmental conditions. The value for each observed and non-observed epidemiological parameter is assigned a “plausible” range. Using both a Cross-sectional Model and a Longitudinal Model, together with established parameter relationships, we explore, iteratively, trillions of potential parameter combinations and determine those combinations (i.e., solutions) that fall within the acceptable range for both the observed and non-observed parameters.ResultsBoth Models and all analyses intersect and converge to demonstrate that probability of genetic-susceptibitly, P(G), is limited to only a fraction of the population {i.e., P(G) ≤ 0.52)} and an even smaller fraction of women {i.e., P(G│F) women) have no chance whatsoever of developing MS, regardless of their environmental exposure. However, for any susceptible individual to develop MS, requires that they also experience a “sufficient” environment. We use the Canadian data to derive, separately, the exponential response-curves for men and women that relate the increasing likelihood of developing MS to an increasing probability that a susceptible individual experiences an environment “sufficient” to cause MS. As the probability of a “sufficient” exposure increases, we define, separately, the limiting probability of developing MS in men (c) and women (d). These Canadian data strongly suggest that: (c d ≤ 1). If so, this observation establishes both that there must be a “truly” random factor involved in MS pathogenesis and that it is this difference, rather than any difference in genetic or environmental factors, which primarily accounts for the penetrance difference between women and men.ConclusionsThe development of MS (in an individual) requires both that they have an appropriate genotype (which is uncommon in the population) and that they have an environmental exposure “sufficient” to cause MS given their genotype. Nevertheless, the two principal findings of this study are that: P(G) ≤ 0.52)} and: (c d ≤ 1). Threfore, even when the necessary genetic and environmental factors, “sufficient” for MS pathogenesis, co-occur for an individual, they still may or may not develop MS. Consequently, disease pathogenesis, even in this circumstance, seems to involve an important element of chance. Moreover, the conclusion that the macroscopic process of disease development for MS includes a “truly” random element, if replicated (either for MS or for other complex diseases), provides empiric evidence that our universe is non-deterministic.</div

MS associations for Class I and Class II <i>HLA-</i>haplotypes in <i>men</i> and <i>women</i>^b'*'.

MS associations for Class I and Class II HLA-haplotypes in men and womenb'*'.</p

Response curves for the likelihood of developing MS in genetically susceptible <i>women</i> (black lines) and <i>men</i> (red lines) with an increasing probability of a “<i>sufficient</i>” environmental exposure–<i>see</i> Methods <i>#1B</i>.

Like Fig 1, the curves depicted are also proportional (R ≤ 1), but, for these, the environmental threshold in women is greater than that it is in men–i.e., these are conditions in which: (λ > 0). Also, these curves represent the same solutions as those depicted in Fig 3 except that these are for conditions in which (c d ≤ 1). The blue lines represent the change in the (F:M) sex ratio (plotted at various scales, indicated in each Figure) with increasing exposure. The thin grey vertical lines represent the portion of the response curve (for the depicted solution), which represents the actual change in the (F:M) sex ratio that occurred between Time Periods #1 & #2). Unlike the curves presented in Fig 3, however, an increase in the (F:M) sex ratio with increasing exposure is observed for any two-point interval along the entire response curves and, except for Fig A, the grey lines are clearly separated.</p

Rank order for the 10 most common extended haplotypes for the entire WTCCC dataset (labeled: <i>c1</i> to <i>c10078</i>; in descending order of frequency).

The rank order of the haplotypes for each participating region are shown separately (see S1 Table for definitions of those haplotypes, which have been colored in the figure based on the overall 10 most common haplotypes in the WTCCC). Regions are ordered (from left to right) based on the descending frequency of the c2 haplotype. Only cases are available for all regions. Nevertheless, both the complete WTCCC (Case and Control) and the EPIC (Case and Control) populations are also included for comparison.</p

Different SNP haplotypes at distances of 1 to 4 hamming units from the <i>a1</i> SNP haplotype (SNP differences highlighted in red; for SNP definitions see text).

Several of these SNP haplotypes (indicated in yellow), at times, carried the HLA-DRB1*15:01~HLA-DQB1*06:02 HLA haplotype whereas others (indicated in blue) never did. HLA haplotypes are highlighted in green. Thus, whether or not a given SNP haplotype carried this HLA haplotype seemed to be, not a function of the hamming distance, but rather, a property of the specific SNP haplotype involved.</p

MS associations for conserved extended <i>HLA-</i>haplotypes in <i>men</i> and <i>women</i>.

MS associations for conserved extended HLA-haplotypes in men and women.</p