Combined multiple transcriptional repression mechanisms generate ultrasensitivity and oscillations

Phosphorylation of DNA-binding domains of CLOCK-BMAL1 complex for PER-dependent inhibition in circadian clock of mammalian cells

In mammals, CLOCK and BMAL1 proteins form a heterodimer that binds to E-box sequences and activates transcription of target genes, including Period (Per). Translated PER proteins then bind to the CLOCK-BMAL1 complex to inhibit its transcriptional activity. However, the molecular mechanism and the impact of this PER-dependent inhibition on the circadian clock oscillation remain elusive. We previously identified Ser38 and Ser42 in a DNA-binding domain of CLOCK as phosphorylation sites at the PER-dependent inhibition phase. In this study, knockout rescue experiments showed that nonphosphorylatable (Ala) mutations at these sites shortened circadian period, whereas their constitutive-phospho-mimetic (Asp) mutations completely abolished the circadian rhythms. Similarly, we found that nonphosphorylatable (Ala) and constitutive-phospho-mimetic (Glu) mutations at Ser78 in a DNA-binding domain of BMAL1 also shortened the circadian period and abolished the rhythms, respectively. The mathematical modeling predicted that these constitutive-phospho-mimetic mutations weaken the DNA binding of the CLOCK-BMAL1 complex and that the nonphosphorylatable mutations inhibit the PER-dependent displacement (reduction of DNA-binding ability) of the CLOCK-BMAL1 complex from DNA. Biochemical experiments supported the importance of these phosphorylation sites for displacement of the complex in the PER2-dependent inhibition. Our results provide direct evidence that phosphorylation of CLOCK-Ser38/Ser42 and BMAL1-Ser78 plays a crucial role in the PER-dependent inhibition and the determination of the circadian period.

Simplifications and approximations in a single-gene circuit modeling

The absence of detailed knowledge about regulatory interactions makes the use of phenomenological assumptions mandatory in cell biology modeling. Furthermore, the challenges associated with the analysis of these models compel the implementation of mathematical approximations. However, the constraints these methods introduce to biological interpretation are sometimes neglected. Consequently, understanding these restrictions is a very important task for systems biology modeling. In this article, we examine the impact of such simplifications, taking the case of a single-gene autoinhibitory circuit; however, our conclusions are not limited solely to this instance. We demonstrate that models grounded in the same biological assumptions but described at varying levels of detail can lead to different outcomes, that is, different and contradictory phenotypes or behaviors. Indeed, incorporating specific molecular processes like translation and elongation into the model can introduce instabilities and oscillations not seen when these processes are assumed to be instantaneous. Furthermore, incorporating a detailed description of promoter dynamics, usually described by a phenomenological regulatory function, can lead to instability, depending on the cooperative binding mechanism that is acting. Consequently, although the use of a regulating function facilitates model analysis, it may mask relevant aspects of the system's behavior. In particular, we observe that the two cooperative binding mechanisms, both compatible with the same sigmoidal function, can lead to different phenotypes, such as transcriptional oscillations with different oscillation frequencies.

Negative feedback systems for modelling NF-κB transcription factor oscillatory activity

Low-dimensional negative feedback systems (NFSs) were developed within a signal flow model to describe the oscillatory activities of NF-κB caused by interactions with its inhibitor IκBα. The NFSs were established as 3rd- and 4th-order linear systems containing unperturbed and perturbed negative feedback (NF) loops with constant or time-varying NF strengths and a feed-forward loop. NF-related analytical solutions to the NFSs representing the time courses of NF-κB and IκBα were determined and their exact mathematical relationship was found. The NFS's parameters were determined to fit the experimental time courses of NF-κB in TNF-α-stimulated embryonic fibroblasts, rela-/- embryonic fibroblasts reconstituted with RelA, C9L cells, GFP-p65 knock-in embryonic fibroblasts and embryogenic fibroblasts lacking Iκβ and IκBε, LPS-stimulated IC-21 macrophages treated or not with DCPA, and anti-IgM-stimulated DT40 B-lymphocytes. The unperturbed and perturbed NFSs describing the above biosystems generated isochronous and non-isochronous solutions, depending on a constant or time-varying NF strength, respectively. The oscillation period of the NF-coupled solutions, the phase difference between them and the time delays in the appearance of cytoplasmic IκBα after stimulation of NF-κB were determined. A significant divergence between the IκBα solutions to the NFSs and the IκBα experimental courses led to a rejection of the NF coupling between NF-κB and IκBα in the above biosystems. It was shown that neither the linearity nor the low dimensionality of the NFSs altered the NF relationship and the divergence between the IκBα solutions to the NFS and IκBα experimental time courses. Although the NF relationship between IκBα and NF-κB was not confirmed in all the experimental data analyzed, delayed negative feedback was found in some cases.

