Mogens Høgh Jensen

Oscillations constitute a defining feature of nonequilibrium processes of life. We analyze a minimal degradation-mediated negative feedback loop, in which the final species in a linear cascade enzymatically degrades the first component. By coupling mean-field ordinary differential equations with a phase-separated component, we reveal novel inhibition scalings that expand the parameter regime supporting oscillations. Extending to arbitrary sublinear exponents and network sizes, we derive general bifurcation criteria and identify universal relations for oscillation onset in a reduced time-delay model. Our results show that phase separation promotes oscillations, uncovering a nonequilibrium mechanism for dynamic regulation in cellular systems.

The epidemiological dynamics of Mycoplasma pneumoniae is characterized by poorly understood complex multiannual cycles. The origins of these cycles have long been debated, and multiple explanations of varying complexity have been suggested. Using Bayesian methods, we fit a dynamical model to half a century of M. pneumoniae surveillance data from Denmark (1958 to 1995, 2010 to 2025) and uncover a parsimonious explanation for the persistent cycles, based on the theory of quasicycles. The period of the multiannual cycle (approx. 5 y in Denmark) is explained by susceptible replenishment due, primarily, to loss of immunity. While an excellent fit to shorter time series (a few decades), the deterministic model eventually settles into an annual cycle, unable to reproduce the persistent cycles. We find that environmental stochasticity (e.g., varying contact rates) stabilizes the multiannual cycles and so does demographic noise, at least in smaller or incompletely mixing populations. The temporary disappearance of cycles during 1979 to 1985 is explained as a consequence of stochastic mode-hopping. The circulation of M. pneumoniae was recently disrupted by COVID-19 nonpharmaceutical interventions (NPIs), providing a natural experiment on the effects of large perturbations. Consequently, the effects of NPIs are included in the model and medium-term predictions are explored. Our findings highlight the intrinsic sensitivity of M. pneumoniae dynamics to perturbations and interventions, underscoring the limitations for long-term prediction. More generally, our findings provide further evidence for the role of stochasticity as a driver of complex cycles across endemic and recurring pathogens.

Living organisms transmit signals through local interactions with their neighbors. However, the precise timing of signals is fundamentally challenged by the presence of numerous stochastic reactions within interacting cells. Here we develop a minimal model to investigate the strength of signal propagation in stochastic environments. We uncover a multimodal frequency dependency with a few local optima, which is robust in both one and two dimensions. Through mathematical analysis we explain the frequency dependency and uncover the interplay between stochasticity and external frequency in order to optimize the signaling strength of the system. Finally we investigate the possibilities of bidirectional reactions in the oscillating source, allowing us to define thermodynamic properties of the system and investigate the relationship between free-energy dissipation and precision of signaling, showing nontrivial frequency dependency in coupled cells.

Type 2 diabetes (T2D) is associated with a systemic increase in the pro-inflammatory cytokine IL-1β. While transient exposure to low IL-1β concentrations improves insulin secretion and β-cell proliferation in pancreatic islets, prolonged exposure leads to impaired insulin secretion and collective β-cell death. IL-1 is secreted locally by islet-resident macrophages and β-cells; however, it is unknown if and how the two opposing modes may emerge at single islet level. We investigated the duality of IL-1β with a quantitative in silico model of the IL-1 regulatory network in pancreatic islets. We find that the network can produce either transient or persistent IL-1 responses when induced by pro-inflammatory and metabolic cues. This suggests that the duality of IL-1 may be regulated at the single islet level. We use two core feedbacks in the IL-1 regulation to explain both modes: First, a fast positive feedback in which IL-1 induces its own production through the IL-1R/IKK/NF-κB pathway. Second, a slow negative feedback where NF-κB upregulates inhibitors acting at different levels along the IL-1R/IKK/NF-κB pathway—IL-1 receptor antagonist and A20, among others. A transient response ensues when the two feedbacks are balanced. When the positive feedback dominates over the negative, islets transit into the persistent inflammation mode. Consistent with several observations, where the size of islets was implicated in its inflammatory state, we find that large islets and islets with high density of IL-1β amplifying cells are more prone to transit into persistent IL-1β mode. Our results are likely not limited to IL-1β but are general for the combined effect of multiple pro-inflammatory cytokines and chemokines. Generalizing complex regulations in terms of two feedback mechanisms of opposing nature and acting on different time scales provides a number of testable predictions. Taking islet architecture and cellular heterogeneity into consideration, further dynamic monitoring and experimental validation in actual islet samples will be crucial to verify the model predictions and enhance its utility in clinical applications.

