Cell dynamics and motility

Cell motility driven by the cytoskeleton is modelled within the CPM using a modified Metropolis algorithm which consists of a series of stochastic pixel-copy attempts, described in more detail in Supplementary Methods (Cell dynamics and motility) in S1 Text [33,35].

One pixel in the simulation was taken to be equal to 3µm, as this seemed to be a reasonable trade of between cellular spatial detail and computational speed. Given this pixel dimension, a typical cell in the simulation is 8x8 pixels for an area or 200um². Cells in the simulation were found to have an average speed of ~0.1 pixel/MCS, which equated to 0.2 microns/MCS. This speed was determined by running multiple simulations of a cell without any hindrance and taking an average of the difference between the current and previous center of mass (COM) values. To calculate the real time equivalent of one MCS, maximum fibroblast migration speed during wound healing was considered as a reference, which peaks towards the end of the healing process with a speed of 40 µm/h [36]. Therefore, one MCS was calculated to be 27 secs (0.3*3600/40).

Cell types, volume, surface and adhesion

The model consists of fibroblasts, myofibroblasts, macrophages, senescent myofibroblasts and ECM defined as individual cell types with distinct properties, as shown in Fig 1. The dermal layer is composed of ECM and resident fibroblasts, whereas the wound is populated by M2-polarised macrophages. Fibroblasts differentiate into myofibroblasts through mechanisms described in later sections. Myofibroblasts can either undergo apoptosis or become senescent myofibroblasts. Terms in the effective energy equation describing cell volume and surface, and cell adhesion are presented in the Supplementary Methods in S1 Text.

Cell growth and proliferation

Within the model, cell growth is limited to fibroblasts, myofibroblasts and macrophages. As discussed previously, PDGF is a primary mediator of fibroblast and myofibroblast migration, proliferation, and ECM production within the wound [37,38]. Hence, fibroblast and myofibroblast growth were modelled by increasing cell target volume according to PDGF concentration using the Monod growth equation given as,

(1)

Where is PDGF concentration at the cell’s COM, is the concentration at which cell growth is half its maximum, and is the maximum cell cycle time for fibroblasts and myofibroblasts. Similarly, CSF1-dependent macrophage growth is given as,

(2)

Where is CSF1 concentration at the cell’s COM, is the concentration at which growth is half its maximum, and is the maximum cell cycle time for macrophages. The Monod equation relates cell growth to the concentration of a limiting factor, which in this case is PDGF for fibroblasts and myofibroblasts, and CSF1 for macrophages [39].

Cell growth and proliferation are limited by contact inhibition, which can occur through two ways: mechanical stress and contact-dependent growth inhibition [40,41]. Mechanical stress-dependent inhibition was modelled by imposing a volume constraint for mitosis whereby cells undergo mitosis only when they reach their doubling volume and then divide along a randomly chosen axis. Cell doubling volume was taken as twice the original target volume of that cell type (fibroblasts, myofibroblasts or macrophages), with the daughter cells acquiring the target volume of the parent cells.

Contact-dependent growth inhibition was modelled by allowing an increase in cell volume only if the surface of the cell in contact with neighbouring cells, , is below a specified threshold [42]. is given by:

(3)

Where is the cell surface area in contact with the medium and is the cell surface area. The ratio measures how much of a cell’s surface area is not in contact with other neighbouring cells. If is below the threshold, then cell growth is arrested at the current cell volume along with the initial lambda value , and if is above , cell volume is determined by equations 1 and 2.

Cell state transitions, growth factors and cytokines

Fibroblasts, myofibroblasts and macrophages interact by exchanging growth factors. Macrophages respond to various external stimuli that can result in a wide range of activation phenotypes [43]. Macrophages within the model shift between classically (M1) and alternatively (M2) activated phenotypes depending on contact with the inflammation field, which represents inflammatory SASP within the model [44]. The inflammatory component of SASP is highly complex and consists of many key factors [32]. However, for the sake of computational feasibility, inflammatory SASP was considered as one chemical field.

If the concentration of the inflammation field at the COM of a macrophage is greater than the threshold parameter INF_thr, then the macrophage secretes MMPs (also referred to as proteinase), characteristic of the M1 phenotype. However, if the inflammation field concentration is less than INF_thr, the macrophage secretes PDGF [45]. MMPs can also be produced by macrophages following contact with ECM, that is, if ECM is surrounding the cell periphery [46]. Since the model begins at the end of the inflammation phase, macrophages are M2 activated and secrete PDGF for fibroblasts and myofibroblasts [47]. For the sake of simplicity, and to focus on senescent cell activity during the proliferative phase of healing, inflammatory SASP is the only form of inflammation considered in this model.

Quiescent fibroblasts become activated in response to PDGF, stimulating the production of CSF1 [48,49]. Myofibroblasts also produce CSF1 for macrophages, as well as PDGF, forming an autocrine loop [50]. In the model, if PDGF concentration at a fibroblast’s COM is above the threshold parameter PDGF_f, then the fibroblast is activated from a quiescent state. Growth factors, especially CSF1, exchange occurs in a cell-cell contact-dependent manner [51]. Therefore, CSF1 secretion by activated fibroblasts and myofibroblasts only occur in cells sharing common surface area with macrophages. Activated fibroblasts and macrophages in the model were removed at a rate of µ [51]. Macrophages also undergo apoptosis following growth factor withdrawal [52,53], which was modelled by removing macrophages with CSF1 concentration less than a threshold parameter CSF1_thr at the cell’s COM.

