The role of cell location and spatial gradients in the evolutionary dynamics of colon and intestinal crypts

BACKGROUND: Colon and intestinal crypts serve as an important model system for adult stem cell proliferation and differentiation. We develop a spatial stochastic model to study the rate of somatic evolution in a normal crypt, focusing on the production of two-hit mutants that inactivate a tumor suppressor gene. We investigate the effect of cell division pattern along the crypt on mutant production, assuming that the division rate of each cell depends on its location. RESULTS: We find that higher probability of division at the bottom of the crypt, where the stem cells are located, leads to a higher rate of double-hit mutant production. The optimal case for delaying mutations occurs when most of the cell divisions happen at the top of the crypt. We further consider an optimization problem where the “evolutionary” penalty for double-hit mutant generation is complemented with a “functional” penalty that assures that fully differentiated cells at the top of the crypt cannot divide. CONCLUSION: The trade-off between the two types of objectives leads to the selection of an intermediate division pattern, where the cells in the middle of the crypt divide with the highest rate. This matches the pattern of cell divisions obtained experimentally in murine crypts. REVIEWERS: This article was reviewed by David Axelrod (nominated by an Editorial Board member, Marek Kimmel), Yang Kuang and Anna Marciniak-Czochra. For the full reviews, please go to the Reviewers’ comments section. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s13062-016-0141-6) contains supplementary material, which is available to authorized users

Stochastic modelling of viral blips in HIV-1-infected patients: Effects of inhomogeneous density fluctuations

We propose a stochastic model of HIV-1 infection dynamics under HAART in order to analyse the origin and dynamics of the so-called viral blips, i.e. episodes of transient viremia that occur in the phase of where the disease remains in a latent state during which the viral load raises above the detection limit of standard clinical assays. Based on prior work in the subject, we consider an infection model in which latently infected cell compartment sustains a residual (latent) infection over long periods of time. Unlike previous models, we include the effects of inhomogeneities in cell and virus concentration in the blood stream. We further consider the effect of burst virion production. By comparing with the experimental results obtained during a study in which intensive sampling was carried out on HIV-1-infected patients undergoing HAART over a long period of time, we conclude that our model supports the hypothesis that viral blips are consistent with random fluctuations around the average viral load. We further observe that agreement between our simulation results and the blip statistics obtained in the aforementioned study improves when burst virion production is considered. We also study the effect of sample manipulation artifacts on the results produced by our model, in particular, that of the post-extraction handling time, i.e. the time elapsed between sample extraction and actual test. Our results support the notion that the statistics of viral blips can be critically affected by such artifacts

Stochastic modelling of the eradication of the HIV-1 infection by stimulation of latently infected cells in patients under highly active anti-retroviral therapy

HIV-1 infected patients are effectively treated with highly active anti-retroviral therapy (HAART). Whilst HAART is successful in keeping the disease at bay with average levels of viral load well below the detection threshold of standard clinical assays, it fails to completely eradicate the infection, which persists due to the emergence of a latent reservoir with a half-life time of years and is immune to HAART. This implies that life-long administration of HAART is, at the moment, necessary for HIV-1-infected patients, which is prone to drug resistance and cumulative side effects as well as imposing a considerable financial burden on developing countries, those more afflicted by HIV, and public health systems. The development of therapies which specifically aim at the removal of this latent reservoir has become a focus of much research. A proposal for such therapy consists of elevating the rate of activation of the latently infected cells: by transferring cells from the latently infected reservoir to the active infected compartment, more cells are exposed to the anti-retroviral drugs thus increasing their effectiveness. In this paper, we present a stochastic model of the dynamics of the HIV-1 infection and study the effect of the rate of latently infected cell activation on the average extinction time of the infection. By analysing the model by means of an asymptotic approximation using the semi-classical quasi steady state approximation (QSS), we ascertain that this therapy reduces the average life-time of the infection by many orders of magnitudes. We test the accuracy of our asymptotic results by means of direct simulation of the stochastic process using a hybrid multi-scale Monte Carlo scheme

