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PCFSiM Tutorial

This tutorial provides a step-by-step guide on how to use the PCFSiM library for analyzing spatial point patterns in single-cell data. We have provided as Example data a CosMx Human Frontal Cortex dataset.

Step 1: Load Metadata

First, we need to load the metadata containing for each observation (here cells), information about the location on both axis and the label associated (here the cluster of each cell).

library(PCFSiM)
Meta_data= read.csv('Example_data/Frontal_cortex_data.csv')
# OR
data(Frontal_cortex_data)

Step 2: Create SCE Object

Next, we create a SingleCellExperiment (SCE) object using the loaded metadata. We specify the index of the columns for cell centroids and labels.

sce= Create_sce_object(Meta_data,cell_centroid_x=2,cell_centroid_y=3,Labels=4)

Step 3: Compute Pair Correlation Function (PCF)

Now, we compute the pair correlation function (PCF) using the SCE object. We define a range of distances according to the size of the tissue and specify the computation method.

List_pcf= Compute_pcf(sce, r_vector= seq(0, 10000, length.out=50), computation_method="direct", verbose=TRUE)

For each cluster, the results consist of 3 lists. 2 of them are of equal length, one containing the r distances, the other with the computed PCF values at each distance.

# Example for cluster 1>List_pcf$List_r[[1]]
[1] 0.0000204.0816408.1633612.2449816.32651020.40821224.48981428.57141632.65311836.7347
[11] 2040.81632244.89802448.97962653.06122857.14293061.22453265.30613469.38783673.46943877.5510
[21] 4081.63274285.71434489.79594693.87764897.95925102.04085306.12245510.20415714.28575918.3673
[31] 6122.44906326.53066530.61226734.69396938.77557142.85717346.93887551.02047755.10207959.1837
[41] 8163.26538367.34698571.42868775.51028979.59189183.67359387.75519591.83679795.918410000.0000>List_pcf$List_pcf[[1]]
[1] Inf2.3160062.3199962.3207912.3145862.3029702.2980972.2955812.2893302.2828222.2758662.269633
[13] 2.2679292.2580332.2521652.2425582.2311612.2232812.2178862.2080932.2038892.1948762.1869212.177837
[25] 2.1652612.1562592.1478992.1380922.1280852.1193212.1096542.1006182.0875692.0786412.0704642.060627
[37] 2.0495332.0397632.0284232.0187282.0075781.9982151.9870321.9770781.9647741.9549311.9453531.933477
[49] 1.9229031.864913>List_pcf$AnnotationROICluster1112123134145156167178189191011011111121121311314114

Step 4: Fit Models for a Specific Cluster

We can fit different models to the PCF data for a specific cluster. In this example, we will fit models for cluster k = 10.

k=10x=List_pcf$List_r[[k]]
y=List_pcf$List_pcf[[k]]
m_expo= try(Fit_exponential(x,y,show_plot=TRUE))
m_sigmoid= try(Fit_sigmoid(x,y,show_plot=TRUE))
Exponential Cluster PlotSigmoid Cluster Plot

Step 5: Retrieve Fitting Results for All Clusters

We can retrieve fitting results for each of the 14 clusters using different parametric models.

Results_sigmoid= Fit_parametric_pcf_model(List_pcf, model="Sigmoid")
Results_gamma= Fit_parametric_pcf_model(List_pcf, model="Gamma")
Results_exponential= Fit_parametric_pcf_model(List_pcf, model="Exponential")
>Results_sigmoidtaupCC_normalisedR211.584778e+041.76608671.31436971.854187e+040.998639227.606279e+031.08446191.97452091.456120e+040.998624731.110755e-030.18988209.70858062.051720e+000.910583841.902233e+041.25063431.64236372.909455e+040.993596455.223852e+030.84342152.40728971.374852e+040.995999869.201043e-040.299084878.27081796.761502e-010.923888774.878858e+031.65561693.34916211.460759e+040.996507687.615746e-050.3809986626.02836061.822708e-010.767135893.165779e+030.92499204.85717981.594629e+040.9960679104.365149e+020.928823417.85764798.066838e+030.9987493111.671197e+030.66354177.46047541.665685e+040.9411136121.759718e-020.248067591.09445704.032513e+010.9659157135.967917e+030.84637402.82485601.839056e+040.9660478143.934422e+040.53152890.69278764.899966e+040.7965860

Step 6: Compare Models with Boxplots

To compare the performance of the fitted models, we can create boxplots showing the R2 values for each fitted model.

Model_comparison_boxplot(list_results=list(Model_Sigmoid=Results_sigmoid,
Model_Gamma=Results_gamma,Model_exponential=Results_exponential))

Boxplots R2 comparison - Cluster 10

Step 7: Plot Selected Cluster

Finally, we can visualize a specific cluster. In this example, we will plot cluster 2.