Myofibroblast differentiation typically requires growth factor stimulation, along with mechanical stimulation [54]. PDGF is one growth factor that is known to play an important role in granulation tissue formation and myofibroblast differentiation during tissue repair [55–57]. In addition, mechanical stimulation is crucial for the formation of the contractile features characteristic of myofibroblasts [58–60]. In the model, myofibroblast differentiation occurs if the value of PDGF at a fibroblast’s COM is greater than PDGF_f and common surface area with ECM is greater than ECM_thr. Every activated fibroblast within the wound region in the model has a chance of differentiation that is calculated by drawing a random integer from a binomial distribution with probability P_MF. Since myofibroblasts are known to produce TIMPs, a simple mechanism to inhibit proteases was included, whereby MMP concentration at a myofibroblast’s COM was reduced by the MMP threshold MMP_thr [61]_. An important feature of fibroblasts and myofibroblasts is their ability to produce large amounts of ECM. Fibroblasts and myofibroblasts produce ECM if PDGF concentration at the cell’s COM is above the threshold parameter PDGF_f. The amount of ECM produced by myofibroblasts (ECM_Myof) is assumed to be double that produced by fibroblasts (ECM_Fib)_. This value was selected to be most appropriate after running multiple preliminary model simulations with different parameter values. ECM degradation by MMP occurs by removing ECM ‘cells’ that have a MMP concentration at their COM greater than MMP_thr.

Myofibroblast activity can resolve in many ways. Myofibroblasts can undergo apoptosis due to release of mechanical tension or exposure to pro-apoptotic inflammatory cytokines, de-differentiate to a fibroblast phenotype or become senescent [62]. To model apoptosis due to release of mechanical tension, myofibroblasts that shared common surface area with ECM below a threshold represented by the parameter ECM_thr, were removed [63]. Apoptosis by exposure to inflammation was modelled by removing a cell if concentration of the inflammatory SASP field at the COM of the cell was greater than the threshold parameter INF_thr [64]. The chance of a myofibroblast becoming senescent was calculated by drawing a random integer from a binomial distribution with probability P_SNC. Senescence can be induced in myofibroblasts through the matricellular protein CCN1 during the mid to late stages of healing [15,16,20]. Therefore, a time constraint T_SEN was set for the induction of senescence to limit it to the mid to late stages of the repair process. In keeping with this, if time is less than T_SEN, a myofibroblast in the model with common surface area with ECM that is greater than the parameter ECM_thr will become a senescent myofibroblast. Senescent myofibroblasts produce two distinct types of SASP: a fibrogenic SASP consisting of PDGF and ECM lasting for about three days (T_NIS), followed by a fibrolytic SASP consisting of CSF1, Inflammation and MMP. This value for T_NIS was chosen because preliminary work suggests that NOTCH-mediated fibrogenic SASP and juxtacrine secondary senescence is prevalent up to approximately three days after senescence activation [32,65].

In addition to CCN1-induced senescence, mechanisms of secondary senescence include juxtacrine and paracrine senescence, which are more prevalent during the fibrogenic and fibrolytic phases of the senescence program respectively [32]. Therefore, within the model, the juxtacrine mechanism involves induction of senescence if a myofibroblast is in contact with a senescent cell in its fibrogenic SASP phase, and if PDGF concentration at the myofibroblast’s COM was greater than the threshold parameter SNC_thr. For paracrine senescence, if a myofibroblast is neighbouring a senescent cell in its fibrolytic SASP phase and had an inflammatory SASP field concentration greater than INF_thr, then the cell would become senescent. Senescent cells during wound healing are removed by immune cells, e.g., phagocytosis by macrophages [66]. Hence, senescent cells within the model are removed on contact with macrophages to model phagocytosis. They also have an equal chance of getting removed if the concentration of the inflammation field at the senescent cell’s COM is greater than INF_thr, to account for other immune-surveillance mechanisms.

The governing reaction-diffusion equations for the four chemical fields in the model are given as below:

(4)

(5)

(6)

(7)

Where represent the concentrations of the chemical fields at pixel at time , D represents the diffusion coefficients, represents the decay constant and represents the rate of secretion for the fields PDGF, CSF1, INF and MMP. All chemical fields were set to no flux in the x and y axes. The solver ‘DiffusionSolverFE’ within CompuCell3D was used to solve the PDEs. Note that for simplicity, and to correct for the limitations of a 2D model, diffusible species are modelled as if they can diffuse across cells. Lastly, Dermal wound closure rate was calculated as the rate at which pixels within the wound area were occupied by cells.

Chemotaxis

Chemotaxis refers to cell migration directed towards a chemical stimulus and is an important element in wound healing as it is one of the main mechanisms by which cells are recruited to the wound site. Within the model, chemical field gradients of PDGF and inflammation cause cells to chemotax towards them. Both fibroblast and myofibroblast chemotaxis towards PDGF [67]. Fibroblast migration is directed by orientation of ECM fibres and they travel along the ECM through integrin-collagen adhesions [68]. To model this effect of ECM fibres on cell migration, the chemotaxis strength coefficient was increased to for fibroblasts and myofibroblasts in contact with ECM. Macrophages, which are involved in immune surveillance for senescent cells, chemotax towards the inflammation field produced by senescent cells [69]. Terms in the effective energy equation describing cell chemotaxis are detailed in Supplementary Methods in S1 Text.

