Introduction
SIV belongs to the group of lentiviruses that infect nonhuman primates. The lentiviruses that cause immunodeficiencies in humans and Asian macaques originated from cross-species transmission of viruses that naturally infect nonhuman primates in Africa1. Like HIV-1 and HIV-2, all known SIV subtypes use CD4 as a receptor and either CCR5, CXCR4, or, as for the red capped mangabey virus, SIVrcm, CCR22, 3, 4 as co-receptors. Moreover, both SIV infection of Asian macaques and HIV-1 infection of humans result in chronic infection, and the majority of infected individuals progress to AIDS.
In contrast, after SIV infection, natural hosts generally do not progress to AIDS. Because natural hosts of SIV have coevolved with the virus to avoid disease progression, dissecting the mechanisms underlying the nonprogressive nature of natural SIV infection will lead to a better understanding of the aspects of HIV infection responsible for the progressive nature of the disease in humans5, 6, 7. Natural hosts do not avoid disease progression by immunological control of the virus, as SIV-infected natural hosts maintain high levels of viremia8, 9, 10, 11, 12. Moreover, experimental depletion of CD8+ T cells does not affect plasma viremia13, and natural hosts do not show superior cellular control of viremia compared to HIV-infected humans or SIV-infected rhesus macaques14. The lentiviruses that infect natural hosts can be pathogenic. SIV infections of African green monkeys and sooty mangabeys have been correlated with short life spans of infected cells in vivo15, 16, 17. Moreover, SIVagm, which naturally infects African green monkeys, can be used to infect pigtail macaques, who subsequently manifest simian AIDS18, 19. Isolates of the sooty mangabey virus, SIVsmm, can also cause progressive infection in rhesus macaques20, 21, 22, 23. One fundamental difference between progressive SIV and HIV infections and nonprogressive SIV infection is the absence of immune activation, associated with disease progression in HIV-infected individuals24, during the chronic phase of infection in natural hosts9, 11, 25, 26, 27, 28.
Previous studies performed in African green monkeys have reported very low frequencies of CD4+ T cells28. African green monkeys, however, remain disease free despite having low numbers of CD4+ T cells. In two reports, the investigators found low frequencies of CD4+ T cells and high frequencies of CD8dim T cells in healthy adult African green monkeys29, 30. They also found that the CD8dim T cells could induce antibody production from B cells in vitro and suggested that the CD8dim T cells might act as substitutes for the CD4+ T cells29. Here we have studied the frequencies, functionalities and in vivo infection frequencies of lymphocyte subsets from 36 African green monkeys: ten naturally infected, eight experimentally infected, eleven uninfected adults and seven uninfected juveniles (Table 1). Our data describe a mechanism by which African green monkeys are able to survive SIVagm infection without succumbing to AIDS.
Results
Inverse correlation between CD4+ and CD4-CD8
dim T cells
Loss of CD4+ T cells is a hallmark of progression to AIDS in humans and Asian macaques. We therefore compared the frequencies of CD4+ T cells in SIVagm-infected and uninfected vervet African green monkeys (one of four subspecies of African green monkeys), HIV-uninfected humans, SIV-uninfected rhesus macaques and SIVsmm-infected and uninfected sooty mangabeys. We observed three distinct T cell populations in African green monkeys, on the basis of expression of CD4 and CD8
: CD4+ T cells, CD4-CD8
dim T cells and CD4-CD8
bright T cells (Fig. 1a). We further analyzed the phenotypes of each subset on the basis of expression of CD28 and CD95 (Fig. 1b). The CD4+ and CD4-CD8
bright T cells consisted of both memory and naive subsets (Fig. 1b). However, the CD4-CD8
dim T cells consisted predominantly of memory T cells (Fig. 1b). Moreover, adult African green monkeys seemed to have unexpectedly low frequencies of CD4+ T cells and low CD4+ T cell counts (Table 1). There were significantly lower frequencies of CD4+ T cells in both SIVagm-infected and uninfected African green monkeys compared to SIVsmm-infected or uninfected sooty mangabeys, SIV-uninfected rhesus macaques or HIV-1–uninfected humans (Fig. 1c). In addition, the decrease in CD4+ T cells was accompanied by an increase in the frequency of CD4-CD8
dim T cells (Fig. 1a). Further phenotypic analysis showed that this CD4-CD8
dim T cell population lacked expression of CD8
(Fig. 1d). In addition, the frequency of activated Ki67+ cells was significantly lower among CD4-CD8
dim T cells compared to either the CD4+ or CD4-CD8
bright subsets, suggesting that the high frequency of CD4-CD8
dim T cells was not due to preferential proliferation of CD4-CD8
dim T cells in vivo (Fig. 1e).
