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Underpaid, overworked: Students speak out about challenges in leadership positions
On a sweltering day in August, groups of students across campus braced themselves for the daunting task ahead of them: spending hours helping new students move into their dorms. Move-in day kicks off Orientation Week every year, and nearly all Rice students are familiar with the ritual of sweaty, beaming advisors running back and forth with labeled cardboard boxes as incoming students start exploring their new home.
But this year, the students running O-Week faced an even greater challenge: planning a way to move in new students while masked, socially distanced and trying to prevent the spread of COVID-19.
The administration told O-Week coordinators to devise their college's move-in plan, according to Lillie Plaza, one of Lovett College's O-Week coordinators. At Lovett, Plaza said they decided that the safest way to move new students in was to follow the coronavirus floor rules laid out by the administration. If an advisor was living on the same floor as a new student, they were in charge of bringing that student's belongings to their room.
Hannah George, a Wiess College senior who co-advised at Lovett, said the Lovett move-in plan was successful. However, she said she doesn't think it should have been up to students to devise that plan in the first place — it should have been the administration.
Kamil Cook, a Brown College junior who coordinated O-Week at his college this year, said he made multiple decisions this summer that he felt shouldn't have been up to him.
"The whole time, I felt like we were doing work that we should not have been normally allowed to do. The decisions we were making were really important, and they were giving it to 20-year-olds who weren't getting paid to do it," Cook said. "We were told to be public health officials, despite the fact that we were never even given a slideshow — we weren't even given one slide about epidemiology, or public health, or anything."
Ishaan Rischie, who coordinated O-Week at Jones College this year, said the greatest difficulty he faced this summer was a lack of communication from the administration regarding planning. Although he said he ultimately doesn't fault them, it made the role harder.
"This summer of planning O-Week was made a million times more difficult than it needed to be because of a number of communication breakdowns between the O-Week coordinators and administration, resulting in us feeling as though our thoughts, proposals and ideas were falling on deaf ears," Rischie, a Jones junior, said.
According to Dean of Undergraduates Bridget Gorman, everyone who helped plan Rice's reopening made decisions they wouldn't normally be having to make. That included O-Week coordinators.
"It was a hard summer. I don't know what to say other than that," Gorman said. "I've never worked this hard in my entire life. I mean never, ever have. And I feel like it was that for every person who was at Rice."
However, this summer wasn't the first time that student leaders at Rice have felt like they've done work that surpassed what should be expected of a young person serving in an unpaid role, according to the 21 student leaders the Thresher spoke to for this story. Many of them — including students behind O-Week, student government, Students Transforming Rice Into a Violence-Free Environment and diversity and inclusion efforts — said they've felt this way for a while.
Back in March, when the majority of students were forced to suddenly vacate campus, it fell on a few students to do the heavy lifting, according to Johnston French and Kelly Dong. Johnston French, Sid Richardson College's chief justice, said that he and fellow Sid students Clarise Trinh, Sarah Mozden, and Nia Prince moved boxes of Sid students' belongings into storage, and again before students moved back in. Overall, French estimates he worked about 75 hours on moving people in and out.
Michel Achard, the college's magister, said he arranged for those students to receive financial compensation from the college budget because he wasn't comfortable with students doing that work for free. However, that wasn't the case at every college.
"It sounded like something that he went out of his way to do and not something Rice as a whole was doing, though," French, a Sid junior, said. "I'm concerned for the people who had to do move-out at other colleges."
As facilities directors at Will Rice, Dong and Manuj Shah were placed in charge of moving Will Rice students' belongings in and out of storage. According to Dong, a Will Rice College senior, it was a surprising amount of work and responsibility and they did not receive financial compensation.
"Coming up with a comprehensive plan was complicated considering there were so many restrictions that we had to work around without any guidance or advice from administration," Dong said.
As chief justice of Lovett for the 2019 to 2020 academic year, Laura Yordán said she felt supported by various individuals at her college and in the administration, including her college's core team, college president Chloe Oani and Henry Cash, who worked for Rice University Police Department for 13 years before becoming a wellbeing advisor.
Still, she said she constantly felt stretched too thin and in charge of things that surpassed her capabilities as a college junior, such as regularly deciding whether an intoxicated student needed to receive medical attention.
"You don't sleep at all on weekends," Yordán, a Lovett senior, said. "I had support, but sometimes it's just like, you do things that are way beyond your pay grade. And it's like, I'm only 20 years old. There [are] just some things that I can't do."
Late nights are also a regular occurrence for STRIVE liaisons, according to Mezthly Pena, a Duncan College junior and liaison. She said it's a full time job, most of which consists of helping survivors of sexual assault work through trauma. Although she believes the work is essential, she said it's incredibly difficult at times.
"It's honestly something probably a therapist should be doing, but students are doing it instead," Pena said.
The most difficult part of being a STRIVE liaison, according to Mallory Newbern, is the emotional toll it can take on a student. The work can be retraumatizing for liaisons who are survivors themselves, she said.
"People are in really difficult situations, and they come to you for emotional support and you need to provide it in that moment, but then there's long-lasting effects of these conversations," Newbern, a Martel College junior and liaison, said. "It really does take a toll on multiple different parts of your life. But it's all worth it. I really do think it's all worth it."
Diversity and inclusion work on campus can also be retraumatizing for the Black students leading those efforts, according to Kendall Vining, a Martel College junior. In addition to serving as internal vice president for the Student Association, Vining serves on the Rice for Black Life steering committee and is a co-leader of the list of Black student demands published this summer. It was especially difficult to do this work in the face of this summer's events.
"It's hard, because while Black students should be at the front of making these changes, our racial traumas and hurt [are] reopened with every news we hear of another Black person shot," Vining said. "When you are faced with so little support from administration and Rice in general that you literally feel the need to create an outside organization — Rice for Black Life — to get anything accomplished, that says a lot right there."
Soha Rizvi and Jiya Ghei, two of this year's diversity facilitators, said that the work diversity facilitators do can take a similar emotional toll, especially on Black facilitators. Although Rizvi and Ghei both said they were passionate about the role and ultimately enjoyed it, they said they did not feel like the administration supported them.
"Part of our role is dealing with some students, particularly new students, who hold little respect for our goals and sometimes even our identities. That has been an emotional burden I didn't expect, so I can't imagine the experience of the [Black, Indigenous, and people of color diversity facilitators]," Rizvi, a Hanszen College junior, said. "We definitely don't get the compensation or administrative support that we deserve considering we do the grunt work of implementing Rice's professed values of diversity and inclusion."
According to Gorman, the administration has been devoting a lot of time and effort to responding to this summer's events and making Rice a more anti-racist institution. She pointed to the five specific actions President David Leebron and Provost Reginald DesRoches announced in an email to the Rice community on June 16. The actions included establishing the new positions of Vice Provost for Diversity, Equity and Inclusion and Scholar in Residence for Racial Justice, designing a course on diversity and cultural understanding that will be required for new students starting in 2021, and creating two funds — one to to support non-partisan student engagement in Houston on issues of racial equity and justice and another to support faculty doing research on race and anti-racism.
"The murder of George Floyd was an incredibly upsetting one, I think for everybody. The students, faculty, staff, the entirety of the Rice community. It's been heartening to see students' reaction to that across the board," Gorman said. "I'm sorry if some [diversity facilitators] felt like we weren't engaged and we weren't caring about this. I think we very much were."
Leslie Loredo said she came out of coordinating O-Week for Jones College in 2019 exhausted, disillusioned with Rice and with damaged relationships at her college. Although she said she doesn't regret coordinating, she said those feelings are common for coordinators, and that the administration doesn't do enough to help former coordinators get through the burnout they may face after O-Week.
"The administration is putting the weight of their biggest, most important event on you, without helping you carry it," Loredo, a Jones College senior, said.
This year, Loredo returned to Jones College O-Week as an advisor. She said she wanted to be there to support the 2020 coordinators, as she could sympathize with some of what they were going through. She was frustrated to see how much work the coordinators were doing, and she thinks some of it — such as their roles as enforcers of social distancing — should have been taken on more by the administration.
"It sucks because it's like, as a student, I have to help these other students because I know the administration's not going to be there for them," Loredo said. "And so I'm having to step up and be like … please let me help you, because I know they're not going to."
Gorman said she has no reason to think that O-Week coordinators aren't being emotionally supported, and said that Araceli Lopez, who leads First Year Programs, does much of that work.
"I know she cares about them a great deal. And I know that she doesn't hesitate to reach out if she feels like there's a coordinator that's struggling," Gorman said. "If we have coordinators who felt that emotionally they weren't getting their needs met, then I am sorry about that."