A robust ultrasensitive transcriptional switch in noisy cellular environments

Ultrasensitive transcriptional switches enable sharp transitions between transcriptional on and off states and are essential for cells to respond to environmental cues with high fidelity. However, conventional switches, which rely on direct repressor-DNA binding, are extremely noise-sensitive, leading to unintended changes in gene expression. Here, through model simulations and analysis, we discovered that an alternative design combining three indirect transcriptional repression mechanisms, sequestration, blocking, and displacement, can generate a noise-resilient ultrasensitive switch. Although sequestration alone can generate an ultrasensitive switch, it remains sensitive to noise because the unintended transcriptional state induced by noise persists for long periods. However, by jointly utilizing blocking and displacement, these noise-induced transitions can be rapidly restored to the original transcriptional state. Because this transcriptional switch is effective in noisy cellular contexts, it goes beyond previous synthetic transcriptional switches, making it particularly valuable for robust synthetic system design. Our findings also provide insights into the evolution of robust ultrasensitive switches in cells. Specifically, the concurrent use of seemingly redundant indirect repression mechanisms in diverse biological systems appears to be a strategy to achieve noise-resilience of ultrasensitive switches.

Beyond microtubules: The cellular environment at the endoplasmic reticulum attracts proteins to the nucleus, enabling nuclear transport

All proteins are translated in the cytoplasm, yet many, including transcription factors, play vital roles in the nucleus. While previous research has concentrated on molecular motors for the transport of these proteins to the nucleus, recent observations reveal perinuclear accumulation even in the absence of an energy source, hinting at alternative mechanisms. Here, we propose that structural properties of the cellular environment, specifically the endoplasmic reticulum (ER), can promote molecular transport to the perinucleus without requiring additional energy expenditure. Specifically, physical interaction between proteins and the ER impedes their diffusion and leads to their accumulation near the nucleus. This result explains why larger proteins, more frequently interacting with the ER membrane, tend to accumulate at the perinucleus. Interestingly, such diffusion in a heterogeneous environment follows Chapman's law rather than the popular Fick's law. Our findings suggest a novel protein transport mechanism arising solely from characteristics of the intracellular environment.

Noisy Delay Denoises Biochemical Oscillators

Genetic oscillations are generated by delayed transcriptional negative feedback loops, wherein repressor proteins inhibit their own synthesis after a temporal production delay. This delay is distributed because it arises from a sequence of noisy processes, including transcription, translocation, translation, and folding. Because the delay determines repression timing and, therefore, oscillation period, it has been commonly believed that delay noise weakens oscillatory dynamics. Here, we demonstrate that noisy delay can surprisingly denoise genetic oscillators. Specifically, moderate delay noise improves the signal-to-noise ratio and sharpens oscillation peaks, all without impacting period and amplitude. We show that this denoising phenomenon occurs in a variety of well-studied genetic oscillators, and we use queueing theory to uncover the universal mechanisms that produce it.

An integrative mathematical model for timing treatment toxicity and Zeitgeber impact in colorectal cancer cells

Increasing evidence points to a role of the circadian clock in the regulation of cancer hallmarks with a strong impact on the understanding and treatment of this disease. Anti-cancer treatment can be personalized considering treatment timing. Here we present a new mathematical model based on data from three colorectal cancer cell lines and core-clock knock-outs, which couples the circadian and drug metabolism network, and that allows to determine toxicity profiles for a given drug and cell type. Moreover, this model integrates external Zeitgebers and thus may be used to fine-tune toxicity by using external factors, such as light, and therefore, to a certain extent, help fitting the endogenous rhythms of the patients to a defined clinic routine facilitating the implementation of time-dependent treatment in clinical practice.

The ups and downs of biological oscillators: a comparison of time-delayed negative feedback mechanisms

Many biochemical oscillators are driven by the periodic rise and fall of protein concentrations or activities. A negative feedback loop underlies such oscillations. The feedback can act on different parts of the biochemical network. Here, we mathematically compare time-delay models where the feedback affects production and degradation. We show a mathematical connection between the linear stability of the two models, and derive how both mechanisms impose different constraints on the production and degradation rates that allow oscillations. We show how oscillations are affected by the inclusion of a distributed delay, of double regulation (acting on production and degradation) and of enzymatic degradation.

Time-keeping and decision-making in living cells: Part I

To survive and reproduce, a cell must process information from its environment and its own internal state and respond accordingly, in terms of metabolic activity, gene expression, movement, growth, division and differentiation. These signal–response decisions are made by complex networks of interacting genes and proteins, which function as biochemical switches and clocks, and other recognizable information-processing circuitry. This theme issue of Interface Focus (in two parts) brings together articles on time-keeping and decision-making in living cells—work that uses precise mathematical modelling of underlying molecular regulatory networks to understand important features of cell physiology. Part I focuses on time-keeping: mechanisms and dynamics of biological oscillators and modes of synchronization and entrainment of oscillators, with special attention to circadian clocks.