Figure 1: Phenotypic analysis of T cell populations in vervet African green monkeys.
(a) Phenotype of T cells in adult African green monkeys, as determined by flow cytometry. (b) Phenotype of individual subsets of T cells in adult African green monkeys, as determined by flow cytometry. (c) Comparison of percentages of CD3+ T cells that express CD4 in peripheral blood in SIV+ and SIV- adult African green monkeys (AGMs), adult SIV+ and SIV- sooty mangabeys (SMs), adult SIV- rhesus macaques (RMs) and HIV- adult humans. (d) Characterization of CD4-CD8
dim T cells as CD8
- by analysis of CD8
expression. Cells were gated on live CD3+ small lymphocytes and analyzed for both CD4 and CD8
expression. (e) Ki67 expression by various subsets of memory T cells. (f) Negative correlation between the frequencies of CD4+ T-cell and CD4-CD8
dim T cells in adult AGMs. (g) Correlation of the frequency of CD4+ T cells and the frequency of CD4-CD8
bright T cells in adult African AGMs. A Mann-Whitney U test was performed for c. A Spearman rank correlation was calculated for f and g. Lines in c and e represent median values, and percentages in a and b represent frequencies of boxed cells.
The increased frequency of CD4-CD8
dim T cells could be a reflection of a mathematical shift in the percentages of T cell populations due to the loss of CD4+ T cells. However, we found that there was a significant negative correlation between the decrease in CD4+ T cells and the increase in CD4-CD8
dim T cells (Fig. 1f), but not between the CD4-CD8
bright T cells and CD4+ T cells (Fig. 1g). Therefore, the increase in the CD4-CD8
dim T cell population was directly related to the decrease in CD4+ T cells, suggesting that some CD4-CD8
dim T cells might develop from CD4+ T cells.
Some CD4-CD8
dim T cells develop from CD4+ memory T cells
Given that the frequencies of the CD4-CD8
dim T cells negatively correlated with the frequencies of CD4+ T cells (Fig. 1f), we hypothesized that some of the CD4-CD8
dim T cells might have developed from CD4+ T cells. Phenotypic analysis of the CD4+ T cells from SIVagm-infected and uninfected African green monkeys illustrated that the CD95+ memory CD4+ T cells downregulated CD4 (Fig. 2a) and upregulated CD8
(Fig. 2b) compared to naive CD4+ T cells. We also performed fluorescence-minus-one analysis for CD8
to confirm that the CD4+ T cells expressed CD8
(Fig. 2c). The median fluorescent intensity (MFI) of CD4 was significantly lower in the memory subset of CD4+ T cells compared to naive CD4+ T cells (Fig. 2d), whereas the MFI of CD8
was significantly higher in the memory CD4+ T cells over naive CD4+ T cells (Fig. 2e). Therefore, we hypothesized that upon stimulation CD4+ T cells are able to transition to become CD4-CD8
dim T cells.
Figure 2: CD8
and CD4 expression by naive and memory CD4+ T cells.
(a) Representative staining of CD4+ memory and naïve T cells for CD4, as determined by flow cytometry. (b) Representative staining of CD4+ memory and naive T cells for CD8, as determined by flow cytometry. (c) Fluorescence-minus-one (FMO) analysis by flow cytometry for all markers except CD8
. (d) Median fluorescence intensity for CD4 expression in naive and memory CD4+ T cells. (e) MFI for CD8
expression in naive and memory CD4+ T cells. A Wilcoxon matched-pairs test was performed for d and e.