Plot_selected_cluster(Meta_data=Meta_data, cell_centroid_x=2, cell_centroid_y=3, Labels=4, selected_cluster=10, title_show="Cluster 10")

Image - Cluster 10

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PCFSiM Tutorial
This tutorial provides a step-by-step guide on how to use the PCFSiM library for analyzing spatial point patterns in single-cell data. We have provided as Example data a CosMx Human Frontal Cortex dataset.
Step 1: Load Metadata
First, we need to load the metadata containing for each observation (here cells), information about the location on both axis and the label associated (here the cluster of each cell).
library(PCFSiM)
Meta_data= read.csv('Example_data/Frontal_cortex_data.csv')
# OR
data(Frontal_cortex_data)
Step 2: Create SCE Object
Next, we create a SingleCellExperiment (SCE) object using the loaded metadata. We specify the index of the columns for cell centroids and labels.
sce= Create_sce_object(Meta_data,cell_centroid_x=2,cell_centroid_y=3,Labels=4)

Step 3: Compute Pair Correlation Function (PCF)
Now, we compute the pair correlation function (PCF) using the SCE object. We define a range of distances according to the size of the tissue and specify the computation method.
List_pcf= Compute_pcf(sce, r_vector= seq(0, 10000, length.out=50), computation_method="direct", verbose=TRUE)
For each cluster, the results consist of 3 lists. 2 of them are of equal length, one containing the r distances, the other with the computed PCF values at each distance.
# Example for cluster 1>List_pcf$List_r[[1]]
[1] 0.0000204.0816408.1633612.2449816.32651020.40821224.48981428.57141632.65311836.7347
[11] 2040.81632244.89802448.97962653.06122857.14293061.22453265.30613469.38783673.46943877.5510
[21] 4081.63274285.71434489.79594693.87764897.95925102.04085306.12245510.20415714.28575918.3673
[31] 6122.44906326.53066530.61226734.69396938.77557142.85717346.93887551.02047755.10207959.1837
[41] 8163.26538367.34698571.42868775.51028979.59189183.67359387.75519591.83679795.918410000.0000>List_pcf$List_pcf[[1]]
[1] Inf2.3160062.3199962.3207912.3145862.3029702.2980972.2955812.2893302.2828222.2758662.269633
[13] 2.2679292.2580332.2521652.2425582.2311612.2232812.2178862.2080932.2038892.1948762.1869212.177837
[25] 2.1652612.1562592.1478992.1380922.1280852.1193212.1096542.1006182.0875692.0786412.0704642.060627
[37] 2.0495332.0397632.0284232.0187282.0075781.9982151.9870321.9770781.9647741.9549311.9453531.933477
[49] 1.9229031.864913>List_pcf$AnnotationROICluster1112123134145156167178189191011011111121121311314114
Step 4: Fit Models for a Specific Cluster
We can fit different models to the PCF data for a specific cluster. In this example, we will fit models for cluster k = 10.
k=10x=List_pcf$List_r[[k]]
y=List_pcf$List_pcf[[k]]
m_expo= try(Fit_exponential(x,y,show_plot=TRUE))
m_sigmoid= try(Fit_sigmoid(x,y,show_plot=TRUE))
Exponential Cluster PlotSigmoid Cluster Plot
Step 5: Retrieve Fitting Results for All Clusters
We can retrieve fitting results for each of the 14 clusters using different parametric models.
Results_sigmoid= Fit_parametric_pcf_model(List_pcf, model="Sigmoid")
Results_gamma= Fit_parametric_pcf_model(List_pcf, model="Gamma")
Results_exponential= Fit_parametric_pcf_model(List_pcf, model="Exponential")
>Results_sigmoidtaupCC_normalisedR211.584778e+041.76608671.31436971.854187e+040.998639227.606279e+031.08446191.97452091.456120e+040.998624731.110755e-030.18988209.70858062.051720e+000.910583841.902233e+041.25063431.64236372.909455e+040.993596455.223852e+030.84342152.40728971.374852e+040.995999869.201043e-040.299084878.27081796.761502e-010.923888774.878858e+031.65561693.34916211.460759e+040.996507687.615746e-050.3809986626.02836061.822708e-010.767135893.165779e+030.92499204.85717981.594629e+040.9960679104.365149e+020.928823417.85764798.066838e+030.9987493111.671197e+030.66354177.46047541.665685e+040.9411136121.759718e-020.248067591.09445704.032513e+010.9659157135.967917e+030.84637402.82485601.839056e+040.9660478143.934422e+040.53152890.69278764.899966e+040.7965860
Step 6: Compare Models with Boxplots
To compare the performance of the fitted models, we can create boxplots showing the R2 values for each fitted model.
Model_comparison_boxplot(list_results=list(Model_Sigmoid=Results_sigmoid,
Model_Gamma=Results_gamma,Model_exponential=Results_exponential))
Boxplots R2 comparison - Cluster 10
Step 7: Plot Selected Cluster
Finally, we can visualize a specific cluster. In this example, we will plot cluster 2.
Plot_selected_cluster(Meta_data=Meta_data, cell_centroid_x=2, cell_centroid_y=3, Labels=4, selected_cluster=10, title_show="Cluster 10")
Image - Cluster 10

