A local uPAR-plasmin-TGFβ1 positive feedback loop in a qualitative computational model of angiogenic sprouting explains the in vitro effect of fibrinogen variants
[['Fibrinogen occurs in three variants , whose relative abundance in fibrin affects its structure and pro-angiogenic capacity: ( 1 ) High molecular weight ( HMW , MW 340 kDa , ∼70% , Fig 1A ) ; ( 2 ) a low molecular weight form ( LMW , MW 305 kDa , ∼26% of total fibrinogen , Fig 1B ) that is formed after partial degradation of the carboxy-terminus of the fibrinogen Aα-chain; and ( 3 ) an alternative low-molecular weight form ( LMW’ ) that is formed after degradation of both Aα-chains ( MW 270 kDa , ∼4% of total fibrinogen ) [2] .', 'HMW fibrin has a more open matrix structure , with larger openings between the fibers compared to LMW fibrin ( Fig 1A and 1B ) .', 'LMW fibrin forms more complex networks with denser fibers .', 'Fibrinogen composition is a key determinant of the number of ingrowth spots ( Fig 1C–1E and S2 Fig ) and the depth of sprouting [2–5] .', 'hMVECs proliferate more and show more angiogenic ingrowth in HMW fibrin than in LMW or an unfractionated fibrin mixture [2] .', 'The relative abundance of the three fibrinogen variants is changed in a number of pathologies .', 'For example , the relative abundance of LMW and LMW’ has been found to be elevated in patients with vascular occlusion [6] and in patients with diabetes mellitus [7] , possibly due to enhanced vascular leakage .', 'In cancer patients the fibrinogen levels were elevated , but no changes in the HMW:LMW ratio were found [6] .', 'In post-operative patients [6 , 8] as well as after extensive acute myocardial infarction [8] the levels of HMW increased , followed by a delayed increase of LMW-fibrin [8] .', 'In full-term newborns the levels of HMW have been found to be 25% lower than in adults [9] .', 'Altogether , our in vitro evidence suggests that HMW-fibrinogen promotes angiogenesis more than LMW-fibrinogen .', 'In vivo , increased levels of HMW are typically found in post-operative patients and after extensive myocardial infarction .', 'It is unknown whether these changes in HMW:LMW ratios have clinical relevance , e . g . , in stimulating angiogenesis ( high HMW ) in post-operative patients or in the inhibition ( high LMW ) of angiogenesis in diabetes mellitus patients .', 'During angiogenic ingrowth , the invading hMVEC proteolytically digest the fibrin matrix , suggesting that the low efficiency of in vitro angiogenesis in LMW fibrin is due to differential regulation of proteolysis .', 'Cell-associated fibrinolysis is mostly performed by the trypsin-like protease plasmin [10–13] .', 'Plasmin is the active conversion product of plasminogen , which is mainly produced by the liver and reaches fibrin scaffolds through the blood stream .', 'Conversion of plasminogen into plasmin occurs by plasminogen activators and is highly regulated .', 'Urokinase-type plasminogen activator ( uPA ) and tissue-type plasminogen activator ( tPA ) are secreted by ECs as inactive single-chain proteins .', 'tPA is expressed in quiescent endothelium [14] and is primarily involved in clot dissolution [15] , whereas uPA and its cellular receptor ( uPAR ) are expressed during angiogenesis and control pericellular proteolysis [14 , 16] .', 'ECs secrete inactive , single chain pro-uPA that binds to uPA receptors ( uPARs ) on the membrane of endothelial cells , and is subsequently converted into an active two-chained form .', 'This active membrane-bound uPA-uPAR complex converts plasminogen into plasmin [11] .', 'To balance fibrin degradation , ECs secrete plasminogen inhibitor type 1 ( PAI-1 ) that binds to tPA and uPA for deactivation and the PAI-1-uPA-uPAR complex is internalized [10 , 12] .', 'Alongside plasmin , membrane-type 1 metalloproteinase ( MT1-MMP ) can perform cell-associated fibrinolysis [17] , although its role is still poorly understood: the MT1-MMP inhibitor TIMP-1 had only minor effects on sprouting in a 100% fibrin matrix , but was inhibiting when a 90% fibrin-10% collagen matrix was used [18] .', 'Altogether , based on the available evidence we assume that hMVEC-associated fibrinolysis [2] is primarily due to the plasminogen-plasmin degradation system .', 'To get more insight into a potential role of fibrinogen variants in regulating angiogenesis , here we ask , using mathematical modeling , what differences between HMW and LMW fibrinogen could explain the differences in angiogenic ingrowth that are observed in vitro .', 'LMW fibrin has a reduced number of binding sites for growth factors , including latent-TGFβ1 [19] .', 'TGFβ1 has a strong pro-angiogenic effect in hMVEC cultured on Matrigel [20] and is present in latent form in fibrin matrices .', 'Thus , apart from the structural differences between fibrin variants discussed above , a possible difference between fibrin HMW and LMW matrices is their binding capacity of TGFβ1 .', 'TGFβ1 upregulates PAI-1 and uPAR and is inhibited by TGFβ1 antagonist peptides .', 'TGFβ1 also induces PAI-1 and uPAR expression in hepatic stellate cells [21] and uPA/PAI-1 levels in human tumor tissues [22] .', 'LTBP1 ( latent transforming growth factor β binding protein', '1 ) potentially binds the C-terminus of this Aα-chain: LMW fibrinogen has a reduced number of C-termini of the Aα-chain compared to HMW fibrinogen .', 'The level of LTBP1 is dramatically reduced in LMW fibrinogen fraction I-9 , compared to commercially available fibrinogen and intact fibrinogen fraction I-2 [19] .', 'LTBP1 sequesters latent-TGFβ1 in the plasma to fibrin , resulting in an inactive TGFβ1 reservoir within the fibrin matrix that can locally be activated and released by plasmin [23–25] .', 'Endothelial cells also secrete TGFβ1 [25]; we here assume that this TGFβ1 fraction can be neglected relative to the high bio-availability of TGFβ1 in the matrix .', 'Thus , the reduced number of LTBP1 binding sites in LMW fibrinogen compared to HMW fibrinogen can result in a lower bio-availability of TGFβ1 , thereby reducing angiogenesis .', 'Based on the experimental data on cell-associated fibrinolysis and TGFβ1 that we have discussed above , we suggest that a local uPAR-plasmin-TGFβ1 positive feedback loop drives angiogenesis ( see Fig 2 ) .', 'For simplicity , we assume that all cell-bound uPAR is active , i . e . , it is bound to uPA .', 'Cell-bound uPAR activates plasmin ( Fig 2 , arrow', '1 ) and plasmin locally degrades fibrin and releases and activates TGFβ1 from its latent binding protein ( see Fig 2 , arrow 2 ) .', 'TGFβ1 stimulates the production/expression of uPAR in the protruding cell ( see Fig 2 , arrow 3 ) , whereas nearby cells , which experience only low TGFβ1-dependent uPAR stimulation , are silenced by self-secreted PAI-1 ( see Fig 2 , arrow 4 ) .', 'The basic principle underlying this hypothesis is a reinforced random walk [26] , as introduced to the problem of angiogenesis previously [27 , 28]: ( 1 ) an external growth factor activates endothelial cells to enzymatically modify the ECM near the sprout , and ( 2 ) the endothelial cells move randomly , but with preference up gradient of the modified ECM .', 'More recent models have described specifically the hMVEC-fibrin culture system in silico [29 , 30] .', 'In both these previous models , the location of the novel capillary sprouts vascular ingrowths was specified a priori , prohibiting their use for analyzing the ‘degree’ of angiogenesis , usually measured as the number ingrowth spots in a cell culture [1] .', 'Therefore , a detailed understanding and analysis of angiogenesis in the Koolwijk et al . [1] experimental 3D fibrin sprouting model requires two modifications of the assumptions in the previous work .', 'Firstly , it is unpredictable which cells in the monolayer become sprout leaders ( ‘tip cells’ ) .', 'Thus we cannot pre-assign the location of the tip cells [29 , 30] , or assign the onset of angiogenesis by punching a hole in the basal lamina [31] or by initiating its local digestion [27 , 28] .', 'Also , previous models assumed that endothelial cells follow a gradient of VEGF .', 'The Koolwijk et al . [1]in vitro model does not include growth factor gradients , so we have not included those in the present in silico model .', 'This implies that both the location and the growth direction of sprouts in the present computational model emerge from local cell-cell and cell-matrix interactions .', 'We hypothesize that such sprout initiation mechanisms may exist alongside the established role of the Dll4-Notch network in the selection of tip cells that lead the sprouts [32–35] .', 'Altogether , to explore our hypothesis that the uPAR-plasmin-TGFβ1 positive feedback loop regulates spontaneous ingrowth , we model the plasminogen-plasmin degradation system in combination with a cell-based model of endothelial cell invasion .', 'following previous continuum models [36–38] .', 'We propose that a differential binding activity of TGFβ1 to HMW and LMW explains the higher ingrowth .', 'We developed a computational model to evaluate if this sprouting mechanism can explain the reduced ingrowth in LMW compared to HMW; it is shown that it regulates the