Stochastic resetting in backtrack recovery by RNA polymerases

Transcription is a key process in gene expression, in which RNA polymerases produce a complementary RNA copy from a DNA template. RNA polymerization is frequently interrupted by backtracking, a process in which polymerases perform a random walk along the DNA template. Recovery of polymerases from the transcriptionally inactive backtracked state is determined by a kinetic competition between one-dimensional diffusion and RNA cleavage. Here we describe backtrack recovery as a continuous-time random walk, where the time for a polymerase to recover from a backtrack of a given depth is described as a first-passage time of a random walker to reach an absorbing state. We represent RNA cleavage as a stochastic resetting process and derive exact expressions for the recovery time distributions and mean recovery times from a given initial backtrack depth for both continuous and discrete-lattice descriptions of the random walk. We show that recovery time statistics do not depend on the discreteness of the DNA lattice when the rate of one-dimensional diffusion is large compared to the rate of cleavage

Regular testing of asymptomatic healthcare workers identifies cost-efficient SARS-CoV-2 preventive measures.

Protecting healthcare professionals is crucial in maintaining a functioning healthcare system. The risk of infection and optimal preventive strategies for healthcare workers during the COVID-19 pandemic remain poorly understood. Here we report the results of a cohort study that included pre- and asymptomatic healthcare workers. A weekly testing regime has been performed in this cohort since the beginning of the COVID-19 pandemic to identify infected healthcare workers. Based on these observations we have developed a mathematical model of SARS-CoV-2 transmission that integrates the sources of infection from inside and outside the hospital. The data were used to study how regular testing and a desynchronisation protocol are effective in preventing transmission of COVID-19 infection at work, and compared both strategies in terms of workforce availability and cost-effectiveness. We showed that case incidence among healthcare workers is higher than would be explained solely by community infection. Furthermore, while testing and desynchronisation protocols are both effective in preventing nosocomial transmission, regular testing maintains work productivity with implementation costs

Absolute Quantification of Transcription Factors Reveals Principles of Gene Regulation in Erythropoiesis.

Dynamic cellular processes such as differentiation are driven by changes in the abundances of transcription factors (TFs). However, despite years of studies, our knowledge about the protein copy number of TFs in the nucleus is limited. Here, by determining the absolute abundances of 103 TFs and co-factors during the course of human erythropoiesis, we provide a dynamic and quantitative scale for TFs in the nucleus. Furthermore, we establish the first gene regulatory network of cell fate commitment that integrates temporal protein stoichiometry data with mRNA measurements. The model revealed quantitative imbalances in TFs' cross-antagonistic relationships that underlie lineage determination. Finally, we made the surprising discovery that, in the nucleus, co-repressors are dramatically more abundant than co-activators at the protein level, but not at the RNA level, with profound implications for understanding transcriptional regulation. These analyses provide a unique quantitative framework to understand transcriptional regulation of cell differentiation in a dynamic context

Absolute Quantification of Transcription Factors Reveals Principles of Gene Regulation in Erythropoiesis.

Dynamic cellular processes such as differentiation are driven by changes in the abundances of transcription factors (TFs). However, despite years of studies, our knowledge about the protein copy number of TFs in the nucleus is limited. Here, by determining the absolute abundances of 103 TFs and co-factors during the course of human erythropoiesis, we provide a dynamic and quantitative scale for TFs in the nucleus. Furthermore, we establish the first gene regulatory network of cell fate commitment that integrates temporal protein stoichiometry data with mRNA measurements. The model revealed quantitative imbalances in TFs\u27 cross-antagonistic relationships that underlie lineage determination. Finally, we made the surprising discovery that, in the nucleus, co-repressors are dramatically more abundant than co-activators at the protein level, but not at the RNA level, with profound implications for understanding transcriptional regulation. These analyses provide a unique quantitative framework to understand transcriptional regulation of cell differentiation in a dynamic context