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PCFSiM Tutorial
This tutorial provides a step-by-step guide on how to use the PCFSiM library for analyzing spatial point patterns in single-cell data. We have provided as Example data a CosMx Human Frontal Cortex dataset.
Step 1: Load Metadata
First, we need to load the metadata containing for each observation (here cells), information about the location on both axis and the label associated (here the cluster of each cell).
library(PCFSiM)
Meta_data= read.csv('Example_data/Frontal_cortex_data.csv')
# OR
data(Frontal_cortex_data)
Step 2: Create SCE Object
Next, we create a SingleCellExperiment (SCE) object using the loaded metadata. We specify the index of the columns for cell centroids and labels.
sce= Create_sce_object(Meta_data,cell_centroid_x=2,cell_centroid_y=3,Labels=4)

Step 3: Compute Pair Correlation Function (PCF)
Now, we compute the pair correlation function (PCF) using the SCE object. We define a range of distances according to the size of the tissue and specify the computation method.
List_pcf= Compute_pcf(sce, r_vector= seq(0, 10000, length.out=50), computation_method="direct", verbose=TRUE)
For each cluster, the results consist of 3 lists. 2 of them are of equal length, one containing the r distances, the other with the computed PCF values at each distance.
# Example for cluster 1>List_pcf$List_r[[1]]
[1] 0.0000204.0816408.1633612.2449816.32651020.40821224.48981428.57141632.65311836.7347
[11] 2040.81632244.89802448.97962653.06122857.14293061.22453265.30613469.38783673.46943877.5510
[21] 4081.63274285.71434489.79594693.87764897.95925102.04085306.12245510.20415714.28575918.3673
[31] 6122.44906326.53066530.61226734.69396938.77557142.85717346.93887551.02047755.10207959.1837
[41] 8163.26538367.34698571.42868775.51028979.59189183.67359387.75519591.83679795.918410000.0000>List_pcf$List_pcf[[1]]
[1] Inf2.3160062.3199962.3207912.3145862.3029702.2980972.2955812.2893302.2828222.2758662.269633
[13] 2.2679292.2580332.2521652.2425582.2311612.2232812.2178862.2080932.2038892.1948762.1869212.177837
[25] 2.1652612.1562592.1478992.1380922.1280852.1193212.1096542.1006182.0875692.0786412.0704642.060627
[37] 2.0495332.0397632.0284232.0187282.0075781.9982151.9870321.9770781.9647741.9549311.9453531.933477
[49] 1.9229031.864913>List_pcf$AnnotationROICluster1112123134145156167178189191011011111121121311314114
Step 4: Fit Models for a Specific Cluster
We can fit different models to the PCF data for a specific cluster. In this example, we will fit models for cluster k = 10.
k=10x=List_pcf$List_r[[k]]
y=List_pcf$List_pcf[[k]]
m_expo= try(Fit_exponential(x,y,show_plot=TRUE))
m_sigmoid= try(Fit_sigmoid(x,y,show_plot=TRUE))
Exponential Cluster PlotSigmoid Cluster Plot
Step 5: Retrieve Fitting Results for All Clusters
We can retrieve fitting results for each of the 14 clusters using different parametric models.
Results_sigmoid= Fit_parametric_pcf_model(List_pcf, model="Sigmoid")
Results_gamma= Fit_parametric_pcf_model(List_pcf, model="Gamma")
Results_exponential= Fit_parametric_pcf_model(List_pcf, model="Exponential")
>Results_sigmoidtaupCC_normalisedR211.584778e+041.76608671.31436971.854187e+040.998639227.606279e+031.08446191.97452091.456120e+040.998624731.110755e-030.18988209.70858062.051720e+000.910583841.902233e+041.25063431.64236372.909455e+040.993596455.223852e+030.84342152.40728971.374852e+040.995999869.201043e-040.299084878.27081796.761502e-010.923888774.878858e+031.65561693.34916211.460759e+040.996507687.615746e-050.3809986626.02836061.822708e-010.767135893.165779e+030.92499204.85717981.594629e+040.9960679104.365149e+020.928823417.85764798.066838e+030.9987493111.671197e+030.66354177.46047541.665685e+040.9411136121.759718e-020.248067591.09445704.032513e+010.9659157135.967917e+030.84637402.82485601.839056e+040.9660478143.934422e+040.53152890.69278764.899966e+040.7965860
Step 6: Compare Models with Boxplots
To compare the performance of the fitted models, we can create boxplots showing the R2 values for each fitted model.
Model_comparison_boxplot(list_results=list(Model_Sigmoid=Results_sigmoid,
Model_Gamma=Results_gamma,Model_exponential=Results_exponential))
Boxplots R2 comparison - Cluster 10
Step 7: Plot Selected Cluster
Finally, we can visualize a specific cluster. In this example, we will plot cluster 2.
Plot_selected_cluster(Meta_data=Meta_data, cell_centroid_x=2, cell_centroid_y=3, Labels=4, selected_cluster=10, title_show="Cluster 10")
Image - Cluster 10

