In this protocol, the pancreatic islets are reconstructed and analyzed using computational algorithms implemented in a dedicated multiplatform application.
Structural properties of pancreatic islets are key for the functional response of insulin, glucagon, and somatostatin-secreting cells, due to their implications in intraislet communication via electric, paracrine, and autocrine signaling. In this protocol, the three-dimensional architecture of a pancreatic islet is firstly reconstructed from experimental data using a novel computational algorithm. Next, the morphological and connectivity properties of the reconstructed islet, such as the number and percentages of the different type of cells, cellular volume, and cell-to-cell contacts, are obtained. Then, network theory is used to describe the connectivity properties of the islet through network-derived metrics such as average degree, clustering coefficient, density, diameter, and efficiency. Finally, all these properties are functionally evaluated through computational simulations using a model of coupled oscillators. Overall, here we describe a step-by-step workflow, implemented in IsletLab, a multiplatform application developed specifically for the study and simulation of pancreatic islets, to apply a novel computational methodology to characterize and analyze pancreatic islets as a complement to the experimental work.
The pancreas is divided into regions referred to as head, neck, body, and tail, each having different structures, functions, and anatomical position1,2. From a functional viewpoint, the pancreas can be divided into endocrine and exocrine systems with the former responsible for the secretion of hormones critically involved in the regulation of glucose homeostasis, while the latter contributes to food digestion via the secretion of enzymes into the duodenum1. Pancreatic islets constitute the endocrine tissue of the pancreas and are responsible for the secretion of glucagon, insulin, and somatostatin, secreted from ɑ, β, and δ-cells, respectively3. In addition to their intrinsic regulatory mechanisms, these cells are regulated via direct electrical communication (between β-cells and likely β and δ-cells), and also by paracrine and autocrine signaling4,5,6. Both mechanisms are highly dependent on the islet architecture (i.e., the composition and organization of the different types of cells within the islet)7,8. Importantly, islet architecture is altered in the presence of diabetes, most likely disturbing intraislet communication as a result9,10.
The study of pancreatic islets involves a wide range of experimental methodologies. Among these, the use of fluorescence techniques to determine the number, location, and type of the different cells in the islet has allowed to study the structural and morphological properties of pancreatic islets11,12,13 and to gain a better understanding of the functional implications in health and disease. As a complement, computational models of pancreatic cells14,15,16 and, more recently, pancreatic islets12,17,18,19 have been used in the last decades to evaluate aspects difficult or even impossible to address experimentally.
In this protocol, we aim to bridge the gap between the experimental and computational work by outlining a methodology to reconstruct islet architectures, to analyze their morphological and connectivity properties through quantitative metrics, and to perform basic simulations to evaluate the functional implications of the islet properties.
The protocol described below is based on computational algorithms specifically designed for the study of pancreatic islets. In summary, in the first step of the protocol, the islet architecture is reconstructed from experimental data using the algorithm recently proposed by Félix-Martínez et al.19 in which nuclear positions obtained through 4′,6-diamidino-2-phenylindole (DAPI) staining and cellular types identified through immunofluorescence (as described in detail by Hoang et al.11,12) are processed in an iterative optimization procedure. This leads to determining the optimal size and position of each cell and obtaining an islet composed of non-overlapping cells. Secondly, based on the reconstructed architecture, cell-to-cell contacts are identified to determine the connectivity properties and to generate the corresponding islet network which allows the user to obtain quantitative metrics to further describe the islet architecture (details about the reconstruction algorithm can be consulted in the original work on the subject19). Finally, basic functional simulations are performed using the modeling approach proposed by Hoang et al.12 in which, based on the pulsatile nature of hormone secretion observed experimentally20,21, each cell is treated as an oscillator, and therefore the islet is represented as a network of coupled oscillators following the connectivity properties of the reconstructed islet.
Given the computational complexity of the algorithms used in this protocol, all the steps involved have been implemented in a standalone application22 with the main objective of approaching these computational tools to all the interested readers regardless of their level of experience in the use of specialized software or programming languages.
NOTE: A schematic diagram of the protocol is shown in Figure 1. A step-by-step description is given is as follows (see Supplementary File 1 for details about the control panels used at every step of the protocol).
Figure 1: Flow diagram. A flow diagram describing the sequential order of the protocol as implemented in IsletLab. Please click here to view a larger version of this figure.
1. Installing IsletLab in Linux
NOTE: Follow the instructions given in sections 2 and 3 of the Supplementary File 2 to install IsletLab in windows or macOS.