Model classifications

To investigate the spatiotemporal dynamics of senescent cells during tissue repair, perturbations to senescent cell dynamics within the model were introduced. Additionally, another model initial state including pre-existing inflammatory senescent cells was created to represent both age-related changes, and the early induction of senescent cells during the inflammatory phase of healing. These inflammatory senescent cells produce inflammatory SASP, CSF1 and proteinase within the model, with all other properties (such as size and contact energies) the same as for senescent myofibroblasts.

To study the changes induced by differences in senescent cell activity alone, no other factors or parameters were changed in this investigation. Two parameters related to senescent cell dynamics in the model were changed to produce the different outcome classifications: The probability of senescence in myofibroblasts, which is dictated by the parameter P_SNC and the time of induction of senescent cells in the model, determined by the time constraint parameter T_SEN. Simply put, the parameter P_SNC controls the population size of senescent cells, and the parameter T_SEN controls when senescent cells are induced at the wound site. Original model values are 0.15 for P_SNC and 12 for T_SEN (see Table A in S1 Text).

To investigate changes in wound healing in response to a lack of senescent cells, P_SNC was set to zero, with no changes to T_SEN. Conversely, to investigate the effects of increased number of senescent cells within the wound, P_SNC, was set to 0.75, with no changes to T_SEN.

To explore the temporal aspects of senescence, two scenarios were considered. The first scenario was the early induction of senescence during the beginning of the inflammatory phase (representing age-related accumulation of senescent cells), for which the model with pre-existing inflammatory senescent cells was used with no other changes. The second scenario was the late induction of senescent cells during the later phases of healing; in this case, for the model, P_SNC was not altered, but T_SEN was set to 15 days. Three replicate runs were performed for each classification.

Multidimensional sensitivity analysis

To investigate the trade-offs between the two parameters, probability of senescence in myofibroblasts P_SNC and time of senescence induction T_SEN, a multidimensional sensitivity analysis was performed using the parameter sweep feature within CompuCell3D. Parameter value ranges were chosen as evenly spaced values within a defined range. Simulation time series data was collected every 500 MCS (model time step; equal to 3.75 hours) for each parameter set considered. A total of 25 simulations were run.

Particle swarm optimisation parameter search

The wound healing model has many parameters, some of which are not available in the literature. To determine these parameters, we used a Particle swarm Optimization (PSO) approach [70]. The metric we used to describe the quality of a particular set of parameters was determined using relative error between simulation output and data from literature where possible. This includes cell population profiles for fibroblasts, myofibroblasts, macrophages and senescent myofibroblasts, ECM production and rate of wound closure, which are shown in Fig A in S1 Text. The parameters within the wound healing model that we varied are fibroblast activation PDGF threshold (PDGF_f), PDGF concentration threshold for myofibroblast juxtacrine senescence (SNC_thr), proteinase threshold for ECM breakdown (MMP_thr), myofibroblast deactivation ECM threshold (ECM_thr), Inflammation threshold (INF_thr) and CSF1 threshold for macrophage depletion (CSF1_thr) (Table B in S1 Text). For more information see S1 Text.

Model classifications reveal that varying spatiotemporal dynamics of senescent cells lead to distinct tissue repair outcomes

To demonstrate the full range of senescent cell function within wound healing, a model of healthy wound healing with baseline parameters was first developed. This model was used to explore the spatiotemporal dynamics of senescent cells within healthy wound healing. Successful wound healing with appropriate levels of ECM, cell composition, and cytokine and growth factor concentrations depends on multiple model parameters. Senescent cell dynamics within the model were primarily controlled by two parameters. These are the probability of senescence in myofibroblasts, which is dictated by the parameter P_SNC and the time of induction of senescent cells in the model, determined by the time constraint parameter T_SEN. Varying these two parameters around their healthy healing simulation baseline values (see Table A in S1 Text) revealed four different scenarios of dysregulated tissue repair ranging from chronic wound to fibrosis. These classifications were based on transient model dynamics and the final simulation state at 18 days.

Chronic wound inflammation resulting from an increased percentage of senescent cells

The probability of myofibroblast senescence P_SNC was increased from 0.15 to 0.75 to examine the model’s response to a high percentage of senescent cells, with no changes made to the time of senescence induction parameter T_SEN. The increased number of senescent cells, as shown in Fig 5C, resulted in a chronic wound outcome as shown in Fig 4. Although, chronic wounds involve several other dysregulated mechanisms, no other parameters were changed here with the aim of exclusively investigating the effects of the senescent cell population size and dynamics on the repair process. This chronic wound model classification is characterised by insufficient ECM production (Fig 5A), and an accumulation of inflammatory and fibrolytic factors namely, CSF1 (Fig 5I), inflammatory SASP (Fig 5G) and MMP (Fig 5H), compared to its healthy wound healing model counterpart. The corresponding spatial configurations of these characteristics are shown in Fig 4: Senescent cells and macrophages accumulate at the chronic wound site as a result of inefficient immunosurveillance, because the wound macrophages are unable to appropriately handle the high senescent cell load in this simulation. The simulation snapshots also show insufficient ECM deposition; additionally, MMP, inflammatory SASP and CSF1 accumulate at the wound site, whereas total PDGF levels are reduced especially at day 18.

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Fig 4. Simulation of chronic wound dynamics in a dermal patch of size 600 µm x 600 µm due to a high percentage of senescent cells.