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PCFSiM Tutorial
This tutorial provides a step-by-step guide on how to use the PCFSiM library for analyzing spatial point patterns in single-cell data. We have provided as Example data a CosMx Human Frontal Cortex dataset.
Step 1: Load Metadata
First, we need to load the metadata containing for each observation (here cells), information about the location on both axis and the label associated (here the cluster of each cell).
library(PCFSiM)
Meta_data= read.csv('Example_data/Frontal_cortex_data.csv')
# OR
data(Frontal_cortex_data)
Step 2: Create SCE Object
Next, we create a SingleCellExperiment (SCE) object using the loaded metadata. We specify the index of the columns for cell centroids and labels.
sce= Create_sce_object(Meta_data,cell_centroid_x=2,cell_centroid_y=3,Labels=4)

Step 3: Compute Pair Correlation Function (PCF)
Now, we compute the pair correlation function (PCF) using the SCE object. We define a range of distances according to the size of the tissue and specify the computation method.
List_pcf= Compute_pcf(sce, r_vector= seq(0, 10000, length.out=50), computation_method="direct", verbose=TRUE)
For each cluster, the results consist of 3 lists. 2 of them are of equal length, one containing the r distances, the other with the computed PCF values at each distance.
# Example for cluster 1>List_pcf$List_r[[1]]
[1] 0.0000204.0816408.1633612.2449816.32651020.40821224.48981428.57141632.65311836.7347
[11] 2040.81632244.89802448.97962653.06122857.14293061.22453265.30613469.38783673.46943877.5510
[21] 4081.63274285.71434489.79594693.87764897.95925102.04085306.12245510.20415714.28575918.3673
[31] 6122.44906326.53066530.61226734.69396938.77557142.85717346.93887551.02047755.10207959.1837
[41] 8163.26538367.34698571.42868775.51028979.59189183.67359387.75519591.83679795.918410000.0000>List_pcf$List_pcf[[1]]
[1] Inf2.3160062.3199962.3207912.3145862.3029702.2980972.2955812.2893302.2828222.2758662.269633
[13] 2.2679292.2580332.2521652.2425582.2311612.2232812.2178862.2080932.2038892.1948762.1869212.177837
[25] 2.1652612.1562592.1478992.1380922.1280852.1193212.1096542.1006182.0875692.0786412.0704642.060627
[37] 2.0495332.0397632.0284232.0187282.0075781.9982151.9870321.9770781.9647741.9549311.9453531.933477
[49] 1.9229031.864913>List_pcf$AnnotationROICluster1112123134145156167178189191011011111121121311314114
Step 4: Fit Models for a Specific Cluster
We can fit different models to the PCF data for a specific cluster. In this example, we will fit models for cluster k = 10.
k=10x=List_pcf$List_r[[k]]
y=List_pcf$List_pcf[[k]]
m_expo= try(Fit_exponential(x,y,show_plot=TRUE))
m_sigmoid= try(Fit_sigmoid(x,y,show_plot=TRUE))
Exponential Cluster PlotSigmoid Cluster Plot
Step 5: Retrieve Fitting Results for All Clusters
We can retrieve fitting results for each of the 14 clusters using different parametric models.
Results_sigmoid= Fit_parametric_pcf_model(List_pcf, model="Sigmoid")
Results_gamma= Fit_parametric_pcf_model(List_pcf, model="Gamma")
Results_exponential= Fit_parametric_pcf_model(List_pcf, model="Exponential")
>Results_sigmoidtaupCC_normalisedR211.584778e+041.76608671.31436971.854187e+040.998639227.606279e+031.08446191.97452091.456120e+040.998624731.110755e-030.18988209.70858062.051720e+000.910583841.902233e+041.25063431.64236372.909455e+040.993596455.223852e+030.84342152.40728971.374852e+040.995999869.201043e-040.299084878.27081796.761502e-010.923888774.878858e+031.65561693.34916211.460759e+040.996507687.615746e-050.3809986626.02836061.822708e-010.767135893.165779e+030.92499204.85717981.594629e+040.9960679104.365149e+020.928823417.85764798.066838e+030.9987493111.671197e+030.66354177.46047541.665685e+040.9411136121.759718e-020.248067591.09445704.032513e+010.9659157135.967917e+030.84637402.82485601.839056e+040.9660478143.934422e+040.53152890.69278764.899966e+040.7965860
Step 6: Compare Models with Boxplots
To compare the performance of the fitted models, we can create boxplots showing the R2 values for each fitted model.
Model_comparison_boxplot(list_results=list(Model_Sigmoid=Results_sigmoid,
Model_Gamma=Results_gamma,Model_exponential=Results_exponential))
Boxplots R2 comparison - Cluster 10
Step 7: Plot Selected Cluster
Finally, we can visualize a specific cluster. In this example, we will plot cluster 2.
Plot_selected_cluster(Meta_data=Meta_data, cell_centroid_x=2, cell_centroid_y=3, Labels=4, selected_cluster=10, title_show="Cluster 10")
Image - Cluster 10