spacing of ingrowth spots and is also consistent with a number of additional observations .'], ['To study how endothelial sprouting is reduced in LMW compared to HMW fibrin matrices , we developed a computational model that mimics the in vitro assay by Koolwijk et al . [1] and Weijers et al . [2] .', 'Our hybrid model consists of a cell-based component to describe the endothelial cells and a continuum component to describe the plasminogen-plasmin system .', 'The model represents a cross-section of the in vitro sprouting model ( Fig 3 ) , and is initialized with a monolayer of fifty endothelial cells on top of a fibrin matrix .', 'Fibrin forms a physical obstruction for cells while , at the same time , offering support to the cells as they can adhere to fibrin .', 'Using cell-based modeling , we explicitly describe cell shape , cell motility , cell-cell adhesion , and cell-fibrin adhesion .', 'Each cell has a level of active uPAR , which homogeneously spread over the cell membrane , and each cell secretes PAI-1 into the extracellular space .', 'PAI-1 , and the other extracellular proteins ( fibrin , latent-TGFβ1 , active TGFβ1 , plasminogen , and plasmin ) are modeled as concentration fields .', 'The extracellular proteins interact with one another and with the membrane-bound uPAR ( Fig 2 ) .', 'uPAR activates plasminogen , forming plasmin that degrades fibrin and locally activates latent-TGFβ1 by releasing it from the fibrin matrix .', 'The active TGFβ1 induces the production of uPAR in nearby cells .', 'These reactions form a local positive feedback loop that keeps the invasion of the endothelial cells going .', 'To represent cells and their physical interactions with the fibrin matrix , the cellular Potts model ( CPM ) [40 , 41] was used .', 'For details see Section Fibrin invasion .', 'Briefly , the CPM represents cells on a regular lattice as patches of connected lattice sites .', 'Cells move by copying lattice sites inward or outward , representing the extension and retraction of pseudopodia .', 'To model the physical obstruction imposed by high concentrations of fibrin , the extension probability of a pseudopodium is reduced if it attempts to invade a lattice site with high fibrin concentration .', 'The concentration of fibrin , f ( x → ) , is initialized at a uniform , non-dimensional concentration of f ( x → ) = 1 .', '0 at all lattice sites x → .', 'No fibrin is produced or added in the simulation , such that the concentration of fibrin will stay in the range f ( x → ) ∈ [ 0 , 1 ] .', 'The invasion probability quickly drops for concentrations f ( x → ) > 0 .', '5 , while for f ( x → ) < 0 .', '3 fibrin does not hinder invasion .', 'Fibrin is digested by the plasmin system , as illustrated in Fig 2 .', 'The concentration of uPAR within each cell is modeled by an ordinary differential equation ( ODE ) .', 'A concentration field for uPAR is projected on the CPM grid , with each lattice site that is occupied by a cell having the uPAR concentration of that cell .', 'The concentration of uPAR moves along with the location of the cell after cell movement .', 'A system of coupled partial differential equations ( PDEs , see Section Methods ) describes the reactions between fibrin , TGFβ1 , plasminogen , plasmin , PAI-1 and all fibrin-bound forms .', 'The equations for the plasmin system were based on the continuum model by Diamond et al . [36] , which studies the penetration of uPA and tPA into a fibrin clot in the blood stream .', 'To adopt this model to our problem , we added the uPAR-plasmin-TGFβ1 positive feedback loop , simplified the implementation of fibrinolysis , and deleted the convective terms .', 'Time steps in our model are measured as Monte Carlo step ( MCS ) .', 'One MCS is defined as the number of lattice site update attempts as there are sites in the lattice .', 'It takes about 6000 MCS to simulate a 10 days long experimental assay , similar to the 3D-fibrin sprouting model of Koolwijk et al . [1]; so a MCS represents approximately 2 . 