Modeling endosymbioses: Insights and hypotheses from theoretical approaches.

Endosymbiotic relationships are pervasive across diverse taxa of life, offering key avenues for eco-evolutionary dynamics. Although a variety of experimental and empirical frameworks have shed light on critical aspects of endosymbiosis, theoretical frameworks (mathematical models) are especially well-suited for certain tasks. Mathematical models can integrate multiple factors to determine the net outcome of endosymbiotic relationships, identify broad patterns that connect endosymbioses with other systems, simplify biological complexity, generate hypotheses for underlying mechanisms, evaluate different hypotheses, identify constraints that limit certain biological interactions, and open new lines of inquiry. This Essay highlights the utility of mathematical models in endosymbiosis research, particularly in generating relevant hypotheses. Despite their limitations, mathematical models can be used to address known unknowns and discover unknown unknowns.

Cell-strain-energy costs of active control of contractility.

Cell mechanosensing is implicated in the control of a broad range of cell behaviors, with cytoskeletal contractility a key component. Experimentally, it is observed that the contractility of the cell responds to increasing substrate stiffness, showing increased contractile force and changing the distribution of cytoskeletal elements. Here, we show using a theoretical model of active cell contractility that upregulation of contractility need not be energetically expensive, especially when combined with changes in adhesion and contractile distribution. Indeed, we show that a feedback mechanism based on the maintenance of strain energy would require an upregulation in contractile pressure on all but the softest substrates. We consider both the commonly reported substrate strain energy and active work done. We demonstrate substrate strain energy would preferentially select for the experimentally observed clustering of cell adhesions on stiffer substrates which effectively soften the substrate and enable an upregulation of total contractile pressure, while the localization of contractility has the greatest impact on the internal work.

Sticking around: Cell adhesion patterning for energy minimization and substrate mechanosensing.

Tissue stiffness (Young's modulus) is a key control parameter in cell behavior and bioengineered gels where defined mechanical properties have become an essential part of the toolkit for interrogating mechanotransduction. Here, we show using a mechanical cell model that the effective substrate stiffness experienced by a cell depends, not just on the engineered mechanical properties of the substrate but critically also on the particular arrangement of adhesions between cell and substrate. In particular, we find that cells with different adhesion patterns can experience two different gel stiffnesses as equivalent and will generate the same mean cell deformations. In considering small patches of adhesion, which mimic focal adhesion complexes, we show how the experimentally observed focal adhesion growth and elongation on stiff substrates can be explained by energy considerations. Relatedly, energy arguments also provide a reason why nascent adhesions do not establish into focal adhesions on soft substrates, as has been commonly observed. Fewer and larger adhesions are predicted to be preferred over more and smaller, an effect enhanced by random spot placing with the simulations predicting qualitatively realistic cell shapes in this case.

Cost-effectiveness of non-surgical periodontal therapy for patients with type 2 diabetes in the UK.

AIM: Periodontal therapy has been shown to reduce glycated haemoglobin in patients with diabetes, although considerable uncertainty remains regarding the sustainability of such changes. We evaluate the cost-effectiveness of non-surgical periodontal therapy and rigorous maintenance treatment in patients with type 2 diabetes and periodontitis from a provider perspective in the UK. METHOD: Lifetime costs relating to periodontal treatment were modelled for a cohort of patients with type 2 diabetes. The projected lifetime impact of changes in glycated haemoglobin on diabetes treatment costs and quality adjusted life expectancy were estimated from a published simulation model. Costs and outcomes were combined to estimate the Incremental Cost-Effectiveness Ratio for periodontal therapy in patients with type 2 diabetes. RESULTS: The Incremental Cost-Effectiveness Ratio was £28,000 per Quality Adjusted Life-Year for a man aged 58 with glycated haemoglobin of 7%-7.9%. The results were particularly sensitive to assumptions on the impact of periodontal therapy on glycated haemoglobin, the proportion of patients who comply with maintenance therapy and the proportion of compliant patients who respond to treatment. CONCLUSION: Assuming improvements in glycated haemoglobin can be maintained, periodontal therapy may be cost-effective for patients with type 2 diabetes at acceptable cost-per-Quality Adjusted Life-Year thresholds in the UK.