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PCFSiM Tutorial
This tutorial provides a step-by-step guide on how to use the PCFSiM library for analyzing spatial point patterns in single-cell data. We have provided as Example data a CosMx Human Frontal Cortex dataset.
Step 1: Load Metadata
First, we need to load the metadata containing for each observation (here cells), information about the location on both axis and the label associated (here the cluster of each cell).
library(PCFSiM)
Meta_data= read.csv('Example_data/Frontal_cortex_data.csv')
# OR
data(Frontal_cortex_data)
Step 2: Create SCE Object
Next, we create a SingleCellExperiment (SCE) object using the loaded metadata. We specify the index of the columns for cell centroids and labels.
sce= Create_sce_object(Meta_data,cell_centroid_x=2,cell_centroid_y=3,Labels=4)

Step 3: Compute Pair Correlation Function (PCF)
Now, we compute the pair correlation function (PCF) using the SCE object. We define a range of distances according to the size of the tissue and specify the computation method.
List_pcf= Compute_pcf(sce, r_vector= seq(0, 10000, length.out=50), computation_method="direct", verbose=TRUE)
For each cluster, the results consist of 3 lists. 2 of them are of equal length, one containing the r distances, the other with the computed PCF values at each distance.
# Example for cluster 1>List_pcf$List_r[[1]]
[1] 0.0000204.0816408.1633612.2449816.32651020.40821224.48981428.57141632.65311836.7347
[11] 2040.81632244.89802448.97962653.06122857.14293061.22453265.30613469.38783673.46943877.5510
[21] 4081.63274285.71434489.79594693.87764897.95925102.04085306.12245510.20415714.28575918.3673
[31] 6122.44906326.53066530.61226734.69396938.77557142.85717346.93887551.02047755.10207959.1837
[41] 8163.26538367.34698571.42868775.51028979.59189183.67359387.75519591.83679795.918410000.0000>List_pcf$List_pcf[[1]]
[1] Inf2.3160062.3199962.3207912.3145862.3029702.2980972.2955812.2893302.2828222.2758662.269633
[13] 2.2679292.2580332.2521652.2425582.2311612.2232812.2178862.2080932.2038892.1948762.1869212.177837
[25] 2.1652612.1562592.1478992.1380922.1280852.1193212.1096542.1006182.0875692.0786412.0704642.060627
[37] 2.0495332.0397632.0284232.0187282.0075781.9982151.9870321.9770781.9647741.9549311.9453531.933477
[49] 1.9229031.864913>List_pcf$AnnotationROICluster1112123134145156167178189191011011111121121311314114
Step 4: Fit Models for a Specific Cluster
We can fit different models to the PCF data for a specific cluster. In this example, we will fit models for cluster k = 10.
k=10x=List_pcf$List_r[[k]]
y=List_pcf$List_pcf[[k]]
m_expo= try(Fit_exponential(x,y,show_plot=TRUE))
m_sigmoid= try(Fit_sigmoid(x,y,show_plot=TRUE))
Exponential Cluster PlotSigmoid Cluster Plot
Step 5: Retrieve Fitting Results for All Clusters
We can retrieve fitting results for each of the 14 clusters using different parametric models.
Results_sigmoid= Fit_parametric_pcf_model(List_pcf, model="Sigmoid")
Results_gamma= Fit_parametric_pcf_model(List_pcf, model="Gamma")
Results_exponential= Fit_parametric_pcf_model(List_pcf, model="Exponential")
>Results_sigmoidtaupCC_normalisedR211.584778e+041.76608671.31436971.854187e+040.998639227.606279e+031.08446191.97452091.456120e+040.998624731.110755e-030.18988209.70858062.051720e+000.910583841.902233e+041.25063431.64236372.909455e+040.993596455.223852e+030.84342152.40728971.374852e+040.995999869.201043e-040.299084878.27081796.761502e-010.923888774.878858e+031.65561693.34916211.460759e+040.996507687.615746e-050.3809986626.02836061.822708e-010.767135893.165779e+030.92499204.85717981.594629e+040.9960679104.365149e+020.928823417.85764798.066838e+030.9987493111.671197e+030.66354177.46047541.665685e+040.9411136121.759718e-020.248067591.09445704.032513e+010.9659157135.967917e+030.84637402.82485601.839056e+040.9660478143.934422e+040.53152890.69278764.899966e+040.7965860
Step 6: Compare Models with Boxplots
To compare the performance of the fitted models, we can create boxplots showing the R2 values for each fitted model.
Model_comparison_boxplot(list_results=list(Model_Sigmoid=Results_sigmoid,
Model_Gamma=Results_gamma,Model_exponential=Results_exponential))
Boxplots R2 comparison - Cluster 10
Step 7: Plot Selected Cluster
Finally, we can visualize a specific cluster. In this example, we will plot cluster 2.
Plot_selected_cluster(Meta_data=Meta_data, cell_centroid_x=2, cell_centroid_y=3, Labels=4, selected_cluster=10, title_show="Cluster 10")
Image - Cluster 10