This figure shows snapshots of spatial configuration vs time for the progression of a simulated wound due to an excessive number of senescent cells, which results in a chronic wound. The model includes fibroblasts, myofibroblasts, macrophages, ECM and senescent myofibroblasts, and chemical species including inflammatory SASP, CSF1, PDGF and MMP. Top row: Snapshots of the simulation cell field at different time points with fibroblasts (blue), myofibroblasts (green), macrophages (brown), ECM (yellow) and senescent myofibroblasts (pink). Snapshots of simulation chemical fields are shown from the second to the last row; Second row: Inflammatory SASP, Third row: CSF1, Fourth row: PDGF, Fifth row: MMP. Fields are shaded where, red corresponds to the maximum value specified in the first snapshot panel for each field, and blue corresponds to zero (shown in the colour bar at the top). Snapshots are shown for the time points, left to right, day 0, 1, 3, 5, 7, 12 and 18.

https://doi.org/10.1371/journal.pcbi.1012298.g004

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Fig 5. Simulation time series for chronic wound dynamics in a dermal patch of size 600 µm x 600 µm due to a high percentage of senescent cells, shown for model cell types, rate of wound closure and model chemical fields.

This figure shows the simulation time series for the progression of a simulated chronic wound due to an excessive number of senescent cells, which results in a chronic wound. Number of cells and total chemical field are shown on the y axis and time (day) is shown on the x axis. Solid lines represent replicate simulation time series for the chronic wound scenario, and the dotted lines in all plots represent simulation time series from the healthy physiological wound healing model (Fig 3), which is included for comparison. Plot are shown for A: ECM, B: Myofibroblasts, C: Senescent myofibroblasts, D: Fibroblast, E: Macrophages, F: PDGF, G: Inflammatory SASP, H: MMP, I: CSF1 and J: Induction of senescence. For the time series plots A-I, the three shades of grey represent the different replicate runs as indicated in the legend (since the model is stochastic). For the plot J, different colours represent the different mechanisms of senescence induction, as indicated in the legend; red: paracrine secondary senescence, blue: juxtacrine secondary senescence and orange: CCN1-induced primary senescence. Replicate runs are not shown for the different mechanisms for ease of readability, but total senescent cell numbers for the three replicate runs are shown in plot C.

https://doi.org/10.1371/journal.pcbi.1012298.g005

ECM production during the late healing stages, which is when most matrix remodelling occurs, is significantly lower compared to its healthy counterpart by day 18 (Fig 5A). The decreased amount of ECM can be attributed to increased production of MMP (Fig 5H) by inflammatory M1-polarised macrophages, and senescent cells as shown by the rise in paracrine senescence compared to the healthy healing model (Fig 5J); as discussed previously, paracrine senescence is prevalent during the inflammatory/fibrolytic SASP phase of senescence. This is coupled with attenuated ECM production from fibroblasts and myofibroblasts due to the drop in PDGF around this time (Fig 5F), in line with the decreased PDGF production because of M2 inflammatory macrophage polarisation.

The decreased production of PDGF also leads to reduced myofibroblast proliferation following day ~11 compared to healthy healing (Fig 5B). However, initial myofibroblast numbers are maintained close to its healthy counterpart since Notch phase (fibrogenic SASP phase) senescent cells promote myofibroblast differentiation through the production of PDGF and matrix components [15,16]. The following decline occurs as senescent cells shift towards an inflammatory fibrolytic phenotype. Furthermore, macrophage numbers remain elevated, compared to the drop in healthy healing at day ~17.5 (Fig 5E). This is the consequence of elevated CSF1 levels from SASP, which along with the inflammation and MMP fields, begins to rise around day ~6 (Fig 5G, 5H and 5I).

Inflammatory SASP has been shown to induce paracrine senescence in surrounding cells [32]. Consistently, paracrine senescence is more prevalent in this scenario compared to healthy healing cells (Fig 5J). Interestingly, the number of fibroblasts within the wound region is slightly increased in this classification (Fig 5D).

The inflammatory and proteolytic activity of senescent cells is usually strongly controlled by macrophage immunosurveillance. However, in this classification, the senescent cell burden is too large for macrophage-mediated clearance resulting in impaired healing.

Fibrotic wound response in the absence of senescent cells

To investigate repair mechanisms in response to a complete removal of senescent cells, the probability of myofibroblast senescence P_SNC was set to zero. The lack of senescent cells (Fig 7C) resulted in a fibrotic response with excessive ECM deposition (Fig 6). The spatial configuration for this response is shown in Fig 6, characterised by: scar tissue formation due to a high level of ECM deposition as shown in the cell field panel; lack of inflammatory SASP due to the absence of senescent cells; high and persistent levels of PDGF; and decreased total MMP levels.

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Fig 6. Simulation of fibrotic wound dynamics in a dermal patch of size 600 µm x 600 µm due to the absence of senescent cells.

This figure shows snapshots of spatial configuration vs time for the progression of a simulated fibrotic wound due to the absence of senescent cells, which results in a fibrotic response. The model includes fibroblasts, myofibroblasts, macrophages and ECM, as well as chemical species including CSF1, PDGF and MMP. Top row: Snapshots of the simulation cell field at different time points with fibroblasts (blue), myofibroblasts (green), macrophages (brown) and ECM (yellow). Snapshots of simulation chemical fields are shown from the second to the last row; Second row: Inflammatory SASP (which is at zero due to the absence of senescent cells; other types of inflammation were not included in this model), Third row: CSF1, Fourth row: PDGF, Fifth row: MMP. Fields are shaded, where red corresponds to the maximum value specified in the first snapshot panel for each field, and blue corresponds to zero (shown in the colour bar at the top). Snapshots are shown for the time points, left to right, day 0, 1, 3, 5, 7, 12 and 18.

https://doi.org/10.1371/journal.pcbi.1012298.g006

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Fig 7. Simulation time series for fibrotic wound dynamics in a dermal patch of size 600 µm x 600 µm due to the absence of senescent cells.