5 minutes in real time .', 'In summary , the model is based on the following mechanistic assumptions: In the in vitro 3D-fibrin sprouting assay by Koolwijk et al . [1] , uroplasmin ( uPA ) and its receptor uPAR were localized specifically at the invading endothelial cells that lead the sprouts [46] .', 'The selection mechanism of these ‘uPAR-rich’ cells in the monolayer is not fully understood .', 'We therefore asked if the uPAR-plasmin-TGFβ1 positive feedback mechanism is sufficient to confine uPAR-expression to the invasive cells .', 'We initialized the cells in our model with a uniform concentration of uPAR ( Fig 4A ) .', 'Random cell movements change the contact-level and contact-duration with fibrin , resulting in local , random differences in the levels of plasmin activation .', 'Fibrin is degraded at sites with a high plasmin activity ( Fig 4B ) , and TGFβ1 is released from the matrix ( Fig 4C ) .', 'The active TGFβ1 induces the expression of uPAR in nearby cells ( Fig 4D ) .', 'The expression of uPAR in more distant cells can also be induced by the released TGFβ1 to some degree , but such uPAR activity is counteracted by the self-secreted PAI-1 .', 'Due to stochasticity , only a few cells in the monolayer can trigger the positive feedback loop sufficiently to overcome inhibition by PAI-1 and gain high levels of uPAR to start ingrowth ( Fig 4E ) .', 'In absence of fibrin-bound latent-TGFβ1 , none of the cells in the monolayer , in a hundred stochastic simulations , manage to gain high levels of uPAR due to the lack of TGFβ1-induced uPAR expression .', 'Thus , our modeling results show that a uPAR-plasmin-TGFβ1 positive feedback loop suffices to select uPAR-rich cells in a monolayer of endothelial cells to form ingrowth spots .', 'Once uPAR-rich cells are selected spontaneously within the monolayer , the uPAR-plasmin-TGFβ1 positive feedback consolidates sprout progression in the model ( see Fig 5 ) .', 'The cell leading the sprout , i . e . , the tip cell , has the highest concentration of uPAR ( see Fig 3E ) in agreement with experimental observations [46] .', 'In agreement with in vitro observations , in the in silico model sprouts branch spontaneously ( see , e . g . , simulation 3 for a constant uPAR production rate of 0 . 003 Relative Units ( RU ) /MCS in Fig 5A ) .', 'This occurs when a cell adjacent to the tip cell moves into another direction , or when a cell higher up in the sprout manages to trigger the feedback loop and starts a branch .', 'Sprouts are not formed in every simulation: due to the stochastic fluctuations in cell shape and movement , in some cases none of the cells activate the positive feedback loop sufficiently to overcome the inhibition of PAI-1 .', 'Similarly , ingrowth is not seen in every in vitro experiment , but is highly variable per cell donor and passage number of the cells within the same donor .', 'In vitro , TNFα is required to induce sprouting of human endothelial cells [1] and the mean tube length increases at higher doses of TNFα .', 'TNFα increases uPA production and the level of cell-bound uPA [1] .', 'To test if the model correctly reproduced this in vitro observation , we mimicked the effect of TNFα by increasing uPAR expression in the endothelial cells .', 'Fig 5A shows a set of simulation results after ten days of sprouting for a uPAR expression level of 0 . 001 , 0 . 002 , 0 . 003 , and 0 . 005 ( RU/MCS ) .', 'In simulations with higher uPAR expression levels , the number of ingrowth spots increases .', 'For each parameter setting , four simulation results for the same parameter settings are shown; these demonstrate the stochasticity of ingrowth frequency and sprout morphology .', 'To quantify sprouting , we defined three measures: the angiogenesis level , the sprouting frequency and the fibrinolysis level .', 'The angiogenesis level simultaneously reflects sprout depth and sprout count ( see Section Methods for the quantification algorithm ) .', 'The blue curve in Fig 5B represents the mean angiogenesis level for all simulations that formed sprouts ( angiogenesis level>0 ) .', 'The sprouting frequency is the number of simulations out of a hundred simulations that formed sprouts ( red curve in Fig 5B ) .', 'The fibrinolysis level , defined as the mean percentage of initial fibrin lattice sites that are invaded by the endothelial cells in all 100 simulations , also increases for higher uPAR expression levels , as is expressed by the green curve in Fig 5B .', 'In summary , an increase of the basal uPAR-bound uPA activity in all cells increases the probability that the uPAR-plasmin-TGFβ1 positive feedback loop is triggered in one of the cells in the monolayer , leading to high uPAR expression and sprout initiation .', 'As a consequence , sprouts form more frequently and more excessively at higher uPAR expression levels .', 'Thus , the model explains mechanically how ubiquitous stimulation of uPAR-bound uPA activity by TNFα leads to confined uPA activity and sprouting .', 'A full quantitative validation of the model is not feasible at present , because only for a few parameters experimental estimates are available , leaving most other parameters