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Inferring viral dynamics in chronically HCV infected patients from the spatial distribution of infected hepatocytes.

Graw F, Balagopal A, Kandathil AJ, Ray SC, Thomas DL, Ribeiro RM, Perelson AS - PLoS Comput. Biol. (2014)

Bottom Line: We found that individual clusters on biopsy samples range in size from 4-50 infected cells.In addition, the HCV RNA content in a cluster declines from the cell that presumably founded the cluster to cells at the maximal cluster extension.Further, we do not find a relationship between the cluster size and the estimated cluster expansion time.

View Article: PubMed Central - PubMed

Affiliation: Los Alamos National Laboratory, Theoretical Biology and Biophysics, Los Alamos, New Mexico, United States of America; Center for Modeling and Simulation in the Biosciences, Heidelberg University, Heidelberg, Germany.

ABSTRACT
Chronic liver infection by hepatitis C virus (HCV) is a major public health concern. Despite partly successful treatment options, several aspects of intrahepatic HCV infection dynamics are still poorly understood, including the preferred mode of viral propagation, as well as the proportion of infected hepatocytes. Answers to these questions have important implications for the development of therapeutic interventions. In this study, we present methods to analyze the spatial distribution of infected hepatocytes obtained by single cell laser capture microdissection from liver biopsy samples of patients chronically infected with HCV. By characterizing the internal structure of clusters of infected cells, we are able to evaluate hypotheses about intrahepatic infection dynamics. We found that individual clusters on biopsy samples range in size from 4-50 infected cells. In addition, the HCV RNA content in a cluster declines from the cell that presumably founded the cluster to cells at the maximal cluster extension. These observations support the idea that HCV infection in the liver is seeded randomly (e.g. from the blood) and then spreads locally. Assuming that the amount of intracellular HCV RNA is a proxy for how long a cell has been infected, we estimate based on models of intracellular HCV RNA replication and accumulation that cells in clusters have been infected on average for less than a week. Further, we do not find a relationship between the cluster size and the estimated cluster expansion time. Our method represents a novel approach to make inferences about infection dynamics in solid tissues from static spatial data.

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Sketch of the characterization of clusters of infected cells.(A) Example of measured data in a  grid of cells with the HCV RNA content per cell (left) and sketch of the ring structure of the cluster (right) as it would be defined by the algorithm shown in (B). Darker shading of cells indicates a higher amount of HCV RNA. The fitting procedure of the Matérn cluster process to estimate the domain radius  accounts for edge effects due to sampling, i.e., only parts of the cluster might be visible on the grid of liver tissue analyzed by scLCM. The sketch in (A) shows an example for a cluster that grew spherically. The algorithm also allows for cluster growth that is skewed in one direction. (B) Example of the algorithm to determine the “ring structure” of a cluster of infected cells for a  grid of cells. The measurements of HCV RNA per cell are transformed into a spatial point pattern (see Materials & Methods). The amount of HCV RNA in those cells with the maximal HCV RNA content is subsequently reduced to the next lower level (red color) (Step I–Step II). For each of the different steps,  spatial point patterns are produced, and a Matérn cluster process is fitted to each pattern to estimate . Step  shows the last step before the cutoff criterion for the maximal cluster extension. For all subsequent steps of this example Pearson's chi-squared statistic for the point patterns indicated spatial heterogeneity for less than 95% of the  bootstrap samples.
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pcbi-1003934-g001: Sketch of the characterization of clusters of infected cells.(A) Example of measured data in a grid of cells with the HCV RNA content per cell (left) and sketch of the ring structure of the cluster (right) as it would be defined by the algorithm shown in (B). Darker shading of cells indicates a higher amount of HCV RNA. The fitting procedure of the Matérn cluster process to estimate the domain radius accounts for edge effects due to sampling, i.e., only parts of the cluster might be visible on the grid of liver tissue analyzed by scLCM. The sketch in (A) shows an example for a cluster that grew spherically. The algorithm also allows for cluster growth that is skewed in one direction. (B) Example of the algorithm to determine the “ring structure” of a cluster of infected cells for a grid of cells. The measurements of HCV RNA per cell are transformed into a spatial point pattern (see Materials & Methods). The amount of HCV RNA in those cells with the maximal HCV RNA content is subsequently reduced to the next lower level (red color) (Step I–Step II). For each of the different steps, spatial point patterns are produced, and a Matérn cluster process is fitted to each pattern to estimate . Step shows the last step before the cutoff criterion for the maximal cluster extension. For all subsequent steps of this example Pearson's chi-squared statistic for the point patterns indicated spatial heterogeneity for less than 95% of the bootstrap samples.

Mentions: If hepatocytes in the liver were infected completely at random, for example due to rapid seeding from the blood, we would expect homogeneous infection and no clusters. Since we observe clusters of infection [15], we make the next most parsimonious assumption that viral spread in vivo is a combination of random spatially scattered infection of some cells that seed the cluster (possibly from virus in the blood) followed by predominantly random local spread from these cells. We assume that seeding of the cluster centers follows a Poisson process, with the mean number of clusters per unit area equal to , and the number of cells in each cluster also following a Poisson process, with the mean number of cells in each cluster equal to . This compound Poisson spatial distribution is called a Matérn cluster process [23], [24]. A Matérn cluster process assumes that the units of a cluster are distributed within a radial disc with domain radius (Figure 1A). Assuming this regular cluster structure allows us to account for edge effects due to the small sampling area, i.e., that only parts of a cluster were sampled on the grid [25].


Inferring viral dynamics in chronically HCV infected patients from the spatial distribution of infected hepatocytes.

Graw F, Balagopal A, Kandathil AJ, Ray SC, Thomas DL, Ribeiro RM, Perelson AS - PLoS Comput. Biol. (2014)

Sketch of the characterization of clusters of infected cells.(A) Example of measured data in a  grid of cells with the HCV RNA content per cell (left) and sketch of the ring structure of the cluster (right) as it would be defined by the algorithm shown in (B). Darker shading of cells indicates a higher amount of HCV RNA. The fitting procedure of the Matérn cluster process to estimate the domain radius  accounts for edge effects due to sampling, i.e., only parts of the cluster might be visible on the grid of liver tissue analyzed by scLCM. The sketch in (A) shows an example for a cluster that grew spherically. The algorithm also allows for cluster growth that is skewed in one direction. (B) Example of the algorithm to determine the “ring structure” of a cluster of infected cells for a  grid of cells. The measurements of HCV RNA per cell are transformed into a spatial point pattern (see Materials & Methods). The amount of HCV RNA in those cells with the maximal HCV RNA content is subsequently reduced to the next lower level (red color) (Step I–Step II). For each of the different steps,  spatial point patterns are produced, and a Matérn cluster process is fitted to each pattern to estimate . Step  shows the last step before the cutoff criterion for the maximal cluster extension. For all subsequent steps of this example Pearson's chi-squared statistic for the point patterns indicated spatial heterogeneity for less than 95% of the  bootstrap samples.
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Related In: Results  -  Collection

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pcbi-1003934-g001: Sketch of the characterization of clusters of infected cells.(A) Example of measured data in a grid of cells with the HCV RNA content per cell (left) and sketch of the ring structure of the cluster (right) as it would be defined by the algorithm shown in (B). Darker shading of cells indicates a higher amount of HCV RNA. The fitting procedure of the Matérn cluster process to estimate the domain radius accounts for edge effects due to sampling, i.e., only parts of the cluster might be visible on the grid of liver tissue analyzed by scLCM. The sketch in (A) shows an example for a cluster that grew spherically. The algorithm also allows for cluster growth that is skewed in one direction. (B) Example of the algorithm to determine the “ring structure” of a cluster of infected cells for a grid of cells. The measurements of HCV RNA per cell are transformed into a spatial point pattern (see Materials & Methods). The amount of HCV RNA in those cells with the maximal HCV RNA content is subsequently reduced to the next lower level (red color) (Step I–Step II). For each of the different steps, spatial point patterns are produced, and a Matérn cluster process is fitted to each pattern to estimate . Step shows the last step before the cutoff criterion for the maximal cluster extension. For all subsequent steps of this example Pearson's chi-squared statistic for the point patterns indicated spatial heterogeneity for less than 95% of the bootstrap samples.
Mentions: If hepatocytes in the liver were infected completely at random, for example due to rapid seeding from the blood, we would expect homogeneous infection and no clusters. Since we observe clusters of infection [15], we make the next most parsimonious assumption that viral spread in vivo is a combination of random spatially scattered infection of some cells that seed the cluster (possibly from virus in the blood) followed by predominantly random local spread from these cells. We assume that seeding of the cluster centers follows a Poisson process, with the mean number of clusters per unit area equal to , and the number of cells in each cluster also following a Poisson process, with the mean number of cells in each cluster equal to . This compound Poisson spatial distribution is called a Matérn cluster process [23], [24]. A Matérn cluster process assumes that the units of a cluster are distributed within a radial disc with domain radius (Figure 1A). Assuming this regular cluster structure allows us to account for edge effects due to the small sampling area, i.e., that only parts of a cluster were sampled on the grid [25].

Bottom Line: We found that individual clusters on biopsy samples range in size from 4-50 infected cells.In addition, the HCV RNA content in a cluster declines from the cell that presumably founded the cluster to cells at the maximal cluster extension.Further, we do not find a relationship between the cluster size and the estimated cluster expansion time.

View Article: PubMed Central - PubMed

Affiliation: Los Alamos National Laboratory, Theoretical Biology and Biophysics, Los Alamos, New Mexico, United States of America; Center for Modeling and Simulation in the Biosciences, Heidelberg University, Heidelberg, Germany.

ABSTRACT
Chronic liver infection by hepatitis C virus (HCV) is a major public health concern. Despite partly successful treatment options, several aspects of intrahepatic HCV infection dynamics are still poorly understood, including the preferred mode of viral propagation, as well as the proportion of infected hepatocytes. Answers to these questions have important implications for the development of therapeutic interventions. In this study, we present methods to analyze the spatial distribution of infected hepatocytes obtained by single cell laser capture microdissection from liver biopsy samples of patients chronically infected with HCV. By characterizing the internal structure of clusters of infected cells, we are able to evaluate hypotheses about intrahepatic infection dynamics. We found that individual clusters on biopsy samples range in size from 4-50 infected cells. In addition, the HCV RNA content in a cluster declines from the cell that presumably founded the cluster to cells at the maximal cluster extension. These observations support the idea that HCV infection in the liver is seeded randomly (e.g. from the blood) and then spreads locally. Assuming that the amount of intracellular HCV RNA is a proxy for how long a cell has been infected, we estimate based on models of intracellular HCV RNA replication and accumulation that cells in clusters have been infected on average for less than a week. Further, we do not find a relationship between the cluster size and the estimated cluster expansion time. Our method represents a novel approach to make inferences about infection dynamics in solid tissues from static spatial data.

Show MeSH
Related in: MedlinePlus