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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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Estimates of domain radius and spatial intensity.Estimates of the domain radius  (left panel) and the spatial intensity  (middle panel) dependent on the minimal HCV RNA content of cells in the clusters for each of the three different grids on the sections of subject 3. Plots should be read from the right to the left as the algorithm starts at point , the maximal amount of HCV RNA measured in an infected cell on the indicated grid. The domain radius of the cluster, , is given on a continuous scale, as well as an estimate of the radius in number of cells. The red line is the median over 10,000 bootstrap replicates of fitting a Matérn cluster process to the data as described in Materials & Methods. The red area denotes the 95%-quantiles of the estimates. The dashed horizontal (left panels) and vertical (middle panels) lines indicate the cutoff of the algorithm, i.e., the maximal extension of the cluster, . The right panels show the observed spatial distribution of infected hepatocytes together with the measured HCV RNA amount. Grey squares indicate infected cells for which the actual HCV RNA amount could not be determined (n.d.). For the analysis, the HCV RNA amount of these cells was extrapolated according to different methods (see Materials & Methods). Plots are combined with a possible distribution of the clusters showing for each the maximal cluster radius,  (dashed circles). On grid 2 and 3, the estimated spatial intensity  is about  times higher than on grid 1, predicting the existence of several individual clusters on these sections.
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pcbi-1003934-g002: Estimates of domain radius and spatial intensity.Estimates of the domain radius (left panel) and the spatial intensity (middle panel) dependent on the minimal HCV RNA content of cells in the clusters for each of the three different grids on the sections of subject 3. Plots should be read from the right to the left as the algorithm starts at point , the maximal amount of HCV RNA measured in an infected cell on the indicated grid. The domain radius of the cluster, , is given on a continuous scale, as well as an estimate of the radius in number of cells. The red line is the median over 10,000 bootstrap replicates of fitting a Matérn cluster process to the data as described in Materials & Methods. The red area denotes the 95%-quantiles of the estimates. The dashed horizontal (left panels) and vertical (middle panels) lines indicate the cutoff of the algorithm, i.e., the maximal extension of the cluster, . The right panels show the observed spatial distribution of infected hepatocytes together with the measured HCV RNA amount. Grey squares indicate infected cells for which the actual HCV RNA amount could not be determined (n.d.). For the analysis, the HCV RNA amount of these cells was extrapolated according to different methods (see Materials & Methods). Plots are combined with a possible distribution of the clusters showing for each the maximal cluster radius, (dashed circles). On grid 2 and 3, the estimated spatial intensity is about times higher than on grid 1, predicting the existence of several individual clusters on these sections.

Mentions: We applied the above procedure to each grid of each subject individually. In Figure 2, we show, for subject 3, the estimates of the cluster radius, , and the corresponding expected number of cluster centers per unit area, , as a function of the minimal HCV RNA content of cells in the clusters at each iteration of our algorithm (from right-to-left). The maximal cluster extension, , is found when the mean number of cluster centers, , starts to decrease from its more or less constant value (Figure 2, reading right-to-left). A decreasing indicates fewer and larger clusters, a more homogeneous distribution, and in the limit indicates that all cells on the grid belong to one single cluster. Since we previously determined that infected cells are clustered [15], such inference of a homogeneous distribution is unreasonable. For each iteration we analyze, in each of our bootstrap replicates, if the resulting spatial distribution still indicates clustering or not. The iterative process is stopped when we start finding a homogeneous spatial distribution, that is when less than 95% of the replicates show evidence of clustering. On grid 1 of subject 3, the algorithm detects one large cluster, while on the other two grids, the existence of several smaller clusters of infected cells is predicted, with the estimated mean number of clusters, , on these grids being times larger than on grid 1. The corresponding figures for all other subjects are shown in the Supporting Information (Figures S1 and S2–S4).


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)

Estimates of domain radius and spatial intensity.Estimates of the domain radius  (left panel) and the spatial intensity  (middle panel) dependent on the minimal HCV RNA content of cells in the clusters for each of the three different grids on the sections of subject 3. Plots should be read from the right to the left as the algorithm starts at point , the maximal amount of HCV RNA measured in an infected cell on the indicated grid. The domain radius of the cluster, , is given on a continuous scale, as well as an estimate of the radius in number of cells. The red line is the median over 10,000 bootstrap replicates of fitting a Matérn cluster process to the data as described in Materials & Methods. The red area denotes the 95%-quantiles of the estimates. The dashed horizontal (left panels) and vertical (middle panels) lines indicate the cutoff of the algorithm, i.e., the maximal extension of the cluster, . The right panels show the observed spatial distribution of infected hepatocytes together with the measured HCV RNA amount. Grey squares indicate infected cells for which the actual HCV RNA amount could not be determined (n.d.). For the analysis, the HCV RNA amount of these cells was extrapolated according to different methods (see Materials & Methods). Plots are combined with a possible distribution of the clusters showing for each the maximal cluster radius,  (dashed circles). On grid 2 and 3, the estimated spatial intensity  is about  times higher than on grid 1, predicting the existence of several individual clusters on these sections.
© Copyright Policy
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4230741&req=5

pcbi-1003934-g002: Estimates of domain radius and spatial intensity.Estimates of the domain radius (left panel) and the spatial intensity (middle panel) dependent on the minimal HCV RNA content of cells in the clusters for each of the three different grids on the sections of subject 3. Plots should be read from the right to the left as the algorithm starts at point , the maximal amount of HCV RNA measured in an infected cell on the indicated grid. The domain radius of the cluster, , is given on a continuous scale, as well as an estimate of the radius in number of cells. The red line is the median over 10,000 bootstrap replicates of fitting a Matérn cluster process to the data as described in Materials & Methods. The red area denotes the 95%-quantiles of the estimates. The dashed horizontal (left panels) and vertical (middle panels) lines indicate the cutoff of the algorithm, i.e., the maximal extension of the cluster, . The right panels show the observed spatial distribution of infected hepatocytes together with the measured HCV RNA amount. Grey squares indicate infected cells for which the actual HCV RNA amount could not be determined (n.d.). For the analysis, the HCV RNA amount of these cells was extrapolated according to different methods (see Materials & Methods). Plots are combined with a possible distribution of the clusters showing for each the maximal cluster radius, (dashed circles). On grid 2 and 3, the estimated spatial intensity is about times higher than on grid 1, predicting the existence of several individual clusters on these sections.
Mentions: We applied the above procedure to each grid of each subject individually. In Figure 2, we show, for subject 3, the estimates of the cluster radius, , and the corresponding expected number of cluster centers per unit area, , as a function of the minimal HCV RNA content of cells in the clusters at each iteration of our algorithm (from right-to-left). The maximal cluster extension, , is found when the mean number of cluster centers, , starts to decrease from its more or less constant value (Figure 2, reading right-to-left). A decreasing indicates fewer and larger clusters, a more homogeneous distribution, and in the limit indicates that all cells on the grid belong to one single cluster. Since we previously determined that infected cells are clustered [15], such inference of a homogeneous distribution is unreasonable. For each iteration we analyze, in each of our bootstrap replicates, if the resulting spatial distribution still indicates clustering or not. The iterative process is stopped when we start finding a homogeneous spatial distribution, that is when less than 95% of the replicates show evidence of clustering. On grid 1 of subject 3, the algorithm detects one large cluster, while on the other two grids, the existence of several smaller clusters of infected cells is predicted, with the estimated mean number of clusters, , on these grids being times larger than on grid 1. The corresponding figures for all other subjects are shown in the Supporting Information (Figures S1 and S2–S4).

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