Figure 2: The user interface of IsletLab. The interface is composed of three main panels: configuration (1), statistics (2), and graphics (3) panels. The graphics toolbar (4) is located at the bottom of the graphics panel. Please click here to view a larger version of this figure.
2. Islet reconstruction
3. Identifying cell-to-cell contacts
4. Building the islet network
5. Functional simulation of the reconstructed islet
6. Save the project (optional)
7. Save figures (optional)
8. Load project (optional)
9. Restart the reconstruction process and analysis (optional)
The reconstruction of pancreatic islets using the methodology proposed by Félix-Martínez et al.19 is highly dependent on the parameters given to the optimization algorithm (defined in the reconstruction settings). An example of this is shown visually in Figure 3 where reconstructed islets obtained using different sets of parameters are shown. First, in Figure 3A, a reconstruction that included 86.6% of the cells included in the initial data is shown (509 out of 588 cells, initial temperature = 1, iterations factor = 1, acceptance factor = 1). When the initial temperature and the iteration and acceptance factors are increased (initial temperature = 10, iterations factor = 5, and acceptance factor = 5, Figure 3B), a higher percentage (93.37%) of initial cells were included in the reconstructed islets (i.e., 549 out of 588 cells). Even better results can be obtained if much higher values are used, particularly for the iteration and acceptance factors, as illustrated in Figure 3C (initial temperature = 10, iterations factor = 1000, acceptance factor = 500), where the reconstructed islet is composed of 99.15% of the initial cells (583 out of 588 cells). The convergence plots (right column in Figure 3A-C), showing the evolution of overlapped cells as a function of the temperature, must be evaluated to determine how the parameters affect the optimization process. As a rule of thumb, the interaction and acceptance factors must be increased when the reconstructed islet includes a low percentage of initial cells. Consequently, the computing time will inevitably increase, since these factors directly increase the number of iterations evaluated. For instance, the computing time of the first reconstruction described above was 6 s. In contrast, the computing times of the second and third reconstructions were 21 s and 24 min 6 s, respectively.
Figure 3: Islet reconstruction using suboptimal sets of parameters in the reconstruction settings Using suboptimal sets of parameters could lead to a low percentage of experimental cells in the reconstructed islets. (A) Left: 86.6% of experimental cells were included in the reconstructed islet (initial temperature = 1, iterations factor = 1, acceptance factor = 1, computing time = 6 s). Right: convergence plot of the reconstruction process. (B) Left: 93.4% of experimental cells were included in the reconstructed islet (initial temperature = 10, iterations factor = 10, acceptance factor = 5, computing time = 21 s). Right: convergence plot of the reconstruction process. (C) Left: 99.15% of experimental cells were included in the reconstructed islet (initial temperature = 10, iterations factor = 1000, acceptance factor = 500, computing time = 24 min, 8 s). Right: convergence plot of the reconstruction process. The arrows in the convergence plots indicate the initial and final number overlapped cells of the reconstruction process (before the postprocessing phase of the reconstruction algorithm). Please click here to view a larger version of this figure.
Identification of cell-to-cell contacts from the reconstructed islet depends on the value of the contact tolerance parameter (defined in the reconstruction settings) as illustrated in Figure 4A–C, where the cell-to-cell contacts (represented by black lines), identified from the reconstructed architectures shown in Figure 3A–C, are presented. For instance, if a contact tolerance of 1 µm is defined, as in Figure 4A, only 290 cell-to-cell contacts are identified. In contrast, if the contact tolerance is increased to 2 µm, as in Figure 4B,C, the total contacts identified increased to 636 and 731, respectively (see the statistics panel in Figure 4A–C). These differences can also be noticed in the visual representation of the cell-to-cell contacts shown in the left column of Figure 4A–C, as the number of contacts between cells clearly increases as a higher value of the contact tolerance is used. It is worth highlighting that the number of contacts also depends on the number of cells included in the reconstructed islets, and therefore, the combination of the temperature parameter, iterations and acceptance factors, and contact tolerance ultimately determine the connectivity of the reconstructed islet, which is reflected on the islet networks formed and the corresponding network metrics, as shown in the right column of Figure 4A–C. The network plot allows the user to visualize how the different cells are connected. Quantitatively, connectivity properties of the islet are described in terms of the following network metrics: average degree, density, average clustering coefficient, efficiency, and diameter (details about these metrics can be consulted in section 9 of the Supplementary File 2).
