Lattice Percolation Approach to 3D Modeling of Tissue Aging
📝 Abstract
We describe a 3D percolation-type approach to modeling of the processes of aging and certain other properties of tissues analyzed as systems consisting of interacting cells. Lattice sites are designated as regular (healthy) cells, senescent cells, or vacancies left by dead (apoptotic) cells. The system is then studied dynamically with the ongoing processes including regular cell dividing to fill vacant sites, healthy cells becoming senescent or dying, and senescent cells dying. Statistical-mechanics description can provide patterns of time dependence and snapshots of morphological system properties. The developed theoretical modeling approach is found not only to corroborate recent experimental findings that inhibition of senescence can lead to extended lifespan, but also to confirm that, unlike 2D, in 3D senescent cells can contribute to tissue’s connectivity/mechanical stability. The latter effect occurs by senescent cells forming the second infinite cluster in the regime when the regular (healthy) cell’s infinite cluster still exits.
💡 Analysis
We describe a 3D percolation-type approach to modeling of the processes of aging and certain other properties of tissues analyzed as systems consisting of interacting cells. Lattice sites are designated as regular (healthy) cells, senescent cells, or vacancies left by dead (apoptotic) cells. The system is then studied dynamically with the ongoing processes including regular cell dividing to fill vacant sites, healthy cells becoming senescent or dying, and senescent cells dying. Statistical-mechanics description can provide patterns of time dependence and snapshots of morphological system properties. The developed theoretical modeling approach is found not only to corroborate recent experimental findings that inhibition of senescence can lead to extended lifespan, but also to confirm that, unlike 2D, in 3D senescent cells can contribute to tissue’s connectivity/mechanical stability. The latter effect occurs by senescent cells forming the second infinite cluster in the regime when the regular (healthy) cell’s infinite cluster still exits.
📄 Content
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Lattice Percolation Approach to 3D Modeling of Tissue Aging
Vyacheslav Gorshkov,a Vladimir Privman,b and Sergiy Libertc,*
aNational Technical University of Ukraine — KPI, Kiev 03056, Ukraine
bDepartment of Physics, Clarkson University, Potsdam, NY 13699, USA
cDepartment of Biomedical Sciences, Cornell University, Ithaca, NY 14853, USA
*E-mail: libert@cornell.edu
ABSTRACT
We describe a 3D percolation-type approach to modeling of the processes of aging and certain other properties of tissues analyzed as systems consisting of interacting cells. Lattice sites are designated as regular (healthy) cells, senescent cells, or vacancies left by dead (apoptotic) cells. The system is then studied dynamically with the ongoing processes including regular cell dividing to fill vacant sites, healthy cells becoming senescent or dying, and senescent cells dying. Statistical-mechanics description can provide patterns of time dependence and snapshots of morphological system properties. The developed theoretical modeling approach is found not only to corroborate recent experimental findings that inhibition of senescence can lead to extended lifespan, but also to confirm that, unlike 2D, in 3D senescent cells can contribute to tissue’s connectivity/mechanical stability. The latter effect occurs by senescent cells forming the second infinite cluster in the regime when the regular (healthy) cell’s infinite cluster still exits.
KEYWORDS Tissue aging; Percolation model; Senescence
Physica A, in print (2016)
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- INTRODUCTION
The processes responsible for aging are of great interest, but are poorly understood. Here we apply three-dimensional (3D) lattice percolation theory modeling to elucidate certain aspects of tissue aging by analyzing structures consisting of interacting cells at lattice sites. A recent study of two-dimensional (2D) models1 identified the mechanism by which cell senescence influences lifespan, confirming experimental in vivo findings.2,3 This success suggests that 2D and 3D percolation modeling incorporating cellular processes has the potential to quantify mechanisms that control longevity and tissue homeostasis (long-duration steady state). Here we demonstrate that 3D modeling allows us to explain how certain cellular dynamics properties contribute to preservation of not only cellular connectivity but also mechanical stability. We confirm the conclusion that cell senescence contributes to tissue integrity over long periods of time,1 and additionally we report that senescence contributes to tissue’s connectivity/mechanical stability, as found experimentally.4 Interestingly, upgrading the modeling from 2D to 3D allows us to study novel phenomena; we will argue below that, unlike 2D, in 3D senescent cells can form the second, percolating infinite cluster at the same time that the healthy dividing cells’ infinite cluster is also still present.
Experimentally, it was shown that several critical cellular properties correlate with longevity. For example, enhanced cellular resistance to stress: resistance to apoptosis (programmed cell death), correlates with extended longevity, both within and across species.5,6 Cells from mammals with longer lifespans have higher rates of DNA repair,7 resistance to transformation by viruses, and capacity to repair oxidative damage.6 However, the extent to which these properties influence lifespan and the overall tissue “health” (integrity, connectivity, mechanical stability), and experimental verification as well as modeling of these correlations is missing. It is not known whether these or other properties contribute significantly to longevity or are merely secondary adaptations.
Processes that ensure tissue homeostasis and integrity, such as damage repair or cell replacement are a topic of a major interest to both medical professionals8 and basic scientists.9 In
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order to identify the parameter relations that ensure tissue homeostasis for extended periods of time, in our lattice-connectivity percolation modeling approach we incorporate time dependence mimicking known cellular processes: cell division, senescence, apoptosis (programmed cell death), etc., and numerically obtain cellular statistics and cluster-connectivity evolution with time. Generally, percolation models can provide information and predictions on the system’s integrity and general connectivity.10-12 Our modeling is to an extent reminiscent of earlier percolation approaches to autonomous self-healing and self-damaging in “smart” materials,13-16 inspired by biological properties of tissues.
Tissues are studied dynamically, incorporating a selection of ongoing cellular processes, depending on the complexity of the model. These can include apoptosis, cell division to fill “vacant sites” left by dead cells, cell senescence, senescent cells disrupting functioning of adjacent healthy cells, etc. The
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