as fitting parameters .', 'To avoid overfitting , we have instead selected a set of ‘default’ parameter values for which the model qualitatively reproduces the fibrin culture system ( see S2 Table ) .', 'To validate the model , we then tested if qualitative shifts in the parameter values , corresponding with published experiments , qualitatively reproduce the outcome of three published in vitro experiments of the plasminogen-plasmin degradation system .', 'Firstly , Koolwijk et al . [1] reported that there was no angiogenic ingrowth and tubule formation in fibrin matrices that were made using plasminogen-depleted fibrinogen .', 'In agreement with this observation , there is no ingrowth in our model for low initial level of fibrin-bound plasminogen ( Fig 6A ) .', 'The sprouting percentage , the fibrinolysis percentage , and the angiogenesis level all increased with the initial fibrin-bound plasminogen concentration .', 'Secondly , inhibition of uPAR-bound uPA activity by addition of uPA specific polyclonal antibodies , or prevention of the binding of uPA to uPAR by soluble uPAR or blocking antibodies inhibited capillary-like tube formation dose-dependently ( see Refs .', '[1 , 46] and Fig 6D ( bt + trasylol and bt + H2 ) ) .', 'We mimicked the inhibition of uPAR activity by increasing the decay rate of uPAR .', 'Consistent with the experimental results , Fig 6B shows that this parameter change results in a decrease of the sprouting percentage , the fibrinolysis percentage , and the angiogenesis level .', 'Thirdly , experiments show that there is an optimum PAI-1 concentration for angiogenesis [47]: addition of PAI-1 to implants in wild-type mice enhanced angiogenesis up to 3-fold at low concentrations but inhibited angiogenesis nearly completely at high concentrations .', 'In the 3D fibrin assay , addition of the anti-PAI-1 antibody MAI-2 shows a similar biphasic effect on angiogenesis ( Fig 6D ) : Moderate inhibition enhances tube formation , whereas strong inhibition reduces tube formation .', 'This is due to excessive fibrinolysis , which is incompatible with normal capillary formation [48 , 49] .', 'As for uPAR , we modeled the manipulation of PAI-1 activity by an increase of the decay rate of PAI-1 .', 'Fig 6C shows that the fibrinolysis percentage strongly increases when the decay rate of PAI-1 is increased .', 'High decay rate of PAI results in low PAI-1 activity , and thus in excessive fibrinolysis; no sprouts are formed , but the entire monolayer lowers simultaneously .', 'Low decay rates of PAI-1 result in high PAI-1 activity and sprouting is completely inhibited .', 'Only for intermediate levels of PAI-1 activity we find sprouting , indicated by the peaks in Fig 6C for the sprouting percentage and the angiogenesis level .', 'In conclusion , the model can reproduce three essential validation experiments for the plasminogen-plasmin system .', 'In absence of fibrin-bound latent-TGFβ1 , no sprouts are formed in all 100 simulations with a parameter set for which sprouts formed well in presence of fibrin-bound latent-TGFβ1 in Figs 5B and 6 ( constant uPAR production rate = 0 . 005 RU/MCS , initial fibrin-bound plasminogen concentration = 1 RU , PAI-1 decay rate = 0 . 01 MCS−1 , and uPAR decay rate = 0 . 0095 MCS−1 , using Relative Units , RU , and Monte Carlo Steps , MCS ) .', 'This shows that initialization and consolidation of sprouts can be driven by activity of the proposed positive feedback loop formed by uPAR , plasmin , and TGFβ1 .', 'Next we used our model to design new hypotheses about the mechanisms that reduce the level of angiogenic ingrowth in LMW fibrin matrices compared to HMW matrices .', 'The level of LTBP1 is dramatically reduced in LMW fibrinogen fraction I-9 , which lacks major parts of the C-termini of the Aα-chain , compared to commercially available fibrinogen and intact fibrinogen fraction I-2 [19] .', 'As LTBP1 sequesters latent-TGFβ1 to fibrin , this could result in a lower level of fibrin-bound latent-TGFβ1 .', 'We hypothesize that this reduced level of fibrin-bound latent-TGFβ1 , in combination with our suggested local uPAR-plasmin-TGFβ1 positive feedback , could cause the reduced level of endothelial sprouting in LMW compared to HMW fibrin matrices .', 'If the levels of inactive TGFβ1 in the fibrin matrix are too low , cells are not able to induce a strong enough uPAR-plasmin-TGFβ1 positive feedback loop to overcome the inhibition of PAI-1 and thus will not form sprouts .', 'In line with this hypothesis , Fig 7A shows that the sprouting percentage , the fibrinolysis percentage , and the