Figure 4: Effect of the contact tolerance parameter in the identification of cell-to-cell contacts. (A-C) Left: cell-to-cell contacts identified from the reconstructed islets shown in Figure 3A–C (290, 636, and 731 total contacts in panels A, B, and C, respectively). Values used for the contact tolerance parameter were 1 µm (A) and 2 µm (B and C). Note that the number of cells included in the reconstructed islets also affects the number of cell-to-cell contacts identified. Right: networks generated from the cell-to-cell contacts are shown in the corresponding left column. Note the impact of the connectivity on the network metrics is highlighted in the statistics panel. Please click here to view a larger version of this figure.
Finally, once the islet has been reconstructed and the cell-to-cell contacts have been identified, a functional simulation can be performed (only when a compatible GPU is available). Typical simulation results are shown in Figure 5, including the summed oscillations of the different cell populations (ɑ, β, and δ-cells) and the whole islet (upper plot of the graphics panel in Figure 5). This figure shows the phase differences over time between the different cell populations as a result of the connectivity and interaction properties and allows the user to determine the contribution of each cell population (red, green, and blue lines) to the oscillatory behavior of the whole islet (black line). For instance, the upper panel of Figure 5 suggests that, at the population level, ɑ and β-cells oscillate completely out of phase, while δ-cells oscillate out of phase with ɑ and β-cells. Moreover, according to the simulation, the oscillatory behavior of the islet is dominated by the oscillations of the ɑ-cells, although the effect of the other cell populations can be also noticed. Note that the oscillatory signals of all the islet cells are saved automatically in a data file (see Table 1 and section 13 in Supplementary File 2), thus allowing the user to perform a detailed analysis of the simulation results. As a complement, the islet synchronization index, which reflects the phase coherence of the oscillations, is also calculated and displayed (bottom plot of the graphics panel in Figure 5). Note that the synchronization index ranges from 0 to 1, where 0 and 1 indicate a null and total synchronization between all the cells in the islet, respectively. The synchronization index plot can be therefore interpreted as a visualization of how the synchronicity between islet cells varies over time as a result of the connectivity and interaction properties of the reconstructed islet. Since the simulation performed is based on the idea of coupled oscillators12 and heavily depends on the connectivity of the reconstructed islet, it is key to reach an acceptable islet reconstruction and cell-to-cell connectivity before performing a functional simulation.
Figure 5: The simulation parameters are defined in the configuration panel of the simulation tab. The results of the simulation are shown in the simulation tab of the graphics panel where the summed oscillatory behavior of the different populations of cells (ɑ, β, and δ) and the whole islet are shown (top). The synchronization index, a measure of phase coherence between the islet cells, is also shown (bottom). Please click here to view a larger version of this figure.
It is worth mentioning that practically at every step of the process, data files are generated. A description of the data files generated can be found in Table 1 and throughout Supplementary File 2.
File | Description |
IsletFileName | Input data (given by the user) |
IsletFileName_initial.txt | Initial islet architecture proposed by the algorithm to as initial step of the reconstruction |
IsletFileName_reconstructed.txt | Reconstructed islet (not posptrocessed) |
IsletFileName_postprocessed_islet.txt | Final reconstructed islet and postrocessed islet |
IsletFileName_processlog.txt | Reconstruction log (optimization algorithm) |
IsletFileName_overlapped_cells.txt | Overlapped cells at the end of the reconstruction process (postprocessing) |
IsletFileName_all_contacts.txt | Adjancency matrix of all contacts |
IsletFileName_aa_contacts.txt | Adjancency matrix of ɑ-ɑ contacts |
IsletFileName_ab_contacts.txt | Adjancency matrix of ɑ-β contacts |
IsletFileName_ad_contacts.txt | Adjancency matrix of ɑ-δ contacts |
IsletFileName_bbbd_contacts.txt | Adjancency matrix of β-β and β-δ contacts |
IsletFileName_bb_contacts.txt | Adjancency matrix of β-β contacts |
IsletFileName_bd_contacts.txt | Adjancency matrix of β-δ contacts |
IsletFileName_dd_contacts.txt | Adjancency matrix of δ-δ contacts |
IsletFileName_Kmat.txt | Interaction matrix used in the simulation |
IsletFileName_kuramoto_angles.txt | Results of the Kuramoto simulation |
Table 1: Description of files saved as a part of the project file. Note that the file name used to save the project files are automatically defined by the initial data file selected by the user.
Supplementary File 1: Graphical description of the protocol using the control panels of IsletLab. Please click here to download this File.
Supplementary File 2: IsletLab documentation. Please click here to download this File.
