Agent-based model of angiogenesis simulates capillary sprout initiation in multicellular networks - PubMed (original) (raw)

Agent-based model of angiogenesis simulates capillary sprout initiation in multicellular networks

J Walpole et al. Integr Biol (Camb). 2015 Sep.

Abstract

Many biological processes are controlled by both deterministic and stochastic influences. However, efforts to model these systems often rely on either purely stochastic or purely rule-based methods. To better understand the balance between stochasticity and determinism in biological processes a computational approach that incorporates both influences may afford additional insight into underlying biological mechanisms that give rise to emergent system properties. We apply a combined approach to the simulation and study of angiogenesis, the growth of new blood vessels from existing networks. This complex multicellular process begins with selection of an initiating endothelial cell, or tip cell, which sprouts from the parent vessels in response to stimulation by exogenous cues. We have constructed an agent-based model of sprouting angiogenesis to evaluate endothelial cell sprout initiation frequency and location, and we have experimentally validated it using high-resolution time-lapse confocal microscopy. ABM simulations were then compared to a Monte Carlo model, revealing that purely stochastic simulations could not generate sprout locations as accurately as the rule-informed agent-based model. These findings support the use of rule-based approaches for modeling the complex mechanisms underlying sprouting angiogenesis over purely stochastic methods.

PubMed Disclaimer

Figures

Figure 1

Construction of ABM from experimental time-lapse movies. Each cell is comprised of multiple agents including mNodes, nuclei, inter-, and intra-cellular links as shown in the cartoon (A). The embryoid body movie’s initial frame is converted to an ABM representation to match EC locations. Simulation predictions of sprout initiations (circles) are then compared to observed sprout initiations from the EB movie (squares) and scored as true positive or false positive (B).

Figure 2

ABM workflow. Each of the main subroutines occur sequentially at every time step: section and binding, rate adjustment, and phenotype switching and chemotaxis.

Figure 3

Parameterization and validation of ABM based on a diverse population of EB Movies. The vessel network characteristics of each EB Movie are not uniform and represent a diverse sampling of possible EC network architectures (A–C). Using three EB Movies the ABM Notch Transfer Coefficient was parameterized to predict the number of sprout initiations (D). The Notch Transfer Coefficient value of 0.6 was then tested in all other EB Movies. The number of sprout initiations observed in the EB Movies (red squares) is shown to fall within the 95% confidence interval of ABM predictions (black circles and error bars, E). Perfoming the same sweep of the Notch Transfer Coefficient from 0.0 through 2.0 for all EB Movies demonstrates a similar trend, possessing a linear response region from 0.0 to 1.0 (shaded region is one standard deviation, F,G).

Figure 4

Comparing ABM and Monte Carlo predictions of sprout initiation locations. For each movie, the Monte Carlo (red) and ABM (black) prediction of sprout initiations (x-axis) and true positive frequency (y-axis) were compared (SEM, A). A performance index, defined as the difference between ABM and Monte Carlo true positive frequency, was calculated. The ABM outperforms the Monte Carlo simulation in 7 out of 11 EB Movie simulations (Green Bars, B). C–F, Metrics of EC network structure from each EB Movie plotted as a function of the performance index; no correlation could be discerned.

Figure 5

Parameter optimization using genetic algorithm to improve performance index. The true positive frequency for each generation was plotted in increasing rank order to highlight four distinct outcome populations: no sprouting, low-, medium-, and high-populations (mean ± SD, A). The Notch Transfer Coefficient (α) was plotted using the same rank-ordered generations and found to approach a value of 0.6 (B). To achieve improved true positive frequency the genetic algorithm attempted to minimize the tip cell activation threshold for phenotype switch from quiescent EC to tip cell (C).

References

1. Balazsi G, van Oudenaarden A, Collins JJ. Cell. 2011;144:910–925. - PMC - PubMed
1. Kaern M, Elston TC, Blake WJ, Collins JJ. Nature reviews. Genetics. 2005;6:451–464. - PubMed
1. Blake WJ, Collins JJ. Cell. 2005;122:147–149. - PubMed
1. Laise P, Di Patti F, Fanelli D, Masselli M, Arcangeli A. J Theor Biol. 2011;272:55–63. - PubMed
1. Alber M, Chen N, Glimm T, Lushnikov PM. Physical Review E. 2006;73:051901. - PubMed

Agent-based model of angiogenesis simulates capillary sprout initiation in multicellular networks - PubMed (original) (raw)