This figure shows the simulation time series for the progression of a simulated fibrotic wound due to the absence of senescent cells, which results in a fibrotic response in the wound. Number of cells and total chemical field are shown on the y axis and time (day) is shown on the x axis. Solid lines represent replicate simulation time series for the fibrotic wound scenario, and the dotted lines in all plots represent simulation time series from the healthy physiological wound healing model, included for comparison. Plot are shown for A: ECM, B: Myofibroblasts, C: Senescent myofibroblasts, D: Fibroblast, E: Macrophages, F: PDGF, G: MMP and H: CSF1. For all the time series plots, the three shades of grey represent the different replicate runs as indicated in the legend (since the model is stochastic).

https://doi.org/10.1371/journal.pcbi.1012298.g007

As stated, this classification shows significantly increased ECM levels compared to healthy healing (Fig 7A). This can be explained in part by elevated PDGF concentration (Fig 7F) and myofibroblast numbers (Fig 7B). Additionally, an important factor contributing to this is the significant decrease in MMP levels compared to healthy healing (Fig 7G). Overall, the simulation shows increased myofibroblast presence and PDGF levels coupled with decreased MMP production to counteract excessive ECM production, all leading to scar tissue production. This can be attributed to insufficient pro-inflammatory polarisation of macrophages by senescent cell factors in the wound, which is necessary for fibrolytic mechanisms during the late stages of healing. This is illustrated by attenuated CSF1 levels (Fig 7H) and a lack of pro-inflammatory SASP (Fig 6), which control macrophage proliferation and pro-inflammatory M1 polarisation, respectively. Furthermore, for this classification, the lack of MMP production by senescent cells contributes to the observed impaired ECM breakdown in the scar tissue.

Therefore, the removal of senescent cells disrupts the balance between fibrogenic and fibrolytic mechanisms within the wound, both necessary for a healthy and controlled matrix reconstitution.

Fibrotic wound response because of delayed induction of senescence

To investigate the effect of a delay in the induction of senescence on wound healing, T_SEN was set to 15 days instead of 12 in the healthy healing model. This means that senescent cells will only appear at the wound site during the later stages of repair. Interestingly, this temporal change resulted in a fibrotic response as shown in Fig 8: This fibrotic response is characterised by an accumulation of ECM as well as senescent cells, as shown in the cell field; the delay in senescent cell induction results in delayed inflammatory SASP production, shown to appear in the day 18 panel.

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Fig 8. Simulation of fibrotic wound dynamics in a dermal patch of size 600 µm x 600 µm when senescent cell induction is delayed.

This figure shows snapshots of spatial configuration vs time for the progression of a simulated fibrotic wound due to the delayed induction of senescent cells during the later stages of healing, which results in a fibrotic response. The model includes fibroblasts, myofibroblasts, macrophages, ECM and senescent myofibroblasts, and chemical species including inflammatory SASP, CSF1, PDGF and MMP. Top row: Snapshots of the simulation cell field at different time points with fibroblasts (blue), myofibroblasts (green), macrophages (brown), ECM (yellow) and senescent myofibroblasts (pink). Snapshots of simulation chemical fields are shown from the second to the last row; Second row: Inflammatory SASP, Third row: CSF1, Fourth row: PDGF, Fifth row: MMP. Fields are shaded, where red corresponds to the maximum value specified in the first snapshot panel for each field, and blue corresponds to zero (shown in the colour bar at the top). Snapshots are shown for the time points, left to right, day 0, 1, 3, 5, 7, 12 and 18.

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As expected, senescent cells in this model classification rise around day ~15.5 (Fig 9C). The resulting fibrotic response is accompanied by elevated ECM levels compared to the healthy healing simulation (Fig 9A). A small drop in ECM is observed, coinciding with an increase in MMP levels at around ~day 18 (Fig 9H), which otherwise remained significantly low throughout the simulation. This response, along with small increases in inflammatory SASP and CSF1 (Fig 9G-H and inflammatory SASP panel shown in Fig 8) implies the shift of senescent cells to an inflammatory phenotype at this time point. MMP levels peak at day 18 as they are produced by senescent cells in their inflammatory phase and M1 polarised macrophages, which is triggered by this short increase in inflammatory SASP (Fig 9G). However, this fibrolytic activity is too late to attenuate the fibrotic response by breaking down the scar tissue. Furthermore, due to the delay in MMP activity, ECM levels remain elevated despite a drop in myofibroblast levels due to senescence induction (Fig 9B). ECM production here is supported by PDGF levels which remain elevated compared to its healthy counterpart as it is produced by fibrogenic phase senescent cells (Fig 9F). CSF1 levels also remain low (Fig 9I) but do not have a major impact of macrophage numbers (Fig 9E). Aside from CCN1-induced senescent cells, juxtacrine secondary senescence is prevalent (Fig 9J). As discussed, this is in accordance with previous work showing that juxtacrine senescence is accompanied by NOTCH-induced fibrogenic SASP rich in PDGF and ECM components [71]. The lack of paracrine secondary senescent cells here is congruent with the lack of fibrolytic activity in the wound model.

