@article {92877, title = {A tale of two rhythms: Locked clocks and chaos in biology.}, journal = {Cell Syst}, volume = {12}, year = {2021}, month = {2021 Apr 21}, pages = {291-303}, abstract = {

The fundamental mechanisms that control and regulate biological organisms exhibit a surprising level of complexity. Oscillators are perhaps the simplest motifs that produce time-varying dynamics and are ubiquitous in biological systems. It is also known that such biological oscillators interact with each other-for instance, circadian oscillators affect the cell cycle, and somitogenesis clock proteins in adjacent cells affect each other in developing embryos. Therefore, it is vital to understand the effects that can emerge from non-linear interaction between oscillations. Here, we show how oscillations typically arise in biology and take the reader on a tour through the great variety in dynamics that can emerge even from a single pair of coupled oscillators. We explain how chaotic dynamics can emerge and outline the methods of detecting this in experimental time traces. Finally, we discuss the potential role of such complex dynamical features in biological systems.

}, issn = {2405-4720}, doi = {10.1016/j.cels.2021.03.003}, author = {Heltberg, Mathias L and Krishna, Sandeep and Kadanoff, Leo P and Jensen, Mogens H} } @article {50999, title = {On chaotic dynamics in transcription factors and the associated effects in differential gene regulation.}, journal = {Nat Commun}, volume = {10}, year = {2019}, month = {2019 01 08}, pages = {71}, abstract = {

The control of proteins by a transcription factor with periodically varying concentration exhibits intriguing dynamical behaviour. Even though it is accepted that transcription factors vary their dynamics in response to different situations, insight into how this affects downstream genes is lacking. Here, we investigate how oscillations and chaotic dynamics in the transcription factor NF-κB can affect downstream protein production. We describe how it is possible to control the effective dynamics of the transcription factor by stimulating it with an oscillating ligand. We find that chaotic dynamics modulates gene expression and up-regulates certain families of low-affinity genes, even in the presence of extrinsic and intrinsic noise. Furthermore, this leads to an increase in the production of protein complexes and the efficiency of their assembly. Finally, we show how chaotic dynamics creates a heterogeneous population of cell states, and describe how this can be beneficial in multi-toxic environments.

}, issn = {2041-1723}, doi = {10.1038/s41467-018-07932-1}, author = {Heltberg, Mathias L and Krishna, Sandeep and Jensen, Mogens H} } @article {65308, title = {Constraints on somite formation in developing embryos.}, journal = {J R Soc Interface}, volume = {16}, year = {2019}, month = {2019 Sep 27}, pages = {20190451}, abstract = {

Segment formation in vertebrate embryos is a stunning example of biological self-organization. Here, we present an idealized framework, in which we treat the presomitic mesoderm (PSM) as a one-dimensional line of oscillators. We use the framework to derive constraints that connect the size of somites, and the timing of their formation, to the growth of the PSM and the gradient of the somitogenesis clock period across the PSM. Our analysis recapitulates the observations made recently in cultures of mouse PSM cells, and makes predictions for how perturbations, such as increased Wnt levels, would alter somite widths. Finally, our analysis makes testable predictions for the shape of the phase profile and somite widths at different stages of PSM growth. In particular, we show that the phase profile is robustly concave when the PSM length is steady and slightly convex in an important special case when it is decreasing exponentially. In both cases, the phase profile scales with the PSM length; in the latter case, it scales dynamically. This has important consequences for the velocity of the waves that traverse the PSM and trigger somite formation, as well as the effect of errors in phase measurement on somite widths.

}, issn = {1742-5662}, doi = {10.1098/rsif.2019.0451}, author = {Juul, Jonas S and Jensen, Mogens H and Krishna, Sandeep} } @article {26658, title = {Time Correlations in Mode Hopping of Coupled Oscillators}, journal = {Journal of Statistical Physics}, volume = {167}, year = {2017}, month = {05/2017}, pages = {792{\textendash}805}, abstract = {

We study the dynamics in a system of coupled oscillators when Arnold Tongues overlap. By varying the initial conditions, the deterministic system can be attracted to different limit cycles. Adding noise, the mode hopping between different states become a dominating part of the dynamics. We simplify the system through a Poincare section, and derive a 1D model to describe the dynamics. We explain that for some parameter values of the external oscillator, the time distribution of occupancy in a state is exponential and thus memoryless. In the general case, on the other hand, it is a sum of exponential distributions characteristic of a system with time correlations.

}, author = {Heltberg, ML and Krishna, Sandeep and Jensen, Mogens H} } @article {1034, title = {The role of mRNA and protein stability in the function of coupled positive and negative feedback systems in eukaryotic cells.}, journal = {Sci Rep}, volume = {5}, year = {2015}, month = {2015}, pages = {13910}, abstract = {

Oscillators and switches are important elements of regulation in biological systems. These are composed of coupling negative feedback loops, which cause oscillations when delayed, and positive feedback loops, which lead to memory formation. Here, we examine the behavior of a coupled feedback system, the Negative Autoregulated Frustrated bistability motif (NAF). This motif is a combination of two previously explored motifs, the frustrated bistability motif (FBM) and the negative auto regulation motif (NAR), which both can produce oscillations. The NAF motif was previously suggested to govern long term memory formation in animals, and was used as a synthetic oscillator in bacteria. We build a mathematical model to analyze the dynamics of the NAF motif. We show analytically that the NAF motif requires an asymmetry in the strengths of activation and repression links in order to produce oscillations. We show that the effect of time delays in eukaryotic cells, originating from mRNA export and protein import, are negligible in this system. Based on the reported protein and mRNA half-lives in eukaryotic cells, we find that even though the NAF motif possesses the ability for oscillations, it mostly promotes constant protein expression at the biologically relevant parameter regimes.

}, issn = {2045-2322}, doi = {10.1038/srep13910}, author = {Moss Bendtsen, Kristian and Jensen, Mogens H and Krishna, Sandeep and Semsey, Szabolcs} }