Loredo said she greatly appreciates the work that Lopez does, but that ultimately, the emotional burdens O-Week coordinators face are too heavy to put on one person.
When Angelica Torres became McMurtry's chief justice in March, she had no idea what she was signing up for. Due to the unforeseen severity of the pandemic, this was the case for students across campus who assumed leadership roles for the 2020 to 2021 school year.
"People look to me now for information and rules about how to interact in a COVID world, but I have never received any training to do so," Torres said. "I am also left out of the Rice decision making, so I can't even give up to date information to the students who are asking me for it."
According to George, who was a diversity facilitator, the work that facilitators did this summer similarly surpassed what they were initially expected to do. She said that diversity facilitators carried the entire burden of talking to new students about the murders of George Floyd, Breonna Taylor and other Black victims of police brutality and racist violence.
"[The increased workload] was because of the Black Lives Matter movement over the summer, and Rice for Black Lives, and the need for the administration to be like, 'Oh, we did something,'" George said. "Except the administration didn't do anything. They said that you as students and you as diversity facilitators need to do the work."
Although the events of this year may have exacerbated them, disparities between what students expect when they sign up for a leadership role and what they end up doing are not new, according to a number of students interviewed.
Milkessa Gaga, who co-led the Black student demands with Vining, said that Black students often end up doing far more activism than they ever expected to do in college.
"I don't think any of us really come into college or Rice thinking that we want to be student activists or whatever. We're just regular people that want to go to school," Gaga, a Martel College junior, said. "But we happen to be in this position where like, I got to do this if I want to improve my experiences and the experiences of others."
Torres said her experience as chief justice this year speaks to a larger problem of expectations versus reality at Rice.
"In some ways, the Culture of Care can be used to guilt students into providing services for free," she said.
Gorman said she believes that although Rice does a lot to support student leaders, nothing can fully prepare them for some of the things they'll face in their roles.
"I don't think there's any way we can perfectly prepare anybody, because I just don't think it's possible," she said. "If there's anything I've learned in life, it's that you don't totally understand a role until you're in it."
In 2019, the Dean of Undergraduate's Office created a need-based stipend program for O-Week coordinators. Students were able to indicate on their application if they needed funding to be able to stay at Rice over the summer as O-Week coordinators. Prior to the stipends, which range from $500 to $2,500, coordinators received no summer compensation other than eight meals per week and on-campus housing from June 1 until advisor training and O-Week.
"We realized that some students weren't able to come and apply to be O-Week coordinators in the summer because [the position was unpaid]. That was really depressing their ability to do that, so we put together the need-based stipend program," Gorman said. "By every measure that I've seen, we did meet their financial needs over [this] summer."
However, some former O-Week coordinators said they aren't fully satisfied with the stipend, although it's a step in the right direction. Former coordinators Loredo, Cook, as well as Aurora Kesler, who coordinated Brown College's O-Week in 2019, all said they think the position should be paid.
"I want to see O-Week coords be paid. I don't care if people think it'll diminish the value of the position, if it'll make it seem like you're just doing it to get paid. No one does this just to get paid," Loredo said. "You could go work somewhere for the summer where you wouldn't have to do as much emotional or mental labor. It's not about that. It's about your dedication."
Max Boekelmann, a Jones College senior who coordinated in 2019, said coordinators are still facing financial barriers to the role.
"It is a lot to ask of students to give up the opportunity to earn money and instead volunteer their summer," Boekelmann said. "Every year, a person's love for O-Week and love for their college is pushed to the front to hide the fact that by choosing to coordinate O-Week you are committing hours upon hours without getting paid. I do love Jones College, but that did not make those hours any less difficult."
Maddy Scannell, executive director of STRIVE, said she wants to see the university financially compensate liaisons.
"On an ethical level, liaisons are doing work for the university — that the university tends to exploit in its communications about Title IX and sexual misconduct. Labor ought to be compensated," Scannell, a Martel College senior, said. "Financial support for liaisons would make this role more accessible, allowing us to diversify our liaisons and better serve the Rice community."
Varsha Varghese, a Baker College senior, said she had a fairly manageable year as Baker's chief justice from 2019 to 2020, thanks to support from students and the A-Team. However, she said that when she tells her friends from home about her role, they ask her if she was a residential associate.
"At other universities, the role of a RA is basically what the CJ does, except they get paid for it," Varghese said.
However, some students are not sure if the answer to these concerns lies in financial compensation. Tim Thomas, who served as Wiess College president from 2019 to 2020, said that the immense workloads and emotional tolls placed on student leaders should be reexamined before the pay situation.
"If [the administration] is not going to try to improve the general quality of life, then I think pay needs to become a factor," Thomas, a Wiess College senior, said. "In order for it not to be, I think there just needs to be a better support system."
Matthew Burns, a Lovett College senior and former O-Week coordinator, said that although he initially wanted coordinators to receive compensation, he learned that this would mean they would have to be treated like employees, which was something he had not considered.
"This means less forgiveness on missed deadlines, less freedom and more control in the hands of the admin," Burns said. "A lot of the creative freedom we have in planning our O-Week comes from the fact that we are volunteers."
Wanting to avoid such an employer-employee relationship between students and the administration is a major reason why the administration has resisted compensating student leaders in the past, according to Gorman. To her, student leadership roles are opportunities for service and experiential learning, not jobs. She also pointed out that colleges have a budget, which they could use to compensate certain students.
According to Associate Provost Matt Taylor, who has worked closely with student leaders at Rice for decades, students have a lot of autonomy in determining what a particular role entails. Taylor said that in various instances over the years, student leaders have resisted the idea of financial compensation, but have clung to their many responsibilities.
"I think it's extremely valuable to be in partnership with student leaders, figuring out how best to shape a student experience that's rewarding and educational and challenging and the best in the country," Taylor said. "But those roles don't have to be roles that eat up a ton of time and create a burden in a way that students feel like they should be compensated because it takes so much of their time."
Kesler, a Brown College senior who coordinated O-Week in 2019, said she's observed that in recent years, the lack of standardized compensation and the immense workload student leaders face has been more and more discouraging to students. In particular, she said she's seen a decline in quality of O-Weeks, and predicts that sooner or later, the administration won't have a choice but to pay coordinators, because otherwise, people won't apply for the job. Alternatively, Kesler said that a student leader strike would move the conversation about pay forward. She said she'd like to see one.
"O-Week coordinators right now, all that's left in their job is to turn in the coordinators for next week. But they have no obligation to do that. Don't do it," Kesler said. "Coordinators should refuse to continue participating as part of this university and as wards of the institution until the university starts listening and actually caring about the things students are saying, and actually taking it seriously. Right now, we're not even at the negotiating table."
Student Association President and Martel College senior Anna Margaret Clyburn said she firmly believes that student leaders need more support. Part of the solution, she said, may lie in supporting existing offices that help student leaders, such as the Office of Multicultural Affairs and Student Success initiatives, and hiring more staff to fill them. It could also lie in making certain leadership positions paid, she said. Regardless, she said the administration needs to start working on a solution to the concerns of student leaders by doing one thing: listening.
"Paying student leaders will not solve all of our problems, and neither will hiring more staff," Clyburn said. "But taking both seriously and listening to students and staff when they voice their frustrations, their concerns, and their exhaustion is a start."
More from The Rice Thresher
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Rice intends to build two new residential colleges with an accompanying servery, President Reggie DesRoches and Vice President for Finance and Administration Kelly Fox announced in an email sent May 19. The old Sid Richardson College building will be demolished as part of this project. One of the new colleges will take its place, and the other will be positioned closer to Wiess College.
Rice's James Tour and YouTuber 'Professor Dave' debate the origins of life
Dave Farina of the YouTube channel ProfessorDaveExplains came to Rice to debate organic chemistry professor James Tour on the topic of abiogenesis, the scientific theory that life on Earth originated from non-living compounds. The debate occurred May 19 in a full Keck Hall, with up to 2,800 viewers watching the event livestreamed on YouTube.
'Always laughing, always smiling and singing': Family, colleagues remember Triny Carranza
María Trinidad "Triny" Carranza, cook III at the Cohen House, passed away May 7 at the age of 50. Carranza's daughter said Triny's cause of death was complications from blood clots. Hailing from the city of Chihuahua, Mexico, Triny visited Houston in her early twenties and chose to stay after meeting her future husband, Salvador Carranza, in the same apartment complex. Once settled, she began working in the cooking industry that, according to her husband, she was in love with.
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DURBAN - 4 April 2014 - Cyril Ramaphosa, the deputy president of South Africa's ruling African National Congress, speaks at a meeting in Durban's predominantly white suburb of Amanzimtoti. The country heads to the polls on May 7 and is trying to attract more white voters who for the most part have backed the main opposition party, the Democratic Alliance. Picture: Allied Picture Press/APP
- Filename
- 20140404gs_6864_Cyril_Ramaphosa.jpg
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- Giordano Stolley 2014
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- http://www.alliedpicturepress.com
- Contained in galleries
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subset: commoncrawl


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Jon Durrant
Depressing 80's sitcom No1:
There are TONS of really well designed new movie posters for classic films, sold as limited edition prints. For some reason .... I've decided to make a range of posters for shit 80's TV sitcoms in a similar style, OK, now this might only amuse me ? so many of these sitcoms I watched under duress as a child were so flipping depressing, Sorry !, Last Of The Summer Wine, Open All Hours, even Only Fools And Horses. Can't stand them all depressing as fuck, not funny either, so they're the ideal topic for me to muck about with. The Sorry! poster is a work in progress. I'll print it in drab grey and ennui inducing black.
Might add an out line and some details as half toning looses a lot from the image.


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Antiretroviral therapy (ART) suppresses viral replication in people living with HIV. Yet, infected cells persist for decades on ART and viremia returns if ART is stopped. Persistence has been attributed to viral replication in an ART sanctuary and long-lived and/or proliferating latently infected cells. Using ecological methods and existing data, we infer that >99% of infected cells are members of clonal populations after one year of ART. We reconcile our results with observations from the first months of ART, demonstrating mathematically how a fossil record of historic HIV replication permits observed viral evolution even while most new infected cells arise from proliferation. Together, our results imply cellular proliferation generates a majority of infected cells during ART. Therefore, reducing proliferation could decrease the size of the HIV reservoir and help achieve a functional cure.
Antiretroviral therapy (ART) limits HIV replication leading to elimination of most infected CD4+ T cells1. Yet, some infected cells persist and are cleared from the body extremely slowly despite decades of treatment2,3. There is debate whether infection remains due to HIV replication within a small population of cells4,5 or persistence of memory CD4+ T cells with HIV integrated into human chromosomal DNA3,6,7. If the latter mechanism predominates, prolonged cellular lifespan and/or cellular proliferation may sustain stable numbers of infected cells.
To optimize HIV cure strategies, mechanisms sustaining infection must be understood. Persistent viral replication in a sanctuary where ART levels are inadequate implies a need to improve ART delivery8. If HIV persists without replication as a latent reservoir of memory CD4+ T cells, then survival mechanisms of these cells are ideal therapeutic targets. Infected cell longevity might be addressed by reactivating the HIV replication cycle9 and strengthening the anti-HIV immune response, leading to premature cellular demise. Anti-proliferative therapies could limit homeostatic or antigen-driven proliferation10,11,12.
These competing hypotheses have been studied by analyzing HIV evolutionary dynamics. Due to the high mutation rate of HIV reverse transcriptase and large viral population size13, HIV replication produces high viral diversity13,14,15. New strains predominate due to continuous positive immunologic selection pressure. Repeated selective sweeps cause genetic divergence, or a positive molecular evolution rate16, measured by increasing genetic distance between the consensus and founder virus17,18,19.
One study documented new HIV mutants during months 0–6 of ART in three participants at a rate equivalent to pre-ART. New mutations were noted across multiple anatomic compartments, implying widespread circulation of evolving strains4. One proposed explanation was a drug sanctuary in which ART levels were insufficient to stop new infection events. Alternative interpretations were experimental error related to PCR resampling, or variable cellular age structure within the phylogenetic trees20,21.
In other studies of participants on ART for at least one year, viral evolution was not observed despite sampling multiple anatomic compartments22,23,24,25. Identical HIV DNA sequences were noted in samples obtained years apart14,26,27, suggesting long-lived latently infected cells as a possible mechanism of persistence3,6,7,24,25. Clonal expansions of identical HIV DNA sequences were observed, demonstrating that cellular proliferation generates new infected cells4,12,24,28,29,30. Multiple, equivalent sequences were noted in blood, gut-associated lymphoid tissue (GALT), and lymph nodes, even during the first month of ART24,29,30.
The majority of these studies relied on sequencing single HIV genes which may overestimate clonality because mutations in other genome segments could go unobserved17,31. These studies also measured total HIV DNA. However, a majority of HIV DNA sequences have deleterious mutations and do not constitute the replication-competent reservoir32,33. A recent study utilized whole-genome sequencing to confirm abundant replication-competent sequence clones34. In another cohort, rebounding HIV arose from replication-competent clonal populations35.
Another approach to define HIV clonality involves sequencing the HIV integration site within human chromosomal DNA36,37,38,39,40. While HIV tends to integrate into the same genes39,41, it is extremely unlikely that two infection events would result in integration within precisely the same chromosomal locus37. Thus, integration site analyses eliminate overestimation of clonality. Previous studies found significant numbers of repeated integration sites, providing strong evidence that these infected cells arose from cellular proliferation42,43, though replication competency of the virus was not confirmed39. These studies documented equivalent sequences in a minority (<50%) of observed sequences, leading to the conclusion that proliferation only partially drives HIV persistence.
Here, we identify that incomplete sampling leads to underestimation of the true proportion of clonal sequences. Using ecologic tools, we show that nearly all observed unique sequences are actually members of clonal populations derived from cellular proliferation. We predict that the HIV reservoir consists of a small number of massive clones, and a massive number of small clones. We next design a mechanistic mathematical model to reconcile apparent evolution during the early months of ART with clonality after a year of ART. The model includes all proposed mechanisms for HIV persistence including a drug sanctuary, long-lived infected cells, and proliferating infected cells. The model highlights that observed HIV evolution during the first 6 months of ART is caused by sampling long-lived cells that were generated by viral replication. Sampling early during ART detects a positive molecular evolution rate due to the fossil record of past infections rather than current viral replication. After one week of ART, a majority of new infected cells are generated by proliferation. While it is impossible to rule out an unobserved drug sanctuary, our results suggest that cellular proliferation predominantly drives HIV persistence on ART. Consequently, anti-proliferative therapies embody a meaningful approach for HIV cure.
Genetic signatures of HIV persistence
When HIV infects a cell, it integrates its DNA into human chromosomal DNA44. A majority of new infected cells are marked by novel integrated HIV sequences and unique integration sites in terms of chromosomal location (Fig. 1) due to the high error rate of HIV reverse transcriptase and the integration process. Thus, a signature suggesting that ongoing viral replication (perhaps due to inadequate drug delivery to certain micro-anatomic regions) sustains the HIV reservoir on ART would be the observation of continual accrual of new mutations during ART.
In a subset of infected CD4+ T cells, HIV replication does not progress beyond chromosomal integration and the virus enters latency44. If the same HIV sequences (or integration sites) are found over long-time intervals, this provides a signature that latent cell longevity or proliferation allows HIV to persist. If equivalent HIV sequences with identical chromosomal integration sites are identified in multiple cells, this provides a signature that these sequences were generated via cellular proliferation, rather than HIV replication (Fig. 1).
As another approach, we contrast the impact of HIV replication and cellular proliferation on HIV persistence during ART by quantifying the numbers or fractions of unique and equivalent sequences. Human DNA polymerase has much higher copying fidelity than HIV reverse transcriptase. Thus, we assume cells arising from viral replication will contain unique sequences while cells arising from cellular proliferation will contain equivalent sequences and be members of clonal populations.
HIV DNA as a marker of replication-competent HIV clonality
Most integrated HIV DNA carries mutations that render the virus replication incompetent. Quantification of total HIV DNA overestimates the size of the replication-competent reservoir by 2–3 orders of magnitude relative to viral outgrowth assays32. Replication incompetent, equivalent HIV sequences are commonly present in multiple cells24,29. Because these sequences are terminally mutated, they are concrete evidence that another mechanism (cellular proliferation) copies HIV DNA. The proportion of clonal sequences is similar when analysis includes only replication-competent sequences, or all HIV DNA34. Therefore, while total HIV DNA may not predict quantity of replication-competent viruses, estimates of clonal frequency using total HIV DNA may be extrapolated to the replication-competent reservoir33. We use total HIV DNA as it allows a greater sample size for analysis.