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Fig 9. Simulation time series for fibrotic wound dynamics in a dermal patch of size 600 µm x 600 µm when senescent cell induction is delayed.

This figure shows the simulation time series for the progression of a simulated fibrotic wound due to the delayed temporal induction of senescent cells during the later stages of healing, which results in a fibrotic response. Number of cells and total chemical field are shown on the y axis and time (day) is shown on the x axis. Solid lines represent simulation time series for this fibrotic wound scenario, and the dotted lines in all plots represent simulation time series from the healthy physiological wound healing model, included for comparison. Plot are shown for A: ECM, B: Myofibroblasts, C: Senescent myofibroblasts, D: Fibroblasts, E: Macrophages, F: PDGF, G: Inflammatory SASP, H: MMP, I: CSF1 and J: Induction of senescence. For the time series plots A-I, the three shades of grey represent the different replicate runs as indicated in the legend (since the model is stochastic). For the plot J, different colours represent the different mechanisms of senescence induction, as indicated in the legend; red: paracrine secondary senescence, blue: juxtacrine secondary senescence and orange: CCN1-induced primary senescence. Replicate runs are not shown for the different mechanisms for ease of readability, but total senescent cell numbers for the three replicate runs are shown in plot C.

https://doi.org/10.1371/journal.pcbi.1012298.g009

In this scenario, due to the timing of senescence induction in the wound, the existing fibrogenic activity of the repair process is augmented by senescent cells which are still in their NOTCH-induced fibrogenic SASP phase, rich in PDGF and ECM in the model [32]. This overlap of fibrogenic activity, with a lack of fibrolytic activity leads to an overall fibrotic response. This lack of fibrolytic activity is due to a delay in the shift to an inflammatory senescence phenotype and insufficient macrophage M1 polarisation during late-stage healing, both of which are required to assist in ECM remodelling.

These results show that aside from SASP composition and secondary senescence mechanisms, the temporal aspect of senescence induction is also a crucial factor in repair outcomes. To summarise, the existing fibrogenic wound activity in this scenario was strengthened by senescent cells, which eventually shift to a fibrolytic phenotype. However, the shift is too late to repair the scar tissue due to a disruption in the sequence of repair mechanisms.

Inflammatory SASP from pre-existing senescent cells leads to chronic wound inflammation

Next, the added effect of inflammatory SASP from pre-existing senescent cells in wound healing was investigated. This scenario represents senescence induction during the early inflammatory phase of the wound healing process, as well as pre-existing senescent cells as seen with age-related accumulation of senescence. To this end, inflammatory senescent cells were introduced at the start of the model simulation with no other parameter changes (Fig 10). This classification simplistically represents an ageing or a diabetic wound, both of which are accompanied by an accumulation of inflammatory senescent cells, which is shown in the first simulation cell field snapshot at day 0 in Fig 10. High levels of inflammatory SASP are also prevalent at day 0, representing increased systemic inflammation, as seen with age. Similarly, MMP and CSF1 levels are also high throughout, whereas PDGF levels are significantly reduced (Fig 10).

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Fig 10. Simulation of chronic wound dynamics in a dermal patch of size 600 µm x 600 µm due to pre-existing (inflammatory) senescent cells.

This figure shows snapshots of spatial configuration vs time for the progression of a simulated chronic wound due to pre-existing senescent cells which produce inflammatory SASP; this represents wound healing during ageing, which is accompanied by an accumulation of senescent cells, as well as senescence induced during the inflammatory phase of the wound healing process, resulting in a chronic wound. The model includes fibroblasts, myofibroblasts, macrophages, ECM, pre-existing (inflammatory) senescent cells and senescent myofibroblasts, and chemical species including PDGF, MMP, inflammatory SASP and CSF1. Top row: Snapshots of the simulation cell field at different time points with fibroblasts (blue), myofibroblasts (green), macrophages (brown), ECM (yellow), pre-existing inflammatory senescent cells (red) and senescent myofibroblasts (pink). Snapshots of simulation chemical fields are shown from the second to the last row; Second row: Inflammatory SASP, Third row: CSF1, Fourth row: PDGF, Fifth row: MMP. Fields are shaded, where red corresponds to the maximum value specified in the first snapshot panel for each field, and blue corresponds to zero (shown in the colour bar at the top). Snapshots are shown for the time points, left to right, day 0, 1, 3, 5, 7, 12 and 18.

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Senescent cell numbers remained steadily elevated throughout the model simulation after an initial drop in numbers at around ~day 2, due to macrophage-mediated clearance (Fig 11C). Macrophage immunosurveillance here is mediated by inflammatory SASP produced by the pre-existing senescent cells, which attracts macrophages towards senescent cells in the model. Inflammatory SASP rises sharply at around ~day 1 followed by a decrease at ~day 2.5 and then continues at steady levels, with levels much higher compared to the healthy healing simulation (Fig 11G).

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Fig 11. Simulation time series for chronic wound dynamics in a dermal patch of size 600 µm x 600 µm due to pre-existing (inflammatory) senescent cells.