angiogenesis level decrease with lower initial concentrations of fibrin-bound latent-TGFβ1 in our model .', 'In conclusion , our simulations results suggest that the angiogenic ingrowth is reduced in LMW fibrin matrices compared to HMW matrices due to a reduction in binding sites for LTBP1 .', 'The addition of active TGFβ1 has a biphasic effect on in vitro sprouting [50] .', 'Addition of active TGFβ1 to the assay stimulates sprouting at low doses and inhibits sprouting at high doses of TGFβ1 .', 'To test this biphasic effect in the model , we initialized the model with a homogeneously spread concentration of active TGFβ1 .', 'The medium containing TGFβ1 was refreshed every two days in vitro [50] .', 'We similarly reset the TGFβ1 concentration to the initial value after every two days in the model .', 'Fig 7B shows that TGFβ1 indeed has the reported biphasic effect on angiogenesis in the simulations .', 'At low concentrations of added TGFβ1 ( TGFβ1 = 0 . 5 RU and TGFβ1 = 10 RU in Fig 7B ) , more sprouts are formed than without addition of TGFβ1 ( TGFβ1 = 0 in Fig 7B ) .', 'The uPAR-bound uPA activity in all cells increases due to the overall addition of TGFβ1 , allowing some cells to overcome the inhibitory PAI-1 threshold for triggering the uPAR-plasmin-TGFβ1 positive feedback loop .', 'This is a similar effect as was seen for the stimulation with TNFα above .', 'The upregulation of uPAR-bound uPA activity is too strong at high doses of TGFβ1 , and consequently all cells degrade the matrix .', 'This results in lowering of the complete endothelial cell monolayer , rather than in local sprouting ( TGFβ1 = 1000 RU in Fig 7B ) .', 'In this case , fibrin is quickly degraded and some cells loose contact with the fibrin .', 'Once the cells loose contact with the fibrin layer , they are no longer stimulated to migrate along with the degrading matrix and form the ‘fingers’ show in Fig 7B .', 'In some simulations stacks of cells hovering above the monolayer were left behind .', 'This is of course a model artifact , so we did not take those into account while quantifying the degree of spouting .'], ['Endothelial cells in the in vitro assay of Koolwijk et al . [1] secrete PAI-1 , but it is unknown if all cells , or only the quiescent cells in the monolayer or perhaps only the invading uPAR-rich cells secrete PAI-1 .', 'Interestingly , the uPAR-plasmin-TGFβ1 positive feedback loop resembles reaction-diffusion systems with activator-inhibitor dynamics [51–53] .', 'Activator-inhibitor systems produce periodic patters , so such dynamics could be responsible for regular placement of tip cells in the in vitro assay .', 'Most conditions for activator-inhibitor dynamics are met: The positive feedback loops stimulates local activation of uPAR-bound uPA , and the inhibitor PAI-1 diffuses faster than the “activator” uPAR , which is expressed intracellularly .', 'A missing element for such activator-inhibitor dynamics is that the inhibitor ( PAI-1 ) must be produced locally , whereas we currently assumed that all cells secrete PAI-1 .', 'We are unsure of this assumption: TGFβ1 induces production of uPAR as well as PAI-1 in MVEC cultured on Matrigel [20] , raising the possibility that uPAR-rich cells secrete most PAI-1 and that all conditions for activator-inhibitor dynamics are met .', 'Thus future work should determine the localization of PAI-1 secretion in the 3D-fibrin sprouting assay [1] .', 'Besides the activator-inhibitor dynamics , the closely related substrate-depletion model [52] is a well-studied theoretical model for pattern formation .', 'In our model , plasminogen is the substrate for plasmin production .', 'Conversion of plasminogen at sites of matrix invasion results in depletion of plasminogen in surrounding regions through diffusion .', 'Indeed , plasminogen is a limiting factor for endothelial sprouting in the fibrin assay [1] .', 'Plasminogen depletion has low impact in the current simulations , because we have initialized them with a high , homogeneous concentration of immobile , fibrin-bound plasminogen .', 'However , plasminogen binds fibrin reversibly and can bind to ECs , so this mechanism might regulate the location of ingrowth spots for lower levels of fibrin-bound plasminogen .', 'Interestingly , there is a delay in sprout initiation when the model is initialized with unbound plasminogen .', 'It takes some time to reach high enough concentrations of fibrin-bound plasminogen , which is then converted to plasmin by uPAR for matrix degradation .', 'A key patterning mechanism that is involved in angiogenesis is lateral