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PCFSiM Tutorial
This tutorial provides a step-by-step guide on how to use the PCFSiM library for analyzing spatial point patterns in single-cell data. We have provided as Example data a CosMx Human Frontal Cortex dataset.
Step 1: Load Metadata
First, we need to load the metadata containing for each observation (here cells), information about the location on both axis and the label associated (here the cluster of each cell).
library(PCFSiM)
Meta_data= read.csv('Example_data/Frontal_cortex_data.csv')
# OR
data(Frontal_cortex_data)
Step 2: Create SCE Object
Next, we create a SingleCellExperiment (SCE) object using the loaded metadata. We specify the index of the columns for cell centroids and labels.
sce= Create_sce_object(Meta_data,cell_centroid_x=2,cell_centroid_y=3,Labels=4)

Step 3: Compute Pair Correlation Function (PCF)
Now, we compute the pair correlation function (PCF) using the SCE object. We define a range of distances according to the size of the tissue and specify the computation method.
List_pcf= Compute_pcf(sce, r_vector= seq(0, 10000, length.out=50), computation_method="direct", verbose=TRUE)
For each cluster, the results consist of 3 lists. 2 of them are of equal length, one containing the r distances, the other with the computed PCF values at each distance.
# Example for cluster 1>List_pcf$List_r[[1]]
[1] 0.0000204.0816408.1633612.2449816.32651020.40821224.48981428.57141632.65311836.7347
[11] 2040.81632244.89802448.97962653.06122857.14293061.22453265.30613469.38783673.46943877.5510
[21] 4081.63274285.71434489.79594693.87764897.95925102.04085306.12245510.20415714.28575918.3673
[31] 6122.44906326.53066530.61226734.69396938.77557142.85717346.93887551.02047755.10207959.1837
[41] 8163.26538367.34698571.42868775.51028979.59189183.67359387.75519591.83679795.918410000.0000>List_pcf$List_pcf[[1]]
[1] Inf2.3160062.3199962.3207912.3145862.3029702.2980972.2955812.2893302.2828222.2758662.269633
[13] 2.2679292.2580332.2521652.2425582.2311612.2232812.2178862.2080932.2038892.1948762.1869212.177837
[25] 2.1652612.1562592.1478992.1380922.1280852.1193212.1096542.1006182.0875692.0786412.0704642.060627
[37] 2.0495332.0397632.0284232.0187282.0075781.9982151.9870321.9770781.9647741.9549311.9453531.933477
[49] 1.9229031.864913>List_pcf$AnnotationROICluster1112123134145156167178189191011011111121121311314114
Step 4: Fit Models for a Specific Cluster
We can fit different models to the PCF data for a specific cluster. In this example, we will fit models for cluster k = 10.
k=10x=List_pcf$List_r[[k]]
y=List_pcf$List_pcf[[k]]
m_expo= try(Fit_exponential(x,y,show_plot=TRUE))
m_sigmoid= try(Fit_sigmoid(x,y,show_plot=TRUE))
Exponential Cluster PlotSigmoid Cluster Plot
Step 5: Retrieve Fitting Results for All Clusters
We can retrieve fitting results for each of the 14 clusters using different parametric models.
Results_sigmoid= Fit_parametric_pcf_model(List_pcf, model="Sigmoid")
Results_gamma= Fit_parametric_pcf_model(List_pcf, model="Gamma")
Results_exponential= Fit_parametric_pcf_model(List_pcf, model="Exponential")
>Results_sigmoidtaupCC_normalisedR211.584778e+041.76608671.31436971.854187e+040.998639227.606279e+031.08446191.97452091.456120e+040.998624731.110755e-030.18988209.70858062.051720e+000.910583841.902233e+041.25063431.64236372.909455e+040.993596455.223852e+030.84342152.40728971.374852e+040.995999869.201043e-040.299084878.27081796.761502e-010.923888774.878858e+031.65561693.34916211.460759e+040.996507687.615746e-050.3809986626.02836061.822708e-010.767135893.165779e+030.92499204.85717981.594629e+040.9960679104.365149e+020.928823417.85764798.066838e+030.9987493111.671197e+030.66354177.46047541.665685e+040.9411136121.759718e-020.248067591.09445704.032513e+010.9659157135.967917e+030.84637402.82485601.839056e+040.9660478143.934422e+040.53152890.69278764.899966e+040.7965860
Step 6: Compare Models with Boxplots
To compare the performance of the fitted models, we can create boxplots showing the R2 values for each fitted model.
Model_comparison_boxplot(list_results=list(Model_Sigmoid=Results_sigmoid,
Model_Gamma=Results_gamma,Model_exponential=Results_exponential))
Boxplots R2 comparison - Cluster 10
Step 7: Plot Selected Cluster
Finally, we can visualize a specific cluster. In this example, we will plot cluster 2.
Plot_selected_cluster(Meta_data=Meta_data, cell_centroid_x=2, cell_centroid_y=3, Labels=4, selected_cluster=10, title_show="Cluster 10")
Image - Cluster 10