This figure shows the simulation time series for the progression of a simulated chronic wound due to pre-existing senescent cells; this represents wound healing during ageing, which is accompanied by an accumulation of senescent cells, as well as senescence induced during the inflammatory phase of the wound healing process, resulting in a chronic wound. Number of cells and total chemical field are shown on the y axis and time (day) is shown on the x axis. Solid lines represent simulation time series for this chronic wound scenario, and the dotted lines in all plots represent simulation time series from the healthy physiological wound healing model, included for comparison. Plot are shown for A: ECM, B: Myofibroblasts, C: Total senescent cells, D: Fibroblasts, E: Macrophages, F: PDGF, G: Inflammatory SASP, H: MMP, I: CSF1 and J: Induction of senescence. For the time series plots A-I, the three shades of grey represent the different replicate runs as indicated in the legend (since the model is stochastic). For the plot J, different colours represent the different mechanisms of senescence induction, as indicated in the legend; red: paracrine secondary senescence, blue: juxtacrine secondary senescence and orange: CCN1-induced primary senescence. Replicate runs are not shown for the different mechanisms for ease of readability, but total senescent cell numbers for the three replicate runs are shown in plot C.

https://doi.org/10.1371/journal.pcbi.1012298.g011

The same pattern is observed with other factors produced by senescent cells including MMPs (Fig 11H) and CSF1 (Fig 11I), coinciding with the senescent cell levels. MMP levels remain chronically elevated resulting in excessive breakdown of ECM (Fig 11A). Rising CSF1 levels result in uncontrolled macrophage proliferation (Fig 11E-I). Aside from triggering macrophage immunosurveillance, pro-inflammatory SASP also induces pro-inflammatory macrophage polarisation (Fig 11G). The rising number of inflammatory macrophages also contributes to increased MMP production alongside that of senescent cells.

Pro-inflammatory M1 polarisation of macrophages also means decreased PDGF production, as shown in Fig 11F. This results in decreased fibroblast proliferation (Fig 11D) and overall ECM production by fibroblasts and myofibroblasts (Fig 11A). Myofibroblast population was significantly reduced compared to healthy healing as shown during the first 7 days of the mid healing stage (Fig 11B). This is due to decreased PDGF production by M1 polarised macrophages and inflammatory SASP-producing senescent cells, resulting in decreased myofibroblast differentiation. However, myofibroblast numbers during the later time points match that of healthy healing during which time myofibroblasts usually begin to be cleared out from the wound site.

Insufficient PDGF production leads to attenuated fibroblast levels, as stated previously (Fig 11D). Interestingly, in this classification, the number of fibroblasts was decreased compared to the chronic wound dynamics shown in Fig 5, which could imply decreased fibroblast activation from quiescence. Furthermore, the more prevalent mechanism for secondary senescence in this classification is paracrine, with minimal juxtacrine induction (Fig 11J). This makes sense since paracrine senescence is more associated with an inflammatory SASP compared to juxtacrine senescence, as discussed previously. Lastly, this model classification exhibited greater run-to-run variability (Fig 11).

Sensitivity analysis reveals that deviation from the tightly controlled senescence program during wound healing leads to dysregulated repair mechanisms

To explore any trade-offs between the population size of senescent cells and the time of senescence induction during wound healing, a multidimensional parameter sweep of probability of myofibroblast senescence P_SNC and senescence induction time constraint T_SEN was performed (see methods). Simulations were run for each parameter set by increasing and decreasing parameter values around their baseline values. For each simulation, cell population and chemical concentrations were examined, as shown for ECM in Fig 13, and for myofibroblasts, macrophages, senescent cells, PDGF, CSF1, Inflammatory SASP and MMP in Figs B-H in S1 Text. Three regions of the parameter space were identified as shown by the final simulation states at day 18 of the parameter sweep in Fig 12, where blue indicates fibrotic wound, red indicates chronic inflammation and green indicates healthy healing.

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Fig 12. Wound healing model simulation snapshots of the last time point from multidimensional parameter sensitivity analysis for variations in the parameters probability of myofibroblast senescence (P_SNC) and senescence induction time constraint (T_SEN) showing regions with distinct repair dynamics.

This plot shows the model simulation snapshots of the final time point ~day 18 from a pairwise parameter sweep of the parameters: percentage of myofibroblast senescence P_SNC (shown vertically on the left) and senescence induction time constraint T_SEN (shown horizontally at the top), around their baseline values (provided in Table A in S1 Text). Along with the different values included in the parameter sweep for the senescence induction time constraint T_SEN parameter, pre-existing inflammatory senescent cells are also shown to represent senescence induced during the inflammatory phase of the wound healing process (i.e., before T_SEN = 0) which was not explicitly included in this model. Arrows above the T_SEN parameter sweep values show the wound healing phases (inflammation, proliferation and remodelling phases) represented by the T_SEN parameter values. The cell types in the snapshots are fibroblasts (blue), myofibroblasts (green), macrophages (brown), ECM (yellow), pre-existing (inflammatory) senescent cells (red) and senescent myofibroblasts (pink). The boxes highlight regions with distinct repair dynamics for chronic wound inflammation (red border box), healthy healing (green border box) and fibrotic wound response (blue border box).

https://doi.org/10.1371/journal.pcbi.1012298.g012

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Fig 13. Wound healing model multidimensional sensitivity analysis of the amount of ECM vs time for variations in the parameters probability of myofibroblast senescence (P_SNC) and senescence induction time constraint (T_SEN) showing regions with distinct repair dynamics.