inhibition by Delta-Notch signaling [32–35] .', 'Cells that have high levels of Delta ligands on their membrane differentiate into so called ‘tip cells’ , which are the leaders of sprouts , and cells with low levels of Delta become ‘stalk cells’ [35] .', 'Lateral inhibition occurs by interaction of Delta ligands with the Notch receptor of neighboring cells , resulting in the suppression of Delta production in those neighbors [32–35] .', 'Lateral inhibition creates a pepper-and-salt pattern of tip and stalk cells , with tip cells surrounded by a rosette of stalk cells in monolayers in silico [54 , 55] .', 'Thus , Delta-Notch signaling alone cannot account for the more widely spaced pattern of uPAR-rich leader cells in a monolayer as observed in vitro [46] .', 'Possibly other regulation mechanisms , e . g . , the proposed uPAR-plasmin-TGFβ1 positive feedback loop , act alongside the Delta-Notch mechanism to distribute tip cells more sparsely .', 'Notably , gene expression levels of Dll4 and Notch4 are significantly higher in endothelial cells cultured in LMW matrices than in HMW matrices [2] .', 'The Dll4 and Notch4 expression differences by themselves cannot explain the reduced ingrowth in LMW fibrin matrices , as specific inhibition of Dll4-Notch was unable to induce recovery of tube formation in LMW .', 'Inclusion of Delta-Notch signaling will likely affect sprout morphology .', 'In simulations of our current model , cells adjacent to the tip cell are also activated by the released TGFβ1 , and they contribute to sprouting .', 'This results in fairly wide , sometimes cyst-like sprouts .', 'In our previous model [29] of the fibrin assay , narrow sprouts formed if only the tip cell secreted proteolytic enzymes for matrix degradation , and cyst-like sprouts formed when the stalk cells contributed to fibrin degradation as well .', 'In this light , Delta-Notch signaling could repress proteolytic activity in cells adjacent to the tip cell , such that thinner sprouts will form .', 'Our model explains differences in ingrowth between LMW and HMW fibrin based on the binding capacity of latent-TGFβ1 .', 'An alternative explanation for the increased ingrowth in HMW fibrin compared to LMW fibrin could be that the ECs can invade the open matrix structure of HMW fibrin more easily .', 'In absence of proteolysis , differences in matrix porosity can explain cell migration speed and persistence [56]; however , with small pore sizes of fibrin ( order 1 μm; see Fig 1 ) and the importance of fibrinolysis for angiogenic ingrowth , small differences in pore size are unlikely to contribute to differences in ingrowth .', 'An alternative , or complementary explanation could lie in differences in the bulk mechanical properties of HMW and LMW fibrin .', 'Indeed mechanical cell-cell communication [57 , 58] through strain-stiffening materials such as fibrin [59] suffices for generating vascular-like patterns [60] .', 'In addition , individual fiber architecture , including fiber thickness and fiber density also affects cell spreading behavior on fibrin substrates independently of the bulk mechanical properties [61] , suggesting that fiber architecture differences ( Fig 1 ) could also contribute to differences in angiogenesis level on HMW and LMW fibrin matrices .', 'The present model reproduces angiogenic sprouting by means of cell-fibrin adhesion and cell-division .', 'A limitation is that the addition of TNFα in the in vitro model inhibits cell division [1] .', 'The general cell invasion mechanism proposed here does not depend on cell division .', 'Alongside the fibrinolysis-driven sprouting mechanisms proposed here , many alternative mechanisms of cell migration during angiogenic sprouting have been proposed that could act alongside or instead of cell division to replenish cells in growing sprouts .', 'A range of models have shown that mutual attraction of endothelial cells suffices for the formation of vascular networks , e . g . , via a chemoattractant [62–70] , via mechanical forces [71 , 72] or via mechanically induced durotaxis [60] , and preferential attraction to elongated structures [73] .', 'Our model could be extended with such sprouting and cell migration mechanisms to replace cell division .', 'A detailed description of the plasminogen-plasmin system is included in our model , but still some simplifications were made .', 'For instance , we did not take into account interactions with matrix metalloproteinases ( MMPs ) .', 'Membrane-type 1 metalloproteinase ( MT1-MMP ) can perform cell-associated fibrinolysis [17] , but only plays a minor role in Koolwijk’s assay [18] .', 'Furthermore , we neglected the low proteolytic activity of pro-uPA [11] , and only modeled active uPAR-bound uPA .', 'Interactions between pro-uPA and plasmin could give interesting dynamics .', 'Venkatraman et al . [37] considered a positive feedback loop in which the initial cleavage of plasminogen into plasmin is more efficient by uPA than pro-uPA , and the conversion of pro-uPA to uPA is driven by plasmin .', 'By the use of a continuum model , they predict that uPA-plasmin activation is bistable in the presence of this positive feedback loop in combination with substrate competition for plasmin .', 'A further limitation of the pre