Type 2 diabetes (T2D) is associated with a systemic increase in the pro-inflammatory cytokine IL-1β. While transient exposure to low IL-1β concentrations improves insulin secretion and β-cell proliferation in pancreatic islets, prolonged exposure leads to impaired insulin secretion and collective β-cell death. IL-1 is secreted locally by islet-resident macrophages and β-cells; however it is unknown if and how the two opposing modes may emerge at single islet level. We investigated the duality of IL-1β with a quantitative in-silico model of the IL-1 regulatory network in pancreatic islets. We find that the network can produce either transient or persistent IL-1 responses, when induced by pro-inflammatory and metabolic cues. This suggests that the duality of IL-1 may be regulated at the single islet level. We use two core feedbacks in the IL-1 regulation to explain both modes: First, a fast positive feedback in which IL-1 induces its own production through IL-1R/IKK/NF-κB pathway. Second, a slow negative feedback where NFκ-κB upregulates inhibitors acting at different levels along the IL-1R/IKK/NF-κB pathway – IL-1 receptor antagonist and A20 among others. A transient response ensues when the two feedbacks are balanced. When positive feedback is dominating over the negative islets transit into the persistent inflammation mode. Consistent with several observations, where the size of islets was implicated in its inflammatory state, we find that large islets and islets with high density of IL-1β amplifying cells are more prone to transit into persistent IL-1β mode. Our results are likely not limited to IL-1β but general for the combined effect of multiple pro-inflammatory cytokines and chemokines. Generalizing complex regulations in terms of two feedbacks of opposing nature and acting on different time scales provides a number of testable predictions, which call for dynamic monitoring of pro-inflammatory cytokines at the single islet level. AUTHOR SUMMARY Different expression or activity dynamics of the same proteins or signaling molecules can lead to opposing fates in cells and tissues. While it is known that brief and prolonged exposure to pro-inflammatory cytokine IL-1β have opposing effects on the functionality and viability of pancreatic β-cells, it is unclear if and how these differences in dynamics may arise at the single islet level. We use a mathematical model of the core feedback loops in the IL-1β regulatory network to show that transient and persistent responses are the two characteristic dynamic modes of the IL-1β response. The likelihood of each mode depends on systemic inflammation and elevated glycaemia and free fatty acids levels. We find that large islets are more prone to transit into the persistent mode, which may provide an explanation for why large islets are underrepresented in type 2 diabetes patients.

The Notch ligands Jag1 and Dll1 guide differentiation of multipotent pancreatic progenitor cells (MPCs) into unipotent pro-acinar cells (PACs) and bipotent duct/endocrine progenitors (BPs). Ligand-mediated trans-activation of Notch receptors induces oscillating expression of the transcription factor Hes1, while ligand-receptor cis-interaction indirectly represses Hes1 activation. Despite Dll1 and Jag1 both displaying cis- and trans-interactions, the two mutants have different phenotypes for reasons not fully understood. Here, we present a mathematical model that recapitulates the spatiotemporal differentiation of MPCs into PACs and BPs. The model correctly captures cell fate changes in Notch pathway knockout mice and small molecule inhibitor studies, and a requirement for oscillatory Hes1 expression to maintain the multipotent state. Crucially, the model entails cell-autonomous attenuation of Notch signaling by Jag1-mediated cis-inhibition in MPC differentiation. The model sheds light on the underlying mechanisms, suggesting that cis-interaction is crucial for exiting the multipotent state, while trans-interaction is required for adopting the bipotent fate.