The subplots show the model simulation time series for ECM levels in the wound from a pairwise parameter sweep of the parameters: probability of myofibroblast senescence P_SNC (shown vertically on the left) and senescence induction time constraint T_SEN (shown horizontally at the top), around their baseline values (provided in Table A in S1 Text). Along with the different values included in the parameter sweep for the senescence induction time constraint T_SEN parameter, pre-existing inflammatory senescent cells are also shown to represent senescence induced during the inflammatory phase of the wound healing process (i.e., before T_SEN = 0) which was not explicitly included in the model. Simulation time in days is shown on the x axis and cell population numbers are shown on the y axis. The boxes highlight regions with distinct repair dynamics: chronic wound inflammation (red shaded box), healthy healing (green shaded box) and fibrotic wound response (blue shaded box). The solid blue line represents simulation time series from the pairwise parameter sweep. The dotted lines in all the plots represent simulation time series from the healthy physiological wound healing model were included for comparison.

https://doi.org/10.1371/journal.pcbi.1012298.g013

For all values considered for the probability of myofibroblast senescence P_SNC, the presence of pre-existing senescent cells in the wound site (or the induction of senescence during the inflammatory phase of healing) leads to chronic inflammation and an inability for the wound to resolve (red boxed and shaded subplots in Figs 12, 13 and B–H-H in S1 Text). As shown in the plots, the chronic wound formation is due to insufficient ECM production, myofibroblast differentiation and PDGF levels, along with high levels of macrophages, MMP, CSF1 and inflammatory SASP. Most cellular and chemical components are similar except for the mechanism of secondary senescence, where higher P_SNC values are accompanied by higher numbers of paracrine-mediated secondary senescence. Overall, pre-existing inflammatory senescence is accompanied by increased paracrine senescence compared to juxtacrine. This may be expected since SASP in chronic wound is rich in inflammatory and proteolytic factors but deficient in growth factors and matrix proteins [28,72,73].

When P_SNC was set to zero (blue boxed and shaded subplots top row in Figs 12, 13 and B–H-H in S1 Text), the simulation resulted in a fibrotic response characterised by excessive ECM deposition and lack of the fibrolytic activity that would usually be mediated by senescent cells and inflammatory M1 polarised macrophages. On the other hand, simulations run with low P_SNC and low T_SEN values result in healthy healing (green boxed and shaded subplots in Figs 12, 13 and B–H in S1 Text). The cell populations and chemical concentrations in these simulations are consistent with their healthy healing counterparts. However, ECM levels remain elevated for a longer duration, until day ~9, for the simulation with a low to moderate T_SEN value compared to a low T_SEN value. This is because the short delay in senescence induction leads to overall ECM production in the wound being augmented by senescent cell-derived ECM and PDGF. This does not lead to a fibrotic state since senescent cell and macrophage derived MMP is able to attenuate ECM levels sufficiently and on time.

In contrast, for high P_SNC and high T_SEN values (blue boxed and shaded subplots bottom right in Figs 12, 13 and B–H in S1 Text), simulations result in fibrotic states, due to an increased number of senescent myofibroblasts that are induced during the late stages of healing. Myofibroblast numbers in these simulations remain significantly elevated compared to healthy healing, as do ECM levels. This is because the fibrogenic SASP phase of senescent cells is augmenting the intrinsic fibrogenic activity of the wound. This happens through sustained anti-inflammatory macrophage activity whereby they continue to produce PDGF, which is also elevated, for fibroblasts and myofibroblasts. A lack of macrophage pro-inflammatory polarisation leads to insufficient MMP production. Myofibroblasts and fibroblasts continue to produce excessive amounts of ECM in an uncontrolled manner resulting in the scar tissue as shown. This behaviour is consistently observed regardless of the myofibroblast senescence probability parameter P_SNC (blue boxed and shaded subplots top right in Figs 12, 13 and B–H in S1 Text). That is, simulations with low P_SNC and high T_SEN values also result in a fibrotic wound state. This highlights the importance of time of induction of senescent cells during the repair process. In all these simulations, juxtacrine induction is the dominant mode of secondary senescence, which is to be expected given that fibrogenic SASP is associated with juxtacrine senescence, as discussed previously several times.

On the other hand, for the moderate to high T_SEN value and low P_SNC value (topmost white subplots in Figs 12, 13 and B-H in S1 Text), the fibrotic response is elevated until day ~15, after which it is rescued by the switch to a fibrolytic SASP in the senescent cells, which is indicated by the sharp rise in inflammatory SASP, MMP and CSF1, and a drop in PDGF levels. This is also accompanied by macrophages switching to a pro-inflammatory phenotype, contributing to the drop in PDGF and rise in MMP. However, for the same T_SEN value but high P_SNC values (second to last white subplots in Figs 12, 13 and B–H in S1 Text), simulations are slightly more fibrotic. These are accompanied by sustained myofibroblast activity and higher inflammatory SASP compared to healthy healing. However, these also eventually resolve.

Lastly, simulations run with high P_SNC and low T_SEN values consistently result in a chronic wound state (red boxed and shaded subplots in Figs 12, 13 and B–H in S1 Text). The end of these simulations is accompanied by decreased ECM production and myofibroblast numbers overall. Macrophage numbers remain elevated towards the end of the simulations, when they usually decrease in healthy healing. This is due to increased CSF1 production by inflammatory senescent cells. Increased inflammation mediated by senescent cells is also characterised by higher inflammatory SASP levels, increased MMP and decreased PDGF levels. Moreover, paracrine secondary senescence is also more prevalent compared to healthy healing. Altogether, increased ECM breakdown and accumulation of inflammatory factors result in an improper wound microenvironment and tissue composition. This is because of a high senescent cell burden that is unable to be resolved by macrophage-mediated immunosurveillance despite their pro-inflammatory polarisation.