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PCFSiM Tutorial
This tutorial provides a step-by-step guide on how to use the PCFSiM library for analyzing spatial point patterns in single-cell data. We have provided as Example data a CosMx Human Frontal Cortex dataset.
Step 1: Load Metadata
First, we need to load the metadata containing for each observation (here cells), information about the location on both axis and the label associated (here the cluster of each cell).
library(PCFSiM)
Meta_data= read.csv('Example_data/Frontal_cortex_data.csv')
# OR
data(Frontal_cortex_data)
Step 2: Create SCE Object
Next, we create a SingleCellExperiment (SCE) object using the loaded metadata. We specify the index of the columns for cell centroids and labels.
sce= Create_sce_object(Meta_data,cell_centroid_x=2,cell_centroid_y=3,Labels=4)

Step 3: Compute Pair Correlation Function (PCF)
Now, we compute the pair correlation function (PCF) using the SCE object. We define a range of distances according to the size of the tissue and specify the computation method.
List_pcf= Compute_pcf(sce, r_vector= seq(0, 10000, length.out=50), computation_method="direct", verbose=TRUE)
For each cluster, the results consist of 3 lists. 2 of them are of equal length, one containing the r distances, the other with the computed PCF values at each distance.
# Example for cluster 1>List_pcf$List_r[[1]]
[1] 0.0000204.0816408.1633612.2449816.32651020.40821224.48981428.57141632.65311836.7347
[11] 2040.81632244.89802448.97962653.06122857.14293061.22453265.30613469.38783673.46943877.5510
[21] 4081.63274285.71434489.79594693.87764897.95925102.04085306.12245510.20415714.28575918.3673
[31] 6122.44906326.53066530.61226734.69396938.77557142.85717346.93887551.02047755.10207959.1837
[41] 8163.26538367.34698571.42868775.51028979.59189183.67359387.75519591.83679795.918410000.0000>List_pcf$List_pcf[[1]]
[1] Inf2.3160062.3199962.3207912.3145862.3029702.2980972.2955812.2893302.2828222.2758662.269633
[13] 2.2679292.2580332.2521652.2425582.2311612.2232812.2178862.2080932.2038892.1948762.1869212.177837
[25] 2.1652612.1562592.1478992.1380922.1280852.1193212.1096542.1006182.0875692.0786412.0704642.060627
[37] 2.0495332.0397632.0284232.0187282.0075781.9982151.9870321.9770781.9647741.9549311.9453531.933477
[49] 1.9229031.864913>List_pcf$AnnotationROICluster1112123134145156167178189191011011111121121311314114
Step 4: Fit Models for a Specific Cluster
We can fit different models to the PCF data for a specific cluster. In this example, we will fit models for cluster k = 10.
k=10x=List_pcf$List_r[[k]]
y=List_pcf$List_pcf[[k]]
m_expo= try(Fit_exponential(x,y,show_plot=TRUE))
m_sigmoid= try(Fit_sigmoid(x,y,show_plot=TRUE))
Exponential Cluster PlotSigmoid Cluster Plot
Step 5: Retrieve Fitting Results for All Clusters
We can retrieve fitting results for each of the 14 clusters using different parametric models.
Results_sigmoid= Fit_parametric_pcf_model(List_pcf, model="Sigmoid")
Results_gamma= Fit_parametric_pcf_model(List_pcf, model="Gamma")
Results_exponential= Fit_parametric_pcf_model(List_pcf, model="Exponential")
>Results_sigmoidtaupCC_normalisedR211.584778e+041.76608671.31436971.854187e+040.998639227.606279e+031.08446191.97452091.456120e+040.998624731.110755e-030.18988209.70858062.051720e+000.910583841.902233e+041.25063431.64236372.909455e+040.993596455.223852e+030.84342152.40728971.374852e+040.995999869.201043e-040.299084878.27081796.761502e-010.923888774.878858e+031.65561693.34916211.460759e+040.996507687.615746e-050.3809986626.02836061.822708e-010.767135893.165779e+030.92499204.85717981.594629e+040.9960679104.365149e+020.928823417.85764798.066838e+030.9987493111.671197e+030.66354177.46047541.665685e+040.9411136121.759718e-020.248067591.09445704.032513e+010.9659157135.967917e+030.84637402.82485601.839056e+040.9660478143.934422e+040.53152890.69278764.899966e+040.7965860
Step 6: Compare Models with Boxplots
To compare the performance of the fitted models, we can create boxplots showing the R2 values for each fitted model.
Model_comparison_boxplot(list_results=list(Model_Sigmoid=Results_sigmoid,
Model_Gamma=Results_gamma,Model_exponential=Results_exponential))
Boxplots R2 comparison - Cluster 10
Step 7: Plot Selected Cluster
Finally, we can visualize a specific cluster. In this example, we will plot cluster 2.
Plot_selected_cluster(Meta_data=Meta_data, cell_centroid_x=2, cell_centroid_y=3, Labels=4, selected_cluster=10, title_show="Cluster 10")
Image - Cluster 10

