Chaos: An Interdisciplinary Journal of Nonlinear Science

Growing interest to describe the electrical behavior of glial cells, mainly astrocytes, in intact brain tissue poses more and more challenges to commonly accepted belief they only respond in a linear manner in uptake of the excess of extracellular potassium and maintenance of their network equipotentiality. Their highly conductive mutual interconnections via gap junction (GJ) connections introduce yet another class of nonlinear elements. As more studies report nonlinearities in membrane voltage Vm dependence of both, the membrane and junctional conductances, the need to formulate minimal dynamical models of their transient behavior is getting more acute. Since ODE models of coupled cells, even in simplest 1-d arrays, require simplified descriptions and small set of parameters, rare quantitative studies on glia makes the task even more difficult. This study attempts to qualify a self-coupled cell, or a glial cell coupled to fixed voltage as useful system for detecting the nature of instabilities and transitions coming from coupling. In a novel biophysical model of coupled astrocyte, we introduce nonlinear kinetics of deactivation for large junctional voltages for the first time. We found that N-shaped nonlinearities and corresponding fold structure in the vector field of isolated cell serves as a baseline on top of which coupling nonlinearities enrich the bifurcation picture. Numerical simulations of 1-d array of coupled astrocytes show that coupling increases the propensity of astrocytic Vm to bistability and front propagation. We believe that presented illustrations of possible effects of coupling nonlinearities will motivate neurobiologists to further explore their impact in disease. Significance statementTransient changes in membrane voltage of glial cells may produce significant transient voltage difference between directly coupled cells. Nonlinear steady-state conductance of their interconnection elements, the gap junctions, introduce nonlinear current profiles which are very difficult to measure and quantitate using the available methods due to marked permeability of the junctions and leakiness of glial membrane in general. We propose a minimal model of glial membrane extended with a self-coupled feedback loop, which under realistic simplifying assumptions could serve for qualitative analysis of the impact of coupling, on the stability of resting membrane voltage. Neuronal cells of the brain and spinal cord cannot exist and function without supportive and neuromodulatory functions of the diverse population of glial cells. This applies to virtually all physiological processes on cell level - from cell development, metabolic support, membrane signaling, slow molecular signal transduction, ion homeostasis, neurovascular coupling, myelination, to mention only a few, manifest neuro-glial interaction. Even though all glial cell types are interconnected, the most abundant ones, the astrocytes are massively interconnected by gap junctions to form ordered networks. Electrically, astrocytic networks display membrane voltage equipotentiality, which is considered system-wide resting state for given neuro-glial circuit or unit. With molecular and cellular substrates of glial connectivity being slowly elucidated, network science and dynamical modeling are slowly "invading" that area with many important issues left open. In this study using classical dynamical systems approaches we give indications how nonlinear intercellular coupling between astrocytes affects physiological resting state and its instabilities compared to isolated, uncoupled cell. We strongly believe the suggested minimal model could fill the gap in ODE modeling of neuro-glial circuits, within broadest scope of hypothesis-driven research in cell-level neuroscience.

Despite extensive study of cellular mechanisms underlying long-term potentiation, no single specific protein or gene has been identified which encodes an individual unit of information, or memory bit. Indeed, the brain engram remains a knowledge gap. The theory of exclusion led us to cancel one-by-one several unrealistic biological options, suggesting that the explanation resides somewhere else. Superposition of up to concentric 300 myelin layers, spiraled, and highly compacted wrapping a single axon and each wrap could host hundreds to thousands of niches, as memory cells, collectively consisting of a massive array of cells. The disjointed 3D spatial superposition allows storage of charges, nodes not facing from a layer to next. The thickness of a single myelin layer ranges from 7.0 to 20 nm. The dimension scale is approximately the exact dimensions of the charge trap, the tunnel and dielectric also equipping current AI microchips. Stored charges are positive ions, with similar effect whether charges are negative or positive charges creating an electromagnetic field. To write data, following an action potential, this voltage applies to the control gates of the myelin layers producing an ionic charge injection. This causes charges to gain energy and tunnel through the myelin layer across Ranvier nodes, via quantum tunneling, and deep into the concentric myelin multilayers. This is creating an insulated trapping of K+ ions isolated from the system. In a long white matter tract bundle, the near-perfect isolation of millions of axons within compressed myelin wrap-ion channel K+/Na+ systems provides quantum coherence and precision of asynchronous firing property. The injected ionic charges (K+) become physically stuck in traps within the myelin layers. The K+ ions may not move freely, completely trapped after AP ceases. Mirroring a single-bit, single-level-cell, a trapped ionic charge (ions K+) may represent a 1, while an empty cell (absence of K+) represents a 0. The trial-and-error process, with a Bayesian inference which may have also been the core evolution of the learning human brain. Based on selected mathematical equations, we analyzed the general scheme on how deep learning may be embedded in the brain

The brain is the most captivating chef doeuvre of nature. Naturally then, the mind wonders about the process that births such a fascinating organ. Neurodevelopment is a complex yet robust phenomenon that conceals answers to our questions in its intricacies. In an attempt to shed some light on this matter, we study the developing brain connectome of the nematode, C. elegans across the post-embryonic phase. A tiny organism with only around 200 neurons comprising its brain and yet a diverse array of behaviors to display, it makes for a great model. Starting with most of its head neurons already present at hatching, the worm brain accumulates numerous more synaptic connections increasing the edge density. It maintains a weak connectivity throughout thereby, balancing global communication as well as hierarchy. At the mesoscopic level, we find that the core has a conserved backbone of persistent neurons along with a dynamic component formed of transient/recurring neurons. Moreover, the connectome has a rich club organization since the early stage which selectively strengthens indicating progressively denser connectivity among the integrators due to the previously reported asymmetric synapse addition. This asymmetry also shows up in the preservation of input hubs across development and the progressively more centralized organization of the in-degree k-core. Our work provides a new perspective into the neurodevelopment of the brain that may facilitate our understanding of its functioning.

The primary objective of system neuroscience is to understand the functional mapping and its causation in the dynamics of the brain network. Some experimental and methodological studies suggest that functional modularity and its hierarchical information processing in the brain network are crucial to understanding the functional role of task-specific or state-specific information flow in the brain. However, because most of the established techniques for detecting effective network structures in the neuroscience research field are strongly based on the "Granger causality" perspective, existing causal discovery methods specified for brain network analysis cannot identify the causal hierarchy in the modular network in the brain due to spurious correlation issues and indistinguishability of causal direction under the Gaussianity of observational noise in a linear system. To address the issues, we developed a causal discovery method for synchronous neural dynamics, called the Jacobian-informed linear non-Gaussian acyclic model, "j-VAR-LiNGAM", by incorporating the information of the Jacobian matrix determined from a phase-coupled oscillator model estimated from observed neural data into the VAR-LiNGAM algorithms. The method was validated by showing that it could extract causal ordering in both synthetic data and empirical neural observed data. Moreover, by analyzing the observed neural oscillatory signals obtained from mice and humans, we confirmed that our method identified causally hierarchical structures in the brain, which aligned with the neurophysiological interpretations. These findings suggested that our proposed method can reveal the neural basis of hierarchical information processing in the brain network.

The awake brain is known to display asynchronous (AS) states during periods of attention and arousal, but the responsiveness properties of such states remain unclear. Here, we investigate this question using computational models of spiking networks of excitatory and inhibitory neurons, mimicking recurrently-connected networks in layer 2/3 of the cerebral cortex. The networks can generate a continuum of AS states, but with different responsiveness characteristics. By using a mean-field model to infer the dynamic properties of the system, we find that there are two families of AS states, which we call "underdamped" (UD) and "overdamped" (OD). Responsiveness is maximised at the transition between OD and UD states, which identifies a "working point" that may present advantageous computational properties.

Thymosin {beta}4 (T{beta}4) is a conserved acidic polypeptide with 43-amino acids participating in multiple pathophysiological processes. In this study in vivo effects of T{beta}4 on liver regeneration are investigated in carbon-tetrachloride (CCL4) induced rodent animal liver jury models. Results illustrate that exogenous T{beta}4 treatment significantly reduced CCL4-rendered liver necrosis around central vein. At 48 hours after CCL4 insults hepatocytes proliferation occur mainly around the periportal area, while hepatocytes proliferation around the necrosis area is prominently increased by exogenous T{beta}4 treatment. The holistic proliferation level of liver tissues are also enhanced by exogenous T{beta}4. Hepatocyte proliferation activities negatively correlate with the necrosis extent of the liver tissue. These results suggested firstly exogenous T{beta}4 treatment could enhance liver regeneration and exhibit prosperous potential for application in clinical conditions such as liver transplantation.

Experimental studies show that tumor cells adopt migratory or proliferative phenotypes depending on the local extracellular matrix (ECM). In this work, we propose a minimal go-or-grow invasion model, comprising two specialist cell phenotypes: proliferating and migratory, with phenotypic switching and cell migration depending on local ECM density. Numerical simulations of this model reveal that the spatial arrangement of proliferative and migratory cells depends on the choice of phenotypic switching function. We then ask whether this specialist cell-phenotype model can be reduced to a generalist cell-phenotype model. We derive a relationship between the reduced model and go-or-grow model in the fast phenotypic switching regime. We observe that the reduced model captures the dynamics of the original model, for a range of realistic phenotypic switching functions. We analytically derive the minimum traveling wave speed of the reduced model in a homogeneous ECM bed. Moreover, using linear stability analysis on the go-or-grow model, we recover the same wave speed expression. In addition, we numerically explore how the key parameters influence the traveling wave speed profile. Our analysis indicated the counter-intuitive result that the wave speed is independent of the matrix degradation rate, and our simulations show that, at most, the speed is weakly dependent on this parameter.

The phenomenon of splitting was originally observed in hamsters which, after prolonged exposure to constant light, exhibit two rest/wake cycles within a subjective day. Splitting is a consequence of the left and right suprachiasmatic nuclei (SCN) falling out of synchrony. While it is known that split activity is characterized by an antiphase relationship between the left and right SCN and between the core and shell within each hemisphere, the role of the commissural projections that connect the right and left SCN is not known. In the present study, we investigate the impact of the inter-hemispheric connections on the split and unsplit dynamics of a computational model of the bilateral SCN. Our model has 4 nodes corresponding to each right and left core and shell. We simulated our bilateral model under different lighting conditions and measured its period and the phase relationships among the 4 nodes. To further characterize the dynamics of the system, we performed a bifurcation analysis. We found that the bilateral model automatically splits unless entrained by bright light/dark cycles, or unless it has excitatory inter-hemispheric connections. This suggests that excitatory cross-connections may be important for freerunning behavior. We found that constant light of varying intensities transitions the model between split and unsplit activity only in very limited conditions, but the strength and polarity of the contralateral connections play a much greater role in this dynamical transition. These findings suggest that splitting may involve plasticity of the inter-hemispheric connections of the SCN.

A novel mathematical framework to define the threshold of action potentials in excitable cells is presented. Unlike previously applied methods that rely on approximations or specific fixed-point bifurcations, the approach focuses on the geometry of membrane potential trajectories. Specifically, the focus is on the concavity changes during the upstroke of an electrical pulse. These changes in concavity form a curve of inflection points that defines a region in phase space crossed by all the action potentials in the system, and containing no non-action potential trajectories. Such region is called the excitability region and its size can be measured, thus providing a measure for the excitability of a dynamical system, and a way to compare the excitability between systems representing different biological phenotypes and stimulus conditions. The work transforms the traditionally vague physiological concept of excitability into a rigorous analytical description applicable across continuous, single compartment models of electrical excitability.

We develop a theoretical proposal linking vacuum stability and brain dynamics through superconductivity-inspired coherence, symmetry reduction, and the thermodynamic stabilization of low-entropy regimes. We take an unbroken SU(3) structure as a candidate stable residue of the low-temperature vacuum. At the neural level, we formulate a coarse-grained analog in which a two-fluid model with dissipative and coherence-supporting components describes brain dynamics. Specifically, the coherence-supporting component is proposed as a possible basis for the efficient binding and integration required to sustain a stable, unified conscious state. The proposal offers a common geometric language for relating physics and neuroscience with falsifiable signatures in coherence and state-dependent transitions. The main technical contribution is a computational algebraic model of conscious-state dynamics, where neural data are mapped to reconstructed state trajectories. Effective generators are inferred from those trajectories, and the two-fluid split is tested as a Cartan-root decomposition of su(3), with a rank-two commuting sector for coherence-preserving balance and six root directions for state transitions. This structure can be tested on neural data and contrasted with alternative dynamical models.

1Endogenous circadian clocks control circadian rhythms in physiology and behavior. The predominant hypothesis of biological timing suggests that the responsible master clock for all endogenous circadian rhythms is constituted by an evolutionary conserved transcriptional-translational feedback loop (TTFL) clock consisting of positive feedforward and negative feedback elements. Unexpectedly, in contrast to the evolutionary derived insect Drosophila, RNAi-dependent knockdown of any of the negative feedback elements of the core TTFL clock in the basal Madeira cockroach Rhyparobia maderae does not delete circadian rhythms in locomotor activity. Shown here, neither RNAi-dependent triple knockdowns of all three negative feedback elements Period, Timeless 1, and Cryptochrome 2, nor single and double knockdown of the positive elements Clock and Cycle did directly delete circadian locomotor rhythms as mRNA levels declined. Thus, our experimental data do not support the predominant hierarchical hypothesis of circadian timing. To explore alternative mechanisms, we constructed a computational model of a neuronal circadian pacemaker network using planar switching affine systems (PSAS). The PSAS model comprises plasma membrane-associated posttranslational feedback loop (PTFL) clocks that are coupled to the TTFL nuclear clocks. Modeling results aligned with our experimental results. Therefore, both our experimental and modeling data support a systemic hypothesis of biological timing. 3 Significance statementBased mostly upon genetic studies in derived taxa like Drosophila it is hypothesized that circadian timing of behavior is strictly controlled by specific circadian clock neurons in the brain, realized through a transcriptional-translational feedback loop (TTFL) clock. In contrast to this common hierarchical model that requires transcription, we provide evidence in a basal taxon - the Madeira cockroach - for a systemic explanation of circadian timing of behavior that is based on coupled TTFL and posttranslational feedback loop (PTFL) clocks in adaptive neuronal networks.

Strongly interconnected neuronal populations, called assemblies, dynamically form through synaptic plasticity mechanisms and are thought to be a substrate for memories in the brain. Many assembly formation models use Hebbian excitatory-to-excitatory plasticity, where coordinated activity strengthens recurrent structure. However, these models typically yield binary assembly outcomes: networks with either weak (no assembly) or maximally strong (assembly) connectivity. We consider networks with a combination of Hebbian excitatory-to-excitatory plasticity and inhibitory-to-excitatory synapses with plasticity that homeostatically stabilizes excitatory neuron firing at a target value. When we set excitatory-to-excitatory plasticity to be homeostatically compliant, in that potentiation and depression are balanced at the homeostatic target firing rate, we find a stable continuum of synaptic strengths, and assembly structure is no longer binary. We use a recurrent network of spiking neuron models and an associated mean-field theory to identify this continuum as a line attractor in synaptic weight space. While along the attractor, homeostasis ensures that neuronal firing rates are invariant, the dynamical response properties of the network are quite malleable, with strongly coupled networks having high gain and longer timescale responses. Using our mean-field theory we show how correlated stochastic spiking activity among the excitatory neurons can destroy the line attractor, yet this can be mitigated when correlated inputs are shared across the excitatory and inhibitory neurons. Altogether, we provide a learning framework based on homeostasis, where a tunable and flexible assembly structure is possible.

Abnormal states such as erroneous behaviors are generally difficult to represent from neural data. However, such states are also known to have specific spatiotemporal features, indicating a feasibility of developing a method to focus on them. If a method can highlight these spatiotemporal features, it may effectively represent such abnormal states, helping evaluate abnormal brain functions. In the present study, we proposed the hierarchy of supported modules (HSM) to highlight spatiotemporal features that can represent abnormal states. HSM spatiotemporally transforms multidimensional neural time-series based on their spatiotemporal context. We evaluated HSM through decoding and similarity analyses using multiple publicly available datasets. In the HSM results, decoding accuracies were higher for erroneous behaviors than for normal behaviors, and similarities were lower between erroneous behaviors and normal behaviors than between normal behaviors, demonstrating the ability of HSM to capture the spatiotemporal features of erroneous behaviors. Surprisingly, many parts of these results were also present even before HSM learning, showing the virtue of HSM as a simple-to-use method. The proposed HSM method may help elucidate the mechanisms underlying erroneous behaviors.

Understanding how complex systems self-organize, exhibit emergent properties beyond their constituent elements remains a challenge across physics, biology, and cognitive science. In resource-constrained neuronal systems, existing theoretical approaches, