Fig 1.
Dynamics in the stratified epithelium.
A) Basal and parabasal cells can divide either asymmetrically (1 − p1 − p2 and 1 − q1 − q2 respectively) or symmetrically, which result in two daughter cells of either the same (p1 or q1) or different phenotype as the mother cell (p2 or q2). B) The squamous epithelium is abstracted into a basal, a parabasal, a mid-upper and a surface layer. Proliferation (ρ) and maturation (ν) rates determine the movement of cells up the layers. Cells die and are shed (μ). Chlamydia trachomatis (in green) infects the most superficial live cells underneath the mucus and surface dying cells. Once inside a cell, the elementary bodies (EB) change into reticulate bodies, which go through several rounds of replication, and then change back into EBs that are released upon cell death. Human papillomaviruses (in purple) must infect basal cells to establish an infection, thus usually requiring a microabrasion. The virus is non-lytic and replicates in host cells as they follow their natural life-cycle up the epithelium column. Progeny virions are released once the cell dies at the surface. Immune cells (in blue) enter the epithelium from the basal layer.
Table 1.
Parameter descriptions for epithelial model, default values, biologically realistic ranges and estimated values.
Literature estimates (a) are for cervicovaginal epithelia, while data-derived estimates (b) are for NIKS cell cultures, which are a common cell-line used to model these systems, but are not identical to in vivo cells in the cervicovaginal squamous epithelium (for example the latter cannot form keratinized layers). Thus, estimates are not expected to be identical. Additionally, (a) parameters are measured from systems already at homeostasis, while in (b) the cultures grow-up from a single layer. Parameter values that were chosen for the results to be biologically consistent are labelled as ‘calibrated’. The values ‘fixed*’ and ‘estimated*’ were derived using data (see S1 Text).
Fig 2.
Epithelial cell growth in 3D raft cultures.
A) NIKS grown from a single layer over a period of three weeks. Dark pink layer in week 3 consist of cornified cells that accumulate on the surface. B) Immunoflourescence staining: DAPI (blue) is nuclear staining for cell counting and BrdU (pink) is for identifying cells undergoing division; white dots are added to delineate basal lines. C) Data of NIKS growth over time with model fitting. Shading corresponds to 95% prediction interval, assuming the data follows a Poisson distribution.
Table 2.
Sensitivity analyses of key infection properties.
For each pathogen, we show the three most important parameters with the associated partial rank correlation coefficient (PRCC) and its 95% confidence interval. Notations for parameter values are in Tables 1 and 3. Peak of infected cells is a measure of the size of the infection, peak of free-virion (or elementary bodies, EBs) load is how much progeny is released for re-seeding the infection or transmission, and day of peak is a measure for how quickly the infection grows. For effects on protection by epithelial parameters we tested: ν, μ, ρb, ρp, ζ, and ζu.
Fig 3.
Simulated population dynamics of epithelial cells, immune effectors and bacteria in chlamydia infections.
In A, the immune cell proliferation is rapid, which leads to an acute infection. In B and C, immune cells do not proliferate fast enough to clear the bacteria and the acute phase is followed by oscillations and the establishment of a chronic phase (plateau of EB density). The infection is lytic reducing the thickness of the epithelium (A, B and C) but only chronic infections manage to infect the lower layers (B and C). Parameter values are default (Table 3 and literature values in Table 1) except in A where βb = 8.0 × 10−7 cell−1⋅ EB−1⋅ day−1, βp = 4.0 × 10−6 cell−1⋅ EB−1⋅ day−1, βu = 2.0 × 10−5 cell−1⋅ EB−1⋅ day−1, and φ = 0.0015 day−1. In C, all four epithelial protective measures happen together, i.e. ζu, ρb, μ, and ν all rise logistically to a threshold above default after infection to mimic the protective epithelial response (see section A.3 S1 Text, eqn 7a with θ = 1). Thresholds used in C: ,
, μmax = 0.9 cell−1⋅ day−1, and νmax = 0.8 day−1.
Fig 4.
Simulated population dynamics of epithelial cells, immune effectors and free viruses in the case of HPV infections.
Wart-like epithelial dynamics in a wart-associated HPV infection (A) and a slow growing high-risk (HR) HPV infection that spontaneously regresses (B). The black shading shows the proportion of infected cells in each layer. (C) Dynamics of virus load (black) and the density of immune effectors (gray) for wart-associated HPV (dashed line) and HR-HPV (full line) infections. Immune cells start to proliferate upon infection but their number remains below −2 log for several months. (D) Simulated scenario where the infection is inoculated with few cells and the microabrasion repairs quickly: this results in both wart-associated and HR types causing asymptomatic infections. Here, the model predicts that infections with HR types have more infected cells, due to their higher proliferative properties, but wart-associated types produce more virions (i, ii, iii), and both infections can last for years, if stochasticity or the innate response do not clear them (i, ii). Parameter values are default (Tables 1 and 3) and infection models are 3. Infection rates of both wart-associated and HR HPVs are identical (β = 10−10) and all infections begin with 10 infected basal cells. In (D) the infection rate, β, decays to zero in 10 days (b = −0.5) to mimic tissue repair (see section A.3 in S1 Text for details).
Table 3.
Parameter descriptions for infection models (equations systems 3 and 4), default values and biologically realistic ranges.
Parameters value that were chosen for the results to be biologically consistent are indicated by ‘calibrated’. Parameter values that can be set arbitrarily without affecting the results qualitatively are referred to as ‘fixed’. Parameters varied without any a priori assumption are indicated by ‘free’.
Fig 5.
Flow diagram of the infection models for HPV (A) and chlamydia (B).
HPV virions, V, only infect uninfected basal cells, Ub, to become basal infected cells, Ib. Since HPV is non-lytic, infected cells follow the typical epithelial life-cycle up to the surface passing through different life stages (parbasal Ip, differentiated Id, differentiated at the surface Is). Model 3. In the case of C. trachomatis, the elementary bodies, EBs, start the infection by infecting uninfected cells in the upper layers (βu Ud Eu creates Id). The EB populations start in the upper layers, Eu, and then migrate down, ηu, into the lower layers, El. As EBs migrate down layers they enter uninfected cells (Ub and Up) and create infected cells (Ib and Ip) which die at rate α (boxes with square represent dead cells). The host immune response, A, is activated by infected basal cells in the case of HPV and all EBs in the case of C. trachomatis. Model 4. Note that for wart-associated HPV infections ρa = 0 and αb = αp = 1. See Table 3 for parameter descriptions and estimates.