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PCFSiM Tutorial
This tutorial provides a step-by-step guide on how to use the PCFSiM library for analyzing spatial point patterns in single-cell data. We have provided as Example data a CosMx Human Frontal Cortex dataset.
Step 1: Load Metadata
First, we need to load the metadata containing for each observation (here cells), information about the location on both axis and the label associated (here the cluster of each cell).
library(PCFSiM)
Meta_data= read.csv('Example_data/Frontal_cortex_data.csv')
# OR
data(Frontal_cortex_data)
Step 2: Create SCE Object
Next, we create a SingleCellExperiment (SCE) object using the loaded metadata. We specify the index of the columns for cell centroids and labels.
sce= Create_sce_object(Meta_data,cell_centroid_x=2,cell_centroid_y=3,Labels=4)

Step 3: Compute Pair Correlation Function (PCF)
Now, we compute the pair correlation function (PCF) using the SCE object. We define a range of distances according to the size of the tissue and specify the computation method.
List_pcf= Compute_pcf(sce, r_vector= seq(0, 10000, length.out=50), computation_method="direct", verbose=TRUE)
For each cluster, the results consist of 3 lists. 2 of them are of equal length, one containing the r distances, the other with the computed PCF values at each distance.
# Example for cluster 1>List_pcf$List_r[[1]]
[1] 0.0000204.0816408.1633612.2449816.32651020.40821224.48981428.57141632.65311836.7347
[11] 2040.81632244.89802448.97962653.06122857.14293061.22453265.30613469.38783673.46943877.5510
[21] 4081.63274285.71434489.79594693.87764897.95925102.04085306.12245510.20415714.28575918.3673
[31] 6122.44906326.53066530.61226734.69396938.77557142.85717346.93887551.02047755.10207959.1837
[41] 8163.26538367.34698571.42868775.51028979.59189183.67359387.75519591.83679795.918410000.0000>List_pcf$List_pcf[[1]]
[1] Inf2.3160062.3199962.3207912.3145862.3029702.2980972.2955812.2893302.2828222.2758662.269633
[13] 2.2679292.2580332.2521652.2425582.2311612.2232812.2178862.2080932.2038892.1948762.1869212.177837
[25] 2.1652612.1562592.1478992.1380922.1280852.1193212.1096542.1006182.0875692.0786412.0704642.060627
[37] 2.0495332.0397632.0284232.0187282.0075781.9982151.9870321.9770781.9647741.9549311.9453531.933477
[49] 1.9229031.864913>List_pcf$AnnotationROICluster1112123134145156167178189191011011111121121311314114
Step 4: Fit Models for a Specific Cluster
We can fit different models to the PCF data for a specific cluster. In this example, we will fit models for cluster k = 10.
k=10x=List_pcf$List_r[[k]]
y=List_pcf$List_pcf[[k]]
m_expo= try(Fit_exponential(x,y,show_plot=TRUE))
m_sigmoid= try(Fit_sigmoid(x,y,show_plot=TRUE))
Exponential Cluster PlotSigmoid Cluster Plot
Step 5: Retrieve Fitting Results for All Clusters
We can retrieve fitting results for each of the 14 clusters using different parametric models.
Results_sigmoid= Fit_parametric_pcf_model(List_pcf, model="Sigmoid")
Results_gamma= Fit_parametric_pcf_model(List_pcf, model="Gamma")
Results_exponential= Fit_parametric_pcf_model(List_pcf, model="Exponential")
>Results_sigmoidtaupCC_normalisedR211.584778e+041.76608671.31436971.854187e+040.998639227.606279e+031.08446191.97452091.456120e+040.998624731.110755e-030.18988209.70858062.051720e+000.910583841.902233e+041.25063431.64236372.909455e+040.993596455.223852e+030.84342152.40728971.374852e+040.995999869.201043e-040.299084878.27081796.761502e-010.923888774.878858e+031.65561693.34916211.460759e+040.996507687.615746e-050.3809986626.02836061.822708e-010.767135893.165779e+030.92499204.85717981.594629e+040.9960679104.365149e+020.928823417.85764798.066838e+030.9987493111.671197e+030.66354177.46047541.665685e+040.9411136121.759718e-020.248067591.09445704.032513e+010.9659157135.967917e+030.84637402.82485601.839056e+040.9660478143.934422e+040.53152890.69278764.899966e+040.7965860
Step 6: Compare Models with Boxplots
To compare the performance of the fitted models, we can create boxplots showing the R2 values for each fitted model.
Model_comparison_boxplot(list_results=list(Model_Sigmoid=Results_sigmoid,
Model_Gamma=Results_gamma,Model_exponential=Results_exponential))
Boxplots R2 comparison - Cluster 10
Step 7: Plot Selected Cluster
Finally, we can visualize a specific cluster. In this example, we will plot cluster 2.
Plot_selected_cluster(Meta_data=Meta_data, cell_centroid_x=2, cell_centroid_y=3, Labels=4, selected_cluster=10, title_show="Cluster 10")
Image - Cluster 10