To study downregulation of CD4 in vitro, we CFSE-labeled and mitogenically stimulated peripheral blood mononucelear cells (PBMCs) from several African green monkeys and, for comparison, from pigtail macaques. We then studied expression of CD4 and proliferation by the cells by flow cytometry after 5, 7 and 9 d in culture (Fig. 3a,b and Supplementary Fig. 1). We found that, whereas African green monkey CD4+ T cells lost CD4 expression, CD4+ T cells from pigtail macaques maintained CD4 expression with cell division (Fig. 3a). It is possible that the CD4 downregulation in African green monkeys was transient; however, we did not see upregulation of CD4 by day 9 (Supplementary Fig. 1). To confirm this finding, we also sorted naive CD4+ T cells (>99% pure) before stimulation and found that after stimulation they became CD4- (Supplementary Fig. 1).
Figure 3: CD4-CD8
dim T cells can develop from memory CD4+ T cells.
(a) Flow cytometric analysis of CD4 downregulation by AGM PBMCs after 5 d of stimulation in vitro with SEB. (b) Flow cytometric analysis of CD4 expression by stimulated PBMCs from pigtail macaques in vitro after 5 d of stimulation with SEB. (c) CD4 mRNA expression in CD14+, CD4-CD8
dim, CD4-CD8
bright or CD4+ lymphocyte subsets of an adult African AGM. Bp, base pairs. (d) Negative correlation between the frequency of memory CD4+ T cells and the frequency of the total CD4+ T cells in adult AGMs. (e) Comparison of the percentage CD4+ T cells in peripheral blood in SIV+ and SIV- adult and SIV- juvenile AGMs. A Spearman rank correlation was calculated for d. A Mann-Whitney U test was performed for e. Horizontal lines in e depict the median value.
Analysis for CD4 messenger RNA within sorted CD4+, CD4-CD8
dim or CD4-CD8
bright T cells and monocytes revealed that CD4 mRNA was only detectable within CD4+ T cells (Fig. 3c). Taken together, these data suggested that African green monkey memory CD4+ T cells can become CD4-CD8
dim T cells. If our hypothesis was correct, African green monkeys would have concomitant decreases in the overall frequencies of total CD4+ T cells with increases in memory CD4+ T cells. Indeed, we found a significant negative correlation between the frequencies of memory CD4+ T cells and the total frequency of CD4+ T cells (Fig. 3d). Hence, as African green monkeys accumulate memory CD4+ T cells, the overall frequency of CD4+ T cells decreases.
We reasoned that if some CD4+ T cells become CD4-CD8
dim T cells upon stimulation into the memory pool, then African green monkeys with very little antigenic experience should have frequencies of CD4+ T cells comparable to those of healthy rhesus macaques and humans (Fig. 1c). Therefore, we measured the frequencies of T cell subsets from PBMCs obtained ex vivo directly from juvenile African green monkeys (all fewer than 2 years old). In a total of seven juvenile African green monkeys, the median frequency of CD4+ T cells was 59% (39.6–64.4%, Fig. 3e). These frequencies were comparable with those from nonimmunocompromised rhesus macaques and humans and were higher than the frequencies of CD4+ T cells in adult African green monkeys (P<0.0006, Fig. 3e). Furthermore, after we vaccinated the juvenile African green monkeys with standard influenza vaccine, we observed an influenza-specific T cell response from the CD4-CD8
dim T cells to the major histocompatibility complex class II (MHC-II)-restricted antigen (Supplementary Fig. 2c). Taken together, these observations strongly suggest that many of the CD4-CD8
dim T cells developed from memory CD4+ T cells.
Although we do not know the ages of many of the African green monkeys, as they were imported from Tanzania, in the few monkeys for whom we do have this information, there was no correlation between age and the frequency of CD4+ T cells (data not shown). However, it is likely that age may be a factor in the accumulation of CD4-CD8
dim T cells, as older monkeys are exposed to more antigens in vivo.