Clonal HIV DNA and replication-competent HIV during ART
To examine the clonal structure of total and replication-competent HIV DNA, we ranked observed sequences from several studies according to their abundance. So-called rank-abundance curves are ordered histograms denoted a(r) such that a(1) is the abundance of the largest clone. These curves facilitate identification of the richness R = max(r), sample size \(N = \mathop {\sum }\nolimits_r a\left( r \right)\), and number of singletons \(N_1 = \mathop {\sum }\nolimits_r I[a(r) = 1]\). Here I[·] is the indicator function equal to 1 when its argument is true and 0 otherwise.
Wagner et al.37 sampled HIV DNA in three participants at three time points 1.1–12.3 years following ART initiation. Maldarelli et al.36 sampled HIV DNA from five participants at one to three time points 0.2–14.5 years following ART initiation. In these studies, 1–16% (mean: 7%) of sequences were members of observed sequence clones (Fig. 2a)36,37, meaning that HIV DNA was in the same chromosomal integration site in at least two cells. The absolute number of observed sequence clones Ni>1 in the 17 samples ranged from 1–150 (mean: 15). The remaining sequences were identified in a specific chromosomal integration site in only one cell (observed singletons)37. For total HIV DNA, at each participant time point, certain sequences predominated: the largest observed clone contained 2–62 sequences (mean: 11), accounting for 3–26% (mean: 9%) of total observed sequences.
Hosmane et al.34 sequenced replication-competent HIV isolates from 12 study participants on ART: 0–28% (mean: 11%) of sequences were members of observed sequence clones (Fig. 2b). Three participants did lack clones, which might reflect low sequence sample size. As a result, we excluded participants with fewer than 20 total sequences from individual analyses but did include these data for population level evaluations. For replication-competent HIV in the five individuals having sequence sample size N > 20, certain sequences dominated: the largest observed sequence clone contained 3–9 sequences (mean: 6.8), accounting for 11–42% (mean = 28%) of total observed sequences. The number of non-singleton sequence clones Ni>1 in the five samples ranged from 1–7 (mean: 3.8).
Low sampling depth relative to total sequence population
Larger sample sizes exist for total HIV DNA (Fig. 2c) than for replication-competent HIV (Fig. 2d). Both for total HIV DNA and the five included replication-competent data sets (where N > 20), the number of observed unique sequences (Robs or observed sequence richness) was always less than N (Fig. 2c, d). In both cases, observed richness (Robs) correlated with sequence sample size (N) (Fig. 2c, d). Thus, we infer that further sampling would uncover new unique sequences. To quantify the relationship between sample size and discovery, we calculated rarefaction curves (Fig. 2e, f: see Methods and Supplementary Methods for details). These curves relate expected sequence discovery and sample size. At low sample size, each additional sample likely uncovers a new sequence. As sampling increases, the chance of sampling a previously documented sequence increases, and the slope of the rarefaction curve begins to flatten. As sample size approaches the true population richness, the curve plateaus and few new unique sequences remain unsampled. Current sampling depth remains on the steep, initial portion of the curve (Fig. 2c, d).
Lower bounds of true HIV sequence richness
To estimate a lower bound for true sequence richness, we used the Chao1 estimator, a nonparametric ecologic tool that uses frequency ratios of observed singletons N1 and doubletons N2 (see Methods and Supplementary Methods)45,46. For the HIV reservoir, theoretical values for true richness range from one (if all sequences are identical and originate from a single proliferative cell) to the total population size (if all sequences are distinct and originate from error-prone viral replication). Estimated lower bounds for true sequence richness exceeded observed richness, typically by an order of magnitude in both total HIV DNA and replication-competent HIV (Fig. 3). These lower bound estimates for sequence richness are far lower than previously estimated population sizes for HIV DNA and replication-competent HIV DNA sequences2,3,6, suggesting that clones may predominate. Asymmetric confidence intervals for these estimates are detailed in the Supplementary Methods.
A majority of observed sequences are clonal
The Chao1 estimator does not integrate information about the total population size. However, estimates for the total number of total HIV DNA and replication-competent sequences in the entire reservoir exist33. Using that additional information, we developed an ecologic model to extrapolate the true rank-abundance of HIV sequences for each participant time point.
Based on the observation that observed data was roughly log-log-linear (Fig. 2a), we chose a power-law model for rank-abundance: a(r) ∝ r−α. Other simple functional forms were explored (exponential, linear, and biphasic power-law) but were worse or equivalent for data fitting. Our model requires three parameters: the power-law exponent (α), the sequence population size (L), and the sequence richness (R). Model fitting is described in the Methods with additional detail in the Supplementary Methods. Briefly, we generated 2500 possible models for each data set, choosing a plausible fixed population size from available data (L = 109 for HIV DNA and L = 107 for intact, replication-competent HIV DNA)2,3,6,33,47. We then recapitulated the experiment by taking N random samples from each model distribution and comparing sampled data to experimental data to find optimal model parameters. This resampling method correctly inferred the power-law exponent from simulated power-law data (Supplementary Fig. 1).
For experimental data, we could not precisely identify R. Recognizing this uncertainty, we developed an integral approximation to estimate the largest possible richness (least clonality) given L and the best-fit α (derivation in Supplementary Methods and illustration in Supplementary Fig. 2). Using the lower bound estimate from the Chao1 estimator, we were able to fully constrain the estimate of true HIV sequence richness in the reservoir. Our maximal estimates for sequence richness were notably several orders of magnitudes higher than Chao1 estimates (Fig. 3) but lower than the total sequence population size (L).
Our method demonstrated excellent fit to cumulative proportional abundances of observed clones for total HIV DNA (Fig. 4a) and replication-competent HIV DNA (Fig. 5a). For total HIV DNA (Fig. 4b) and replication-competent HIV DNA (Fig. 5b), optimal fit was noted within narrow ranges for the power-law slope parameter but across a wide range of true sequence richness. Using the five best-fit models, we generated extrapolated distributions of the entire HIV sequence rank-abundance for all participant time points. For the participant in Fig. 4c, between 104 and 107 clones were needed to reach 100% cumulative abundance. The ratio of these estimates of true sequence richness to the total number of infected cells with HIV DNA (109), or R/L, represents an upper bound on the fraction of sequences that are true singletons: we estimate that >99% of infected cells contain true clonal sequences. Similarly, the ratio of estimated true sequence richness to the total number of infected cells with replication-competent HIV for the participant in Fig. 5c was 105/107. Hence, at least 99% of cells are members of clonal populations. Of note, these ratios are relatively stable regardless of assumed reservoir size. For instance, if we assume a true reservoir size of 106, then our estimate of true sequence richness is ~104. In these examples, the best-fit models gave similar estimates for the population size of the largest clones—those accounting for ~50% of the reservoir—103 to 104 clones for HIV DNA in Fig. 4c and 2–20 clones for replication-competent HIV DNA in Fig. 5c. However, the tail of the reservoir, which consists of thousands of smaller clones, could vary considerably across parameter sets with 104 to 106 possible clones accounting for 90% of total HIV DNA and 102 to 104 possible clones accounting for 90% of replication-competent HIV. This variability reflects the fact that true sequence richness is only partially identifiable using our procedure. The extrapolated rank-abundances for each representative data set are presented in Figs. 4d and 5d.
We applied our model fitting procedure to all data in Fig. 2a and sufficiently sampled data in Fig. 2b (see asterisks). We biased against a clonally dominated reservoir to the greatest extent possible by selecting the best fitting power-law exponent and then calculating the maximum possible sequence richness (see details in Supplementary Information and Supplementary Fig. 2). For all cases, even under this conservative assumption, the vast majority of sequences were predicted to be members of true sequence clones. The power-law exponent was lower for HIV DNA (α = 0.9 ± 0.1) than for replication-competent HIV DNA (α = 1.4 ± 0.2) on average. Here, errors (±) represent standard deviation across 17 and 5 participant data sets, respectively. As a result, the predicted cumulative distribution of HIV DNA (Fig. 4e) was often concave-up with log rank as compared to concave-down with log rank noted for replication-competent HIV DNA (Fig. 5e), suggesting that a smaller number of extremely large clones might make up a higher proportion of the replication-competent HIV reservoir.
For both total HIV DNA (Fig. 4f) and replication-competent sequences (Fig. 5f), the top 100 clones in all participants are estimated to be massive (>105 and >104 associated cells, respectively). However, there are also massive numbers of smaller clones with fewer than 1000 associated cells (>107 and >104, respectively). In contrast to observed data, a majority of sequences are clonal, suggesting that proliferation is the major generative mechanism of persistent HIV-infected cells.
Modeling combined population data
To increase sample size and eliminate bias related to excluding participants with low sample sizes, we combined results from all participant time points for HIV DNA (17 time points) and replication-competent HIV (12 time points) into single rank order distribution curves. We then fit the power-law models to both sets of data (Supplementary Fig. 3A, B, E, F). We again noted a narrow range of possible values for the power-law exponent and a large range of possible values for true sequence richness. The exponent was again α < 1 for total HIV DNA and α ≈ 1 for replication-competent virus (Supplementary Fig. 3A, E), leading to concave-up and linear relationships between log cumulative proportional abundance and log rank, respectively (Supplementary Fig. 3C, G). We estimated that at least 99.9% of total HIV DNA (Supplementary Fig. 3C) or replication-competent HIV (Supplementary Fig. 3G) contain true clonal sequences. The top 100 HIV DNA clones (Supplementary Fig. 3D) and replication-competent clones (Supplementary Fig. 3H) contained >106 and >104 associated cells, respectively.
Using the population level data, we generated sample rarefaction curves from the extrapolated rank-abundance curves. These curves show that after 10,000 sequences were sampled, the observed sequence richness would continue to increase with more sampling (Supplementary Fig. 4). Even if experimental sample sizes could be increased 100-fold from the present data, sequences would likely continue to be dominated by those from large clones. Our methods, or other inference techniques, may therefore be necessary to realistically estimate the clonal distribution of the HIV reservoir.
Mathematical model of persistent infected cell dynamics
Our analyses above identify the critical role of cellular proliferation in generating infected cells after a year of ART but do not capture the dynamic mechanisms underlying this observation or explain possible evidence of viral evolution during months 0–6 of ART4. We therefore developed a viral dynamic mathematical model. Our model (Fig. 6a) consists of differential equations, described in detail in the Methods. Most model parameter values are obtained from the literature (Table 1).
Briefly, we classify rapid death δ1 and viral production within actively infected cells I1. Cells with longer half-life I2 are activated to I1 at rate ξ2. I2 may represent CD4+ T cells with a prolonged pre-integration phase, but their precise biology does not affect model outcomes48. The state I3(j)represents latently infected cells. We assume each cell carries a single chromosomally integrated HIV DNA provirus44. The probabilities of a newly infected cell entering I1, I2, I3(j), are τ1, τ2, τ3(j). Because we are focused on the role of proliferation, we include CD4+ T cell subsets12 including effector memory (Tem), central memory (Tcm), and naive (Tn) CD4+ T cells, which have been experimentally proven to turn over at different rates α3(j), δ3(j)12,42,43. We assume all subsets I3(j) reactivate to I1 at rate ξ349.
We allow ART potency \({\it{\epsilon }} \in [0,1]\) to decrease viral infectivity50. Other dynamic features of infection such as death rate of infected cells and latent cell proliferation and reactivation rates are unchanged on ART. On ART, the basic reproductive number becomes \(R_0\left( {1 - {\it{\epsilon }}} \right) < 1\) when \({\it{\epsilon }} > 0.95\). In a completely susceptible population a reproductive number <1 implies each cell infects fewer than one other cell on average and viral loads decline from steady state. In this setting, only short stochastic cycles of viral replication can occur.
To make a model inclusive of viral evolution despite ART, we allow for the possibility of a drug sanctuary state (IS) that reproduces with reproductive number \(R_0\left( {1 - {\it{\epsilon }}_{\mathrm{S}}} \right) \approx 8\). In the drug sanctuary, ART potency is negligible \(({\it{\epsilon }}_{\mathrm{S}} \approx 0)\) such that the sanctuary reproductive number is equivalent to the value from a model without ART. However, target cell limitation or a local immune response causes a sanctuary viral set point to prevent infected cells and viral load from growing unabated. In the absence of contradictory information, we assumed homogeneous mixing of V1 and VS in blood and lymph nodes4. Thus, we find that the sanctuary size must be limited to 0.001–0.01% of the original burden of replicating HIV to achieve realistic viral decay kinetics (Fig. 6b)51.
Based on the observation that activated, uninfected CD4+ T cells (S), the targets for replicating HIV, decrease in numbers after initiation of ART we also perform a subset of model simulations with a slow target cell decline within the HIV drug sanctuary. We approximate this process with an exponential decay of target cells with rate ζ (per day)52,53. The decay rate is lower than concurrent decay rates measured from HIV RNA50,51,54 because abnormal T cell activation persists for more than a year after ART53.
Accurate simulation of HIV dynamics during ART
We fit the model to ultra-sensitive viral load measurements collected from multiple participants in Palmer et al.51. We included experimentally derived values for most parameter values (Table 1), solving only for activation rates ξ2 and ξ3 by fitting to viral load. Simulations reproduce three phases of viral clearance (Fig. 6b) and predict trajectories of infected cell compartments (Fig. 6c). The model fit is flexible to assumptions of starting values of the three infected cell compartments (the relative proportion of which are unknown pre-ART): in this circumstance, we arrive at different values of ξ2 and ξ3 without impacting overall model conclusions regarding the HIV reservoir. The size of the sanctuary (expressed as the fraction of infected cells φS) is only constrained to be below a value <10−5 to ensure accurate model fit for a static sanctuary model. This value can be higher for a decaying sanctuary (Fig. 7a, third column).
Cellular proliferation sustains HIV infection during ART
We next used the model to estimate the fraction of cells generated by cellular proliferation versus viral replication. We conservatively assumed that prior to ART all infected cells were generated by viral replication. Then, we tracked the number of cells whose origin was replication and the number whose origin was cellular proliferation. Without directly simulating a phylogeny, the fraction of all cells that derive from replication provides a surrogate for the expected fraction of cells that would give a signal of evolution. We also distinguish the current replication percentage, the fraction of infected cells currently being generated from viral replication, from the net replication percentage, the fraction of total infected CD4+ T cells remaining at a given time whose origin was HIV replication. This distinction contrasts the surviving, historically infected cells with those presently being generated via HIV infection. Because many long-lived cells were once generated by HIV infection, the net replication percentage typically exceeds the current replication percentage.
We simulated the model under several plausible sanctuary and reservoir conditions to assess the relative contributions of infection and cellular proliferation in sustaining infected cells. We considered different reservoir compositions based on evidence that effector memory (Tem), central memory (Tcm), and naive (Tn) cells proliferate at different rates and that distributions of infection in these cells differ among infected patients12,42,43. Further, because a drug sanctuary has not been observed, its true volume is unknown and may vary across persons. We therefore conducted simulations with a static sanctuary, a slowly diminishing sanctuary, and no drug sanctuary (Fig. 7a).
Regardless of assumed pre-treatment reservoir composition and sanctuary size, the contribution of replication to generation of new infected cells is negligible after one year of ART. The contribution of current replication diminishes rapidly with time on ART regardless of whether a sanctuary is assumed (Fig. 7b). The fraction of long-lived latently infected cells (I3) generated by viral replication (Fig. 7c, note log scale) is negligible within days of ART initiation. This finding captures the extent of the impact of proliferation even when a sanctuary is assumed.
A fossil record of prior replication events
In all simulations, the net fraction of cells generated from viral replication rather than cellular proliferation at 6 months of ART (5–25% in Fig. 7d) is higher than the current percentage generated by replication (Fig. 7b). A higher fraction of slowly proliferating Tn cells exacerbates the difference between historical and contemporaneous generation of infected cells (Fig. 7d, green line). Because the net fraction is what will be observed experimentally, the model reveals why ongoing evolution might be observed even while the dominant mechanism sustaining the reservoir is cellular proliferation. In keeping with the first section of our paper, after 12 months of ART, the net and current percentage of infected cells generated by HIV replication become negligible for all simulated parameter sets. The lag between net and current viral replication generation emerges whether or not a small drug sanctuary is included in the model.
We refer to the phenomenon that long-lived cells may contain signatures of past viral replication as the fossil record. To emphasize the concept, the fossil record finding is qualitatively illustrated in Fig. 8 using a population of 30 infected cells. At 3 time points following the initiation of ART, we compare the net and current percentage of cells generated by viral replication. At day 60, 30% of cells remain that were originally generated by viral replication. This means 30% of observed sequences might produce a signal of evolution. However, at that time an overwhelming majority of new infected cells are being generated by proliferation.
Differing drivers of observed and current replication
We next performed sensitivity analyses to identify parameters that impact the timing of transition from HIV replication to cellular proliferation as a source for current and observed infected cells. Under all parameter assumptions, the majority of current infected cells arose from proliferation after a year of chronic ART (Fig. 9a). Only the sanctuary decay rate (ζ) had an important impact on generation of current infected cells. When target cell availability did not decay at all, 25% of current infected cells were generated by HIV replication after a year of ART (Fig. 9a)—not consistent with lack of viral evolution observed at this time point. Rapid disappearance of HIV replication as a source of current infected cells was identified regardless of initial reservoir volume, drug sanctuary volume, ART efficacy, and reservoir composition (fraction of Tem, Tcm, and Tn).
The net replication percentage was not affected by the decay rate of target cells within the drug sanctuary. Only an increase in the percentage of slowly proliferating reservoir cells (Tn) predicted an increase in the net replication percentage (Fig. 9a). The drivers of current infected cell and net infected cell origin therefore differed completely, highlighting the major differences between observed sequence data and contemporaneous mechanisms generating new infected cells.
To confirm these results, we simulated 104 patients in a global sensitivity analysis in which all parameter values were simultaneously varied. A rapid transition to proliferation as the source of new infected cells occurred during year one of ART in a majority of simulated patients, and the same variables correlated significantly with net and current replication percentage, respectively (Fig. 9b, c). Overall, this analysis does not rule out the possibility of a drug sanctuary but confirms that its impact relative to cellular proliferation is likely to be minimal.
To eliminate HIV-infected cells during prolonged ART, it is necessary to understand the mechanisms by which they persist. We use existing data and two methods—inference of HIV clone distributions and mechanistic mathematical modeling—to determine that a majority of infected cell persistence is due to cellular proliferation rather than HIV replication. Strategies that enhance ART delivery to anatomic drug sanctuaries are less likely to reduce infected cell burden relative to lymphocyte anti-proliferative therapies.
While the raw data indicate substantial fractions of observed singleton sequences, when the total reservoir size is considered, these observed singletons are revealed to be members of clonal populations. The HIV reservoir appears to be defined by a rank-abundance distribution of clone sizes that can be roughly approximated as a power-law relationship. This distribution implies that a small number of massive clones and a massive number of small clones together-comprise a large percentage of sequences.
A power-law distribution can be created when a heterogeneous population grows multiplicatively with a widely variable growth rate55, which suggests that the distribution of clone sizes in the reservoir has a mechanistic basis. It is plausible, though unproven, that variable growth arises from rapid bursts of CD4+ T cell proliferation due to cognate antigen recognition. HIV integration into tumor suppression genes could also account for clonal dominance36,37. Smaller clones may arise from homeostatic proliferation, or less frequent exposure to cognate antigen.
While we cannot rule out cellular longevity as a cause of HIV persistence in certain cells, the observation of multiple clonal sequences cannot arise purely from long-lived latently infected cells. Our analysis suggests that most observed singleton sequences arise from populations that have undergone many rounds of clonal proliferation.
We developed a mathematical model because our inference techniques do not capture time-dynamics of the reservoir or reconcile observations from early and late ART. This model is the first to include the three main mechanistic hypotheses for reservoir persistence: an ART sanctuary, long-lived latent cells, and latent cell proliferation. The model recapitulates known HIV RNA decay kinetics while tracking cells that originate from ongoing replication and cellular proliferation.
We demonstrate why a fossil record of evolution is observed early during ART, whether or not a small drug sanctuary exists. The model differentiates the fraction of infected cells contemporaneously generated by HIV replication (current replication percentage) from the fraction that were generated by viral replication in the past (net, or observed, replication percentage). The observed replication percentage remains non-negligible in the first months of ART while the current replication percentage drops rapidly. An observed sequence that gives a signal of divergence from the founder virus likely represents a historic rather than a current replication event. Because time of detection does not correlate linearly with sequence age, inference of evolution early during ART is problematic20,21. However, the fossil record is transient: within a year of effective ART, observed phylogenetic data represents true reservoir dynamics. Our model agrees with observations reflecting a lack of contemporaneous HIV evolution after this time14,22,23,24,25,26,27,29,30,36,37.
Our sensitivity analysis shows that the variable correlating with higher observed replication percentages (larger proportion of slowly proliferating CD4+ T cells in the reservoir) differs from the variable correlating with higher current replication percentages (slower decrease in sanctuary size). Yet, only current replication percentage represents the true amount of ongoing HIV evolution. Without requiring any phylogenetic simulation, this simple model provides an explanation for observed pseudo-evolution during the first months of ART and none thereafter14,22,23,24,25,26,27,29,30,36,37. If we assume a large drug sanctuary that does not contract with time, a persistent low-level sanctuary would emerge that stabilizes at 6 months and generates ongoing evolution at later ART time points. Notably, this has not been observed in clinical studies.
Our modeling results inform experiments in two ways. First, using rarefaction, we suggest sample sizes to verify our hypotheses experimentally (Supplementary Fig. 4). Observed values of sequence richness and clone size, are substantial underestimates. Current studies only sample the tip of the iceberg of the HIV reservoir. Hundreds of thousands of infected cells from a single time point would be required to capture true reservoir diversity. This sampling depth could only be feasibly achieved as part of an autopsy study. Second, we demonstrate that the wash-out period for the fossil record may be up to a year post ART. Future reservoir studies should be conducted after this time point to avoid observation of historic rather than contemporaneous evolution.
Our study has important caveats. Current integration site data, while robust, is limited to a handful of participants in only a few studies. Modeling rank-abundance curves makes a large assumption about the continuity of the data. The power-law model represents but one approach. Future work should address why that distribution provides good fit to the data. Extrapolating abundance curves has been criticized: our attempt to design a simple parametric model was based on the additional information of reservoir size and our goal to define an upper limit on reservoir richness56; nevertheless, the tail of our distributions is impossible to precisely characterize with our methods.
Our approach is calibrated against sequence data from blood. However, the dynamics of HIV within lymph tissue may have different distributions. While historically, blood samples have been taken as a surrogate for HIV-infected cells, we cannot rule out a small drug sanctuary that does not exchange virus or infected cells with blood. It seems unlikely that such a sanctuary could be sustained because some trafficking of CD4+ T cells from other compartments may be necessary to avoid terminal target cell limitation.
In conclusion, we demonstrate that the majority of HIV-infected cells arise from proliferation during ART and provide an explanation for incongruent observations of evolution before and after a year of ART. Because proliferation is the dominant force sustaining the HIV reservoir34, we suggest limiting proliferation as a prime therapeutic target10,11,57.
Rank-abundance of HIV integration sites
We used an ecological framework to study the abundance of clonal HIV. To do so, we applied methods to integration site and replication-competent HIV sequence data. Unique sequences or integration define distinct clonal populations. The population size of that clone defines its abundance. By ranking the clones from largest to smallest by abundance, we developed a rank-abundance curve, a(r), for each participant time point. No assumptions were made about the stability or dynamics of the reservoir rank-abundance over time.
In our analysis of data from Wagner et al.37, we combine measurements taken closely in time and use the median time point as in the original publication. In our analysis of Maldarelli et al.36, we used unedited published integration site counts. It is important to note that the methods used by Wagner et al. and Maldarelli et al. are slightly different. The ISLA method used by Wagner et al. is lower throughput than the next generation shotgun sequencing method used by Maldarelli et al. The absolute number of viruses identified by each group therefore differs. However, the fraction of observed singletons is similar between the two studies. We manually counted the abundance of replication-competent HIV sequences from phylogenetic trees in Hosmane et al.34.
Calculation of rarefaction curves
We used rarefaction curves to estimate the expected number of distinct sequences that would still be present in a subsample of k sequences from the observed data with sample size of N:
where the parentheses indicate binomial coefficients, e.g., \(({{N}\atop {k}}) = \frac{{N!}}{{k!\left( {N - k} \right)!}}\). Later, we extrapolated rarefaction curves using the modeled distributions for the total reservoir size L. Because the number of samples we allowed was orders of magnitude smaller than the number of cells in the reservoir, k ≪ L, we used Stirling's approximation to simplify the binomial coefficients. The expected number of sequences after k samples is then
an expression which avoids computation of large factorials (derivation in the Supplementary Methods).
Nonparametric estimation of species richness
We employed the Chao1 estimator to set a lower bound on the sequence or integration site richness58. A derivation of the estimator is included in the Supplementary Methods. Chao1 is not a mechanistic model and requires no free parameters. Inference relies on only the number of observed singleton (N1) and observed doubleton (N2) sequences such that
We display an asymmetric confidence interval in Fig. 3 (see Chao et al.58 or Supplementary Methods for the definition). We also note it is possible the data are undersampled to the extent that a one-sided confidence interval may be more appropriate. Thus, for our biological conclusions we take the Chao1 point estimate as a lower bound, and constrain the upper bound using the parametric model (Eq. 4). Other richness estimators (jackknife 1 and 2) were tested but provided similar and consistently lower estimates of richness than the Chao1 estimator. These were not included in our results because the Chao1 was interpreted as a lower bound on true sequence richness.
Parametric models of rank-abundance
Estimates of the size of the HIV reservoir (both replication-competent and total) were gathered from the published literature33. We then developed a parametric model to quantify the true rank-abundance distribution of the complete HIV reservoir. Examination of the data indicated a possible log-log-linear relationship, so we chose a discrete integer power-law model so that the probability of a rank is described by p(r) = ψ(R)r−α where the coefficient \(\psi \left( R \right) = \mathop {\sum}\nolimits_{r = 1}^R {r^{ - \alpha }}\) is the normalization constant for the power-law. Then, to describe the true rank-abundance a(r) we chose the reservoir size depending on the model context (replication-competent L = 107 or total HIV DNA L = 109). To ensure integer number of cells, we rounded this distribution, and forced the total number of cells to equate with reservoir size. That is,
where |[]| indicates rounding to the nearest integer. Thus, our model depended on two free parameters, a power-law exponent α, and the reservoir richness R. Other functional forms were explored but simplicity and accurate reproduction of the data were optimal with the power-law.
Fitting rank-abundance models
Using the experimental data we found the best-fit model using the following procedure. We fixed the reservoir size L depending on the model context (replication-competent or total HIV DNA). We chose a value for R and α from ranges R ∈ [103,107] and α ∈ [0,2] to specify the model. Then, we sampled the extrapolated distribution 10 times using multinomial sampling with the same number of samples as the experimental data being fit, \({\cal M}(N,p(r))\). This procedure assumes that sampling cells does not change the distribution of the reservoir, which is reasonable given the reservoir size. Each sampled data set was compared to the experimental data by computing the residual sum of squares (rss) error of the cumulative proportional abundance (cpa) curves. For each model then, the reported error is the average rss over the 10 resamplings. Because the rss error is not symmetric across the domain of the cpa, this approach becomes similar to minimizing the Kolmogorov–Smirnov (KS) statistic: the maximum deviation between two cumulative distributions. For each experimental data set 2500 model parameter sets were generated, and fitting results were visualized as heat maps (see Figs. 4a and 5a for example). Because the procedure becomes computationally expensive as R > 107, we did not explore values above this threshold. In theory, it is possible to have a distribution with all clones having a single member R = L, α = 0. For the total DNA reservoir, this value would result in R = 109. However, this model was never optimal. In fact, as richness increased beyond ≈106, the model was no longer sensitive to R. Thus, it appeared that finding the best-fit α was sufficient to specify the model if proper bounds on richness were included.
We excluded models where R < RChao1, but we also sought to identify an upper bound for R. Indeed, certain model parameter combinations are mathematically impossible. For example, for a given power-law exponent, the richness is constrained below a certain value for a given reservoir size. Similar arguments have been made in ecology under the terminology of feasible sets59. To determine the largest possible richness that still optimized fit, we chose the roughly constant value of α that emerged when R was large enough to be unidentifiable. Then, we noted that for large R it is reasonable to allow \(\mathop {\sum}\nolimits_{r = 1}^R a (r) = {\int}_1^R a (r){\mathrm{d}}r\). R is thus approximately bounded, and we solved for the maximal value or the upper bound on the richness given the best-fit α and the chosen L. A discussion and numerical validation of this approximation is presented in the Supplementary Methods and Supplementary Fig. 2. Choosing the model with largest richness provides the sequence abundance most permissive of true singleton sequences—the model most favoring ongoing replication as an explanation for HIV persistence. In extrapolated reservoirs, we used the maximum richness model to ensure we were biasing the results as strongly as possible against our own hypothesis.
Model fitting validation with simulated data
A discussion and demonstration of model validation is included in the Supplementary Methods and Supplementary Fig. 1. The exercise shows that simply fitting a power-law to the experimental data (using log-log-linear regression) without the extra sampling step necessarily underestimates the power-law exponent, demonstrating the utility of our approach. Moreover, it shows that a published maximum likelihood approach60 is not as accurate for these data as our resampling approach (code hosted at http://tuvalu.santafe.edu/~aaronc/powerlaws/ last accessed July 2018). We simulated a reservoir with known power-law exponent Supplementary Fig. 1A and tested for recovery of this known value. The fitting validation proceeded identically to the data fitting: 2500 distributions were generated (225 examples are shown in Supplementary Fig. 1D), the simulated data was sampled Supplementary Fig. 1B, and reranked Supplementary Fig. 1C. Fitting results Supplementary Fig. 1E, F are shown analogous to Figs. 4 & 5A, B. Model comparison demonstrating optimal accuracy with our resampling approach is shown in Supplementary Fig. 1G.
Mechanistic model for the persistence of the HIV reservoir
The canonical model for HIV dynamics describes the time-evolution of the concentrations of susceptible S and infected I CD4+ T cells and HIV virus V50,54,61. Our model grows from the canonical model, simplifying with several approximations and extending the biological detail to simulate HIV dynamics on ART, including a long-lived latent reservoir and a potential drug sanctuary. Perelson et al. first noticed and quantified a biphasic clearance of HIV virus upon initiation of ART and showed that viral half-lives of 1.5 and 14 days correspond with the half-lives of two infected cell compartments50,54. With longer observation times and single-copy viral assays, Palmer et al.51 documented four-phases of viral clearance after initiation of ART. Because of uncertainty in distinguishing the third and fourth phase in that study, we focus on the first three decay rates and corresponding cellular compartments, attributing a mixture of the third and fourth phase decay to the clearance of the productively infectious latent reservoir (half-life 44 months) as measured by Siliciano et al.3 and corroborated by Crooks et al.2 and the clearance of HIV DNA47. We developed a mechanistic mathematical model that has three types of infected cells I1, I2, I3 that are meant to simulate productively infected cells, pre-integration infected cells, and latently infected cells, respectively. We classify rapid death δ1 and viral production within actively infected cells I1. Cells with longer half-life that may represent pre-integration infected cells I2 are activated to I1 at rate ξ2. I2 may represent CD4+ T cells with a prolonged pre-integration phase, but their precise biology does not affect model outcomes48.
The state I3(j) represents latently infected reservoir cells of phenotype j, which contain a single chromosomally integrated HIV DNA provirus44. I3 reactivates to I1 at rate ξ3 which at present is assumed to be constant across cell phenotypes49. The probabilities of a newly infected cell entering I1, I2, I3(j), are τ1, τ2, τ3(j). Because we are focused on the role of proliferation, we assume sub-populations of I312, including effector memory (Tem), central memory (Tcm), and naive (Tn) CD4+ T cells, which proliferate and die at different rates α3(j), δ3(j)12,42,43. Parameter values and initial conditions for the model are collected in Table 1.
Modeling with an ART sanctuary
A recent hypothesis about reservoir persistence suggests there may be a small, anatomic sanctuary (1 in 105 infected cells) in which ART is not therapeutic4. Thus, we included the state variable IS that is maintained at a constant set-point level prior to ART, where all new infected cells arise from ongoing replication. The amount of virus produced by the sanctuary VS is extremely low relative to non-sanctuary regions because ART results in levels undetectable by sensitive assays51.
Many studies have demonstrated that HIV accelerates immunosenescene through abnormal activation of CD4+ T cells62,63,64. ART results in a marked reduction of T cell activation and apoptosis, a potential signature of HIV susceptible cells65. By examining the decline of activation markers for CD4+ T cells, we approximated the decay kinetics of activated T cells upon ART, inferring approximate decay kinetics of the target cells in our model52,53,66. A range of initial values exists (from ~5 to 20% activation) depending on stage of HIV infection, yet after a year of ART, a large percentage of patients return to almost normal, or slightly elevated CD4+ T cell activation levels (2–3%)52. Because we assume that target cell depletion is minimal at viral load set-point, we allow susceptible cell concentrations to decrease over time as immune activation decreases. We choose an exponential model, i.e., S = S(0)e−ζt, which is an obvious simplification (it could also be biphasic but the data are not granular enough to discriminate this dynamic subtlety). From existing data, the decay constant should be in the range ζ ~ [0.002, 0.01] day–1 52,66. We extend this decay into the sanctuary, allowing the number of susceptible cells over the whole body to decrease so that IS = I1(0)φSe−ζt where φS is the fraction of infected cells in a sanctuary. Model simulations are also performed without this assumption of target cell contraction.
Last, we use the quasi-static approximation that virus is proportional to the number of actively infected cells in all compartments V = n(I1 + IS) where n = π/γ, the ratio of the viral production rate to the viral clearance rate (Table 1). The model is thus
where the over-dot denotes derivative in time.
Comparing proliferation to viral replication
By solving the ODE model (Eq. 5), we computed the total number of newly infected cells generated in a given time interval Δt by ongoing replication. That value is \(I^{{\mathrm{rep}}}(t) = \left( {\beta _{\it{\epsilon }}{{SV}} + \phi _{\mathrm{S}}\beta {{SV}}_{\mathrm{S}}} \right){\mathrm{\Delta }}t\). The total number of newly infected cells generated by proliferation of a previously infected cell can be computed similarly in a time interval as \(I^{{\mathrm{pro}}}(t) = \mathop {\sum}\nolimits_{i(j)} {\alpha _{i(j)}I_{i(j)}{\mathrm{\Delta }}t}\). Therefore, the percentage of infected cells generated by current replication is written
We can further subset this current replication fraction by examining the percentage of infected cells that enter the long-lived latent state I3 by defining \(I^{{\mathrm{rep}}(3)}(t) = \tau _3(\beta _{\it{\epsilon }}{{SV}} + \phi _{\mathrm{S}}\beta {{SV}}_{\mathrm{S}}){\mathrm{\Delta }}t\) and \(I^{{\mathrm{pro}}(3)}(t) = \mathop {\sum}\nolimits_j {\alpha _{3(j)}I_{3(j)}{\mathrm{\Delta }}t}\) so that
The net (or observed) replication percentage, is the fraction of cells that were once generated by viral replication. To compute this quantity, we use an additional set of ODEs that we refer to as tracking equations because they do not change the dynamics of the system, and only are used to track specific variables. To denote the net value as opposed to current value we use a superscript Σ. The net cells generated by viral replication in state i of phenotype j is governed by the differential equation
Likewise, the net cells generated by proliferation in state i of phenotype j is governed by the differential equation
We note that because we only allow these two mechanisms, \(\dot I_{i(j)} = \dot I_{i(j)}^{({\mathrm{\Sigma }}){\mathrm{rep}}} + \dot I_{i(j)}^{({\mathrm{\Sigma }}){\mathrm{pro}}}\) and \(I_{i\left( j \right)}(t) = I_{i\left( j \right)}^{\left( {\mathrm{\Sigma }} \right){\mathrm{rep}}}(t) + I_{i\left( j \right)}^{({\mathrm{\Sigma }}){\mathrm{pro}}}\). We solved the tracking equations separately and took the sum over cell types and phenotypes. Ultimately, the net replication fraction is
In all simulations, we assumed that 100% of infected cells at the initiation of ART were generated by viral replication, that is ΦΣ(0) = 100. This assumption biases results in favor of replication. However, we choose it because, to the best of our knowledge, studies of proliferation during chronic untreated HIV have not been performed.
Sensitivity analysis
Using estimated parameter bounds [lower, upper], we completed a local and global sensitivity analysis. These ranges were chosen to cover a wide range of possible assumptions. We allowed I3(0) = [0.02,2] cells µL−1, φS = [10−6,10−4] unitless, ζ = [0,0.2] day−1, \({\it{\epsilon }} = [0.9,0.99]\) unitless, \({\it{\epsilon }}_{\mathrm{S}} = [0,0.9]\) unitless, I3(n)(0) = [0,0.5] × I3(0) cells µL−1. For the local analysis, we used all values as in Table 1 and modified one parameter at a time over each listed range above. The global analysis was performed in Python by using 104 Latin Hypercube samplings of the complete 6-dimensional parameter space using PyDOE67. The key outcome, the replication percentage (net and current) at 1 year of ART, was correlated to each parameter using the Spearman correlation coefficient—defined by the ratio of the covariance between the outcome and the variable divided by the standard deviations of each when the variables were rank-ordered by value.
Code availability
Computational code for all calculations and simulations was performed in Python and Matlab. and is freely available at https://github.com/dbrvs/reservoir_persistence.
Data availability
Sequence data were obtained from the Retrovirus Integration Database (RID)68. The authors declare that all other data supporting the findings of this study are available within the article and its Supplementary Information files, or are available from the authors upon request.
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D.B.R. thanks F. Boshier and O. Hyrien for many illuminating conversations and J.M. Drake for originally suggesting the Chao1 estimator. D.B.R. is supported by a Washington Research Foundation (WRF) Postdoctoral Fellowship. E.R.D. is supported by the National Center for Advancing Translational Sciences of the NIH under Award Number KL2 TR002317. T.A.W. is supported by UM1 AI126623 (defeat HIV). S.A.P is supported by the Delaney AIDS Research Enterprise (DARE) to Find a Cure (1U19AI096109 and 1UM1AI126611-01), Australian Centre for HIV and Hepatitis Virology Research (ACH2), and the Australian National Health and Medical Research Council (AAP1061681). J.T.S. is supported by NIH grants: P01 AI030371-24, U19 AI113173-02, R01 AI121129-01, UM1 AI126623 (defeatHIV), UM1 AI068635.
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Reeves, D.B., Duke, E.R., Wagner, T.A. et al. A majority of HIV persistence during antiretroviral therapy is due to infected cell proliferation. Nat Commun 9, 4811 (2018). https://doi.org/10.1038/s41467-018-06843-5
DOI: https://doi.org/10.1038/s41467-018-06843-5
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Minerva Reef is situated in the Pacific Ocean between Fiji and Tonga. In early 1972 it housed for a short period of time the Republic of Minerva, a liberalist micro nation founded by an American real estate millionaire, Michael Oliver (Strauss 1999: 155). His organization, the Ocean Life Research Foundation, had raised approximately $200 million to establish the nation and in May 1971 the organization hired a ship in Australia to transport considerable amounts of sand to the reef to raise it eight feet above sea level (ibid.).The Ocean Life Research Foundation had received legal advice that unclaimed land could be claimed if some practical use could be made of it and had therefore built a tower with a radar mounted on the sand banks (Jenkins 2006). They proceeded to claim the land officially in January 1972 (Trumbull 1972).
The intention was for the Republic of Minerva to be a tax haven, a retreat from bureaucratic control, and a potential headquarter for ecological and marine research (Trumbull 1972). Having only recently gained independence from the United Kingdom or from UN trusteeship, the surrounding pacific island countries were alarmed. The Fijian Prime Minister found that accepting the Republic of Minerva would set dangerous precedence: What was to stop anyone from setting up mini-nations at every other reef? Or as Prince Tuiplehake, the Tongan Prime Minister reportedly said: "We can't have people setting up empires on our doorstep" (ibid.). The South Pacific Forum had been established the previous year as a forum to discuss matters of regional interest. The new governments of Tonga, Fiji, Nauru, Western Samoa, and the Cook Islands met with the more seasons counterparts from Australia and New Zealand in February 1972 to discuss the Minerva situation. It was decided that Tonga should claim the reefs as they were situated in their territorial waters (ibid.). Subsequently two small islands made from coral and concrete were built by Tongan prisoners during the spring of 1972 leaving the structure permanently above the high tide mark. This enabled the Tongan government to reclaim the Minerva reef and all adjacent reefs within a radius of app. 20 km. This was according to an eye-witness account done in an elaborate and peaceful ceremony attended by the king, a brass band, various government officials, and a journalist (Jenkins 2006). Barring a brief unsuccessful attempt to reclaim the reef by Oliver's business associates in the 90ies the interest in the Minerva Reef waned.
If it looks inconsequential, one is fooled. The political implications were serious enough. One could say that the Republic of Minerva was an occasion for the South Pacific Forum to legitimize itself and for the recently autonomous Tonga to assert its territorial claims. And they weren't the only ones practicing politics. The Republic of Minerva was not the first island nation Michael Oliver had attempted to found and it only marked the beginning of his involvement in the Pacific (Strauss 1999). Around 1980 it was reported by staff at a guesthouse in Australia that they had a curious group of visitors calling themselves the Phoenix Foundation, addressing each other by pompous names such as the King (New Internationalist 1981). The guests were talking about arms sale and capital transfers into Pacific Island states. I don't know about the veracity of this anecdote that reportedly amused the staff so much, but Michael Oliver is linked by various sources to the rebellion at Espitito Santo in the New Hebrides in 1980, today known as Vanuatu. The New Internationalist, a now internet based publication, report that the Phoenix Foundation had channeled $250,000 worth of weapon and equipment smuggled into the New Hebrides formenting the rebellion (ibid.) Another prominent member and founder of the Phoenix Foundation was Harry Schultz the high profile advisor on tax-avoidance who was famous in the 70s and 80s for his newsletter International Harry Schultz Letter reportedly read by both Margaret Thatcher and her adviser Sir Keith Joseph (New Internationalist 1981).