Mathias Luidor Heltberg

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.

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.

The modelling of pandemics has become a critical aspect in modern society. Even though artificial intelligence can help the forecast, the implementation of ordinary differential equations which estimate the time development in the number of susceptible, (exposed), infected and recovered (SIR/SEIR) individuals is still important in order to understand the stage of the pandemic. These models are based on simplified assumptions which constitute approximations, but to what extent this are erroneous is not understood since many factors can affect the development. In this paper, we introduce an agent-based model including spatial clustering and heterogeneities in connectivity and infection strength. Based on Danish population data, we estimate how this impacts the early prediction of a pandemic and compare this to the long-term development. Our results show that early phase SEIR model predictions overestimate the peak number of infected and the equilibrium level by at least a factor of two. These results are robust to variations of parameters influencing connection distances and independent of the distribution of infection rates.

The transcription factor NF-κB plays a vital role in the control of the immune system, and following stimulation with TNF-α its nuclear concentration shows oscillatory behaviour. How environmental factors, in particular temperature, can control the oscillations and thereby affect gene stimulation is still remains to be resolved question. In this work, we reveal that the period of the oscillations decreases with increasing temperature. We investigate this using a mathematical model, and by applying results from statistical physics, we introduce temperature dependency to all rates, resulting in a remarkable correspondence between model and experiments. Our model predicts how temperature affects downstream protein production and find a crossover, where high affinity genes upregulates at high temperatures. Finally, we show how or that oscillatory temperatures can entrain NF-κB oscillations and lead to chaotic dynamics presenting a simple path to chaotic conditions in cellular biology.

The spatial organization of complex biochemical reactions is essential for the regulation of cellular processes. Membrane-less structures called foci containing high concentrations of specific proteins have been reported in a variety of contexts, but the mechanism of their formation is not fully understood. Several competing mechanisms exist that are difficult to distinguish empirically, including liquid-liquid phase separation, and the trapping of molecules by multiple binding sites. Here, we propose a theoretical framework and outline observables to differentiate between these scenarios from single molecule tracking experiments. In the binding site model, we derive relations between the distribution of proteins, their diffusion properties, and their radial displacement. We predict that protein search times can be reduced for targets inside a liquid droplet, but not in an aggregate of slowly moving binding sites. We use our results to reject the multiple binding site model for Rad52 foci, and find a picture consistent with a liquid-liquid phase separation. These results are applicable to future experiments and suggest different biological roles for liquid droplet and binding site foci.

Neurons are traditionally grouped in two excitability classes, which correspond to two different responses to external inputs, called phase response curves (PRCs). In this paper we have considered a network of two neural populations with delayed couplings, bound in a negative feedback loop by a positive PRC (type I). Making use of both analytical and numerical techniques, we derived the boundaries of stable incoherence in the continuum limit, studying their dependance on the time delay and the strengths of both interpopulation and intrapopulation couplings. This led us to discover, in a system with stronger delayed external compared to internal couplings, the coexistence of areas of coherence and incoherence, called chimera states, that were robust to noise. On the other hand, in the absence of time delays and with negligible internal couplings, the system portrays a family of neutrally stable periodic orbits, known as “breathing chimeras.”