Function and SIVagm infection of CD4-CD8
dim T cells in vivo
To elucidate the functions of the CD4-CD8
dim T cells, we obtained PBMCs from SIVagm-infected and uninfected adult African green monkeys. As it seemed apparent that many of the CD4-CD8
dim T cells developed from CD4+ T cells, we examined these T cells for functions generally attributed to CD4+ T cells. We found that upon stimulation with staphylococcal enterotoxin B (SEB), the CD4-CD8
dim T cells could produce IL-2 and IL-17 (Supplementary Fig. 2 and Fig. 4a) and expressed CD40 ligand (CD40L) (Fig. 4a and Supplementary Fig. 2). CD40L is typically expressed by activated CD4+ T cells, resulting in enhancement of antigen presentation and induction of B cell class switching31. Additionally, a portion of the CD4-CD8
dim T cells expressed the transcription factor forkhead box P3 (FoxP3), thought to be predominantly expressed by regulatory CD4+ T cells (Fig. 4a and Supplementary Fig. 2)32. Hence, the CD4-CD8
dim T cell subset includes T cells that perform functions normally restricted to CD4+ T cells. Although the overall frequency of memory CD4+ T cells that could perform each function was significantly higher compared to the CD4-CD8
dim T cells (Fig. 4a), the total frequency of CD4-CD8
dim T cells was significantly higher than the overall frequency of CD4+ T cells (Fig. 1a). We therefore calculated the relative number of cytokine-expressing, CD40L+ and FoxP3+ T cells for each T cell subset (Fig. 4b). For IL-2, IL-17 and FoxP3, the relative number of CD4-CD8
dim T cells was significantly larger than the numbers of the CD4+ and CD4-CD8
bright T-cell subsets (Fig. 4b). The relative number of CD40L+CD4-CD8
dim T cells was equal to the number of CD40L+CD4+ T cells (Fig. 4b). These observations suggest that there are actually greater numbers of CD4-CD8
dim T cells performing CD4+ T cell functions compared to classical CD4+ T cells.
Figure 4: CD4-CD8
dim T cells can preserve CD4+ T-cell function.
(a) Comparison of the frequency of memory CD4+, CD4-CD8
dim and CD4-CD8
bright T cells for IL-2 and IL-17 production and FoxP3 and CD40L expression. (b) Comparison of the relative numbers of memory CD4+, CD4-CD8
dim and CD4-CD8
bright T cells producing IL-2 and IL-17 and expressing FoxP3 and CD40L. (c) Responses of CD4-CD8
dim T cells to CMV whole antigen (ag) in the presence or absence of blocking antibodies to MHC-II or MHC-I. IFN-
, interferon-
. Percentages represent frequencies of boxed cells. A Wilcoxon matched-pairs test was performed for a and b.
CD4+ T cells are restricted by MHC-II, whereas CD8+ T cells are restricted by MHC-I. Therefore, to test further our hypothesis that the CD4-CD8
dim T cells were acting as CD4+ T cells, we screened PBMCs from adult African green monkeys for T cell responses to a cytomegalovirus (CMV) whole-antigen preparation. Presentation of this antigen requires processing through MHC-II33. We found one African green monkey that had T cells responsive to CMV (AG731) whose entire CMV-specific T cell response was restricted to CD4-CD8
dim T cells (Fig. 4c and Supplementary Fig. 2b,c). To confirm that these CMV-specific CD4-CD8
dim T cells were restricted by MHC-II, we stimulated the T cells in the presence of blocking antibodies specific to either MHC-II or MHC-I and measured production of cytokines. Blocking with MHC-II–specific antibody decreased the frequency of responding CMV-specific CD4-CD8
dim T cells by more than two thirds, whereas blocking MHC-I had virtually no effect on the ability of CMV-specific CD4-CD8
dim T cells to respond (Fig. 4c). Hence, CD4-CD8
dim T cells can be restricted by MHC-II in African green monkeys.
Vervets are one of four subspecies of African green monkey, along with sabeus, tantalus and grivets. To determine whether the phenomena that we observed are specific to vervet African green monkeys, we examined T cell populations in six adult sabeus African green monkeys. Indeed, we found CD4-CD8
dim T cells among their T cell populations (Supplementary Fig. 3). Similar to the case in vervets, the CD4-CD8
dim T cells from sabeus were able to perform CD4+ T cell functions (Supplementary Fig. 3). Confirmation of this phenomenon occurring in a second subspecies of African green monkeys suggests that downregulation of CD4 may be characteristic of all African green monkeys.
Since the CD4-CD8
dim T cells have many functional characteristics of CD4+ T cells, we next determined which lymphocytes were infected by SIVagm in vivo. We used flow cytometry to sort individual subsets of lymphocytes from 18 SIVagm-infected African green monkeys and measured the in vivo infection frequency by quantitative real-time PCR for SIVagm DNA. We sorted naive and memory CD4+ T cells, memory CD4-CD8
dim T cells, memory CD4-CD8
bright T cells, memory CD4-CD8
- T cells and monocytes. We found that memory CD4+ T cells were the primary targets for SIVagm in vivo (Fig. 5). Consistent with the infection frequency patterns of HIV34, we also found that SIVagm could infect naive CD4+ T cells, but memory CD4+ T cells were preferentially infected (Fig. 5). Notably, CD4-CD8
dim T cells, which we have shown can develop from CD4+ T cells and maintain functions of CD4+ T cells, were only very rarely, if ever, infected by SIVagm in vivo (Fig. 5). In 78% of the SIVagm-infected African green monkeys, we detected no viral DNA within the CD4-CD8
dim T cell subset (Fig. 5). Cell numbers were often limiting, and it is conceivable that, in some cases, we did not detect any viral DNA as a result of the small number of sorted cells in each PCR. Therefore, in samples in which we did not detect viral DNA, we reported values calculated as one-half of the lower limit of detection; these values are based on the number of sorted cells (Fig. 5). In the few (22%) African green monkeys in whom we did detect viral DNA within the CD4-CD8
dim T cell subset, the infection frequencies were very low (<0.01%). Taken together, these data suggest that CD4-CD8
dim T cells preserve CD4+ T cell function while evading SIV infection in vivo, and, in turn, these findings suggest a mechanism by which African green monkeys are able remain disease free despite SIV infection.
Figure 5: Infection frequencies of lymphocyte subsets.
Infection frequencies of sorted lymphocyte subsets from SIVagm-infected adult AGMs, as determined by quantitative PCR for viral DNA. White circles represent cells with detectable viral DNA, and black circles represent an undetectable infection frequency reported as one-half the lower limit of detection on the basis of the number of cells within each PCR reaction. A Wilcoxon matched pairs test was performed for this analysis.
Full size image (48 KB)Discussion
We have shown that African green monkeys, regardless of infection with SIVagm, have decreased numbers of total CD4+ T cells, compared to other primates, and the low numbers of CD4+ T cells correlate with an increased population of CD4-CD8
dim T cells. We showed that some of these CD4-CD8
dim T cells developed from memory CD4+ T cells. This conclusion is strengthened by the observation that juvenile African green monkeys, who have very low frequencies of memory T cells in vivo, have high frequencies of CD4+ T cells and low frequencies of CD4-CD8
dim T cells, and that in vitro stimulation of naive CD4+ T cells results in downregulation of CD4 and upregulation of CD8
. In addition, we have shown that in adult African green monkeys some of these CD4-CD8
dim T cells, upon stimulation, have functions generally attributed to CD4+ T cells. The CD4-CD8
dim T cells can be restricted by MHC-II. Despite the fact that many of the T cells in this population probably developed from CD4+ T cells and maintain the ability to perform functions attributed to CD4+ T cells, they are able to evade infection by SIVagm. These data provide a mechanism by which African green monkeys are able to survive chronic SIVagm infection without progression to simian AIDS.
Our proposed mechanism underlying the nonpathogenic nature of SIVagm infection could contribute to the lack of immune activation seen in the natural hosts of SIV. Indeed, preservation of CD4+ T cell function may well contribute to the lack of immune activation in African green monkeys and sooty mangabeys28, 35, 36. Additionally, there is a markedly lower frequency of CD4+CCR5+ T cells in natural hosts of SIV when compared to non-natural hosts16, 37, suggesting that the lack of CCR5 expression results in decreased homing to sites of inflammation, thereby preventing activation and inflammation. This lower number of activated T cells could reduce the number of targets for SIV. Taken together, these data suggest that in natural hosts the virus may be preferentially targeting macrophages. However, we have found no SIVagm DNA within highly purified monocytes, consistent with previous reports that SIVagm preferentially replicates in lymphocytes during chronic infection16, 28. Also, previous comparative studies between pathogenic HIV infection of humans or SIV infection of Asian macaques and SIV infection of sooty mangabeys or African green monkeys have shown that, whereas both sooty mangabeys and African green monkeys lose CD4+ T cells from the gastrointestinal tract during the acute phase of infection, these animals do not show immune activation11, 28, 36. Microbial translocation, which causes immune activation in the chronic phase of HIV and SIV infection of Asian macaques38, 39, 40, 41, 42, 43, 44, 45, does not occur in the chronic phase of SIV infection of either African green monkeys or sooty mangabeys28, 42. The functionality of mucosal CD4-CD8
dim T cells, which are present at high frequencies in African green monkeys28, should be assessed for a role in preventing microbial translocation and immune activation in SIVagm-infected African green monkeys.