['Introduction', 'Results', 'Discussion', 'Methods']
['In experimental assays of angiogenesis in three-dimensional fibrin matrices , a temporary scaffold formed during wound healing , the type and composition of fibrin impacts the level of sprouting .', 'More sprouts form on high molecular weight ( HMW ) than on low molecular weight ( LMW ) fibrin .', 'It is unclear what mechanisms regulate the number and the positions of the vascular-like structures in cell cultures .', 'To address this question , we propose a mechanistic simulation model of endothelial cell migration and fibrin proteolysis by the plasmin system .', 'The model is a hybrid , cell-based and continuum , computational model based on the cellular Potts model and sets of partial-differential equations .', 'Based on the model results , we propose that a positive feedback mechanism between uPAR , plasmin and transforming growth factor β1 ( TGFβ1 ) selects cells in the monolayer for matrix invasion .', 'Invading cells releases TGFβ1 from the extracellular matrix through plasmin-mediated fibrin degradation .', 'The activated TGFβ1 further stimulates fibrin degradation and keeps proteolysis active as the sprout invades the fibrin matrix .', 'The binding capacity for TGFβ1 of LMW is reduced relative to that of HMW .', 'This leads to reduced activation of proteolysis and , consequently , reduced cell ingrowth in LMW fibrin compared to HMW fibrin .', 'Thus our model predicts that endothelial cells in LMW fibrin matrices compared to HMW matrices show reduced sprouting due to a lower bio-availability of TGFβ1 .']
['Therapies for a range of medical conditions , including cancer , wound healing and diabetic retinopathy can benefit from a better control over the growth of blood vessels .', 'The chemical properties of fibrin , the material that forms scabs in wounds and can also occur in large concentrations in tumors , can regulate the degree of blood vessel growth ( angiogenesis ) .', 'Angiogenesis can be mimicked in cell cultures .', 'These allow us to modulate the chemical properties of fibrin and study the effect on angiogenesis .', 'Fibrin occurs in high molecular weight ( HMW ) and in low molecular weight ( LMW ) forms .', 'Interestingly , there is more ingrowth of angiogenic-like structures into HMW than in LMW fibrin , but the mechanisms are poorly understood .', 'To get more insight into these , we constructed a computational model .', 'Using the model , we propose and analyse a hypothetical mechanism for sprouting that could explain the differences in endothelial cell sprouting in LMW and HMW fibrin matrices .', 'Our model suggests that cells digest fibrin , thus creating space for ingrowth .', 'At the same time , digestion frees growth factors bound to fibrin , that activates further secretion of digestive enzymes by the cells .', 'We propose that the resulting positive feedback loop spontaneously selects cells in the endothelial monolayer for ingrowth and helps the blood vessel sprout move deeper into the fibrin .', 'This could be a complementary mechanism to lateral-inhibition by Delta-Notch for the selection of leader cells , also called ‘tip cells’ .', 'Our model predicts that endothelial cells in LMW fibrin compared to HMW fibrin show reduced sprouting due to a lower bio-availability of TGFβ1 .']
['medicine and health sciences', 'cardiovascular physiology', 'fibrinogen', 'enzymes', 'endothelial cells', 'enzymology', 'fibrin', 'epithelial cells', 'angiogenesis', 'developmental biology', 'glycoproteins', 'plasmins', 'cellular structures and organelles', 'fibrinolysis', 'animal cells', 'proteins', 'extracellular matrix', 'biological tissue', 'hematology', 'biochemistry', 'signal transduction', 'blood coagulation', 'cell biology', 'anatomy', 'physiology', 'tgf-beta signaling cascade', 'epithelium', 'biology and life sciences', 'cellular types', 'cell signaling', 'glycobiology', 'signaling cascades']