Supplementary File 3: Includes all the files needed to install IsletLab. Please click here to download this File.
The above protocol outlines a practical approach to reconstruct and analyze pancreatic islet architectures using novel computational algorithms. The main objective of this work is to enable the islet research community to derive quantitative metrics to characterize the morphological and connectivity properties of pancreatic islet architectures and to evaluate the possible functional implications of such properties via computational simulations.
While the algorithms adopted in this protocol have been previously described in detail12,19, a direct and user-friendly implementation was lacking due to their relative complexity, thus limiting their use as a complementary tool to the experimental and theoretical work.
Firstly, a recent algorithm proposed by Félix-Martínez et al.19 is used to reconstruct the islet architectures from experimental data (e.g., nuclear coordinates and cell type). As a result, the user obtains an islet architecture composed of non-overlapping spherical cells with radii automatically assigned in accordance with the reported experimental distributions. In practice, the reconstruction algorithm is an iterative optimization procedure that becomes expensive from the computational standpoint as the number of cells in the islet increases. For this reason, it is highly recommended to use a multiprocessor system to take advantage of the parallel processing implementation of the algorithm described in this protocol. As described above, a key step for the reconstructing process is to define appropriate values for the parameters involved (i.e., iterations, acceptance factors, and initial temperature), since the computing time will be directly related to the number of iterations performed, in addition to the number of parallel processes used (i.e., threads parameter in the reconstruction settings). If computing time is not an issue, we strongly recommend using the highest values possible for the iterations and acceptance factors in order to increase the number of iterations performed.
The next steps of the protocol are the identification of cell-to-cell contacts and the generation of the islet network. Both steps are directly related to the reconstruction process and as such, the number of cells included in the reconstructed islets (and therefore the parameters involved), as well as the value of the contact tolerance used, is key to obtaining the best results possible.
Finally, if desired by the user, functional simulations can be performed through the implementation of the model of coupled oscillators proposed by Hoang et al.12 using the connectivity network derived from the reconstruction process to configure the oscillatory system. Given that the simulation process involves solving a system of hundreds or thousands of coupled differential equations (one for each cell in the islet), the simulation algorithm has been implemented taking advantage of the possibility of performing parallel computations using the GPU, thus allowing the user to simulate considerable long simulations in a relatively short computing time. Key steps in the simulation stage of the protocol are to determine the appropriate number of blocks and threads available in the computing platform settings section of the simulation panel, an aspect directly related to the characteristics of the hardware used. The other parameters involved (intrinsic frequency, initial phase, and interaction strengths in the simulation panel), although relevant for the simulation results, are mainly related to the problem under investigation and must be defined by the user after thoughtful consideration in order to represent the desired simulation scenario.
Despite the advantages offered by the protocol, some limitations must be acknowledged. Firstly, the parameters related to the reconstruction process and identification of the cell-to-cell contacts are not unique and might vary from case to case. For this reason, although a rule of thumb can be used to determine the value of the required parameters, a trial-and-error approach is still unavoidable. Another aspect that could limit the applicability of the protocol is the computational resources needed, particularly for the reconstruction and simulation stages of the protocol. Despite these limitations, the fact that programming knowledge is not needed for the implementation of the protocol allows researchers from diverse backgrounds to readily make use of the proposed algorithms that otherwise would remain obscure for the non-specialized user.
Potential uses of the proposed protocol include the visualization of experimental data, comparative analysis of normal and altered islets (e.g., in the presence of type 1 or 2 diabetes), or even comparison between islets from different species using quantitative morphological, structural, and network-based metrics23. Moreover, reconstructed islets using the protocol outlined here can be readily used to generate detailed functional mathematical models in which the connectivity and cell sizes determined by the reconstruction algorithm are complemented with detailed electrophysiological models of pancreatic cells to elucidate the functional implications of the intercellular communication within reconstructed islets.
The authors have nothing to disclose.
G.J. Félix-Martínez thanks CONACYT (Consejo Nacional de Ciencia y Tecnología, México) and the Department of Electrical Engineering of the Universidad Autónoma Metropolitana (México City) for the support given to this project. We thank Dr. Danh-Tai Hoang, Dr. Manami Hara, and Dr. Junghyo Jo for their outstanding work and generosity in sharing the islet architectures that made this work possible with the research community.
CUDA-capable NVIDIA graphics card | Required for the functional simulations | ||
IsletLab | https://github.com/gjfelix/IsletLab (Follow the instructions to download and install the application.) |