Many other cellular populations, such as natural killer cells, 
T cells and natural killer T cells, express the CD8
homodimer. Indeed, some of the CD4-CD8
dim T cells from African green monkeys express the 
T cell receptor (data not shown). Moreover, many of the CD28- memory T cells within the CD4-CD8
dim T cell subset express granzyme B (data not shown), not typically expressed by CD4+ T cells. Therefore, it is clear that not all of the CD4-CD8
dim T cells were originally CD4+ T cells. Although African green monkeys have considerably higher frequencies of CD4-CD8
dim T cells compared to humans, one study recently showed that slow-progressing HIV-1–infected individuals have a markedly higher frequency of CD4-CD8
dim T cells compared to chronically HIV-infected individuals46. This finding suggests that a similar phenomenon to what we observed here could slow disease progression in HIV-infected humans.
Although CD4-CD8
dim T cells have previously been studied29, 30, it has not been demonstrated that memory CD4+ T cells downregulate CD4 and upregulate CD8
. How these T cells are able to perform functions without the CD4 molecule is unclear. Notably, one group of researchers showed normal development and function of lymphoid organs, B cells and CD8+ T cells in CD4-knockout mice47. However, antibody production, IL-2 secretion and MHC-II–restricted responses were substantially abrogated47. The authors subsequently showed that CD4-CD8- T cells in CD4-knockout mice could partially compensate for the lack of CD4+ T cells48, similar to what we observed in African green monkeys. CD4 has been shown to be important for initiating the downstream kinase signaling that results in T cell activation49. It is possible that in African green monkey CD4-CD8
dim T cells sufficient leukocyte-specific protein tyrosine kinase (lck) phosphorylation occurs, or alternative signals exist, but the actual mechanism(s) underlying the switch from CD4+ to CD4-CD8
dim remains unclear. Indeed, previous studies have reported genetic differences between certain regulatory elements from African green monkeys compared to other primates50. One possibility is that a change may occur in the methylation states of the enhancer and silencer regions in the genome51. Also, differential expression of Myc-associated zinc finger–related factor protein, a suppressor of the CD8
enhancer region52, may also exist.
It is not unprecedented that changes in the frequencies of T cells within individual subsets occur in lentiviral infections. For example, although sooty mangabeys generally maintain healthy CD4+ T cell counts during chronic SIVsmm infection, infection with a dual tropic (CXCR4-CCR5) strain of SIVsmm resulted in the loss of CD4+ T cells but preservation of CD4-CD8- T cells53. Moreover, one report identified several naturally SIV-infected sooty mangabeys with very low frequencies of CD4+ T cells26. The functions and ontogeny of T cells in these SIVsmm-infected sooty mangabeys are currently under investigation but could represent a similar phenomenon to what we have described in African green monkeys.
Natural hosts have coevolved with SIV to avoid disease progression, although the mechanisms by which this occurs may diverge, as most sooty mangabeys maintain healthy frequencies of CD4+ T cells. In African green monkeys, we have shown that this coevolution with SIVagm has occurred, in part, through the development of CD4-CD8
dim T cells from memory CD4+ T cells. Additionally, African lions, who remain disease free after infection with feline immunodeficiency virus, maintain a high frequency of CD8
dull T cells regardless CD4+ T cell loss54. Hence, downregulation of CD4 may be associated with lack of disease progression in multiple immunodeficiency lentiviral infections.
We have identified and characterized a mechanism by which African green monkeys are able to survive chronic SIVagm infection. In non-natural hosts of immunodeficiency lentiviruses, depletion of CD4+ T cells leads to AIDS. However, SIVagm-infected African green monkeys maintain immune responses, remain healthy and have normal life spans. We provide evidence for the conversion of CD4+ T cells to CD4-CD8
dim T cells, which probably has a key role in the lack of clinical signs of AIDS in African green monkeys. Once the mechanism by which the CD4+ T cells are able to convert to CD4-CD8
dim T cells has been understood, interventions aimed at mimicking this phenomenon could be developed for preventative and therapeutic trials.
Note: Supplementary information is available on the Nature Medicine website.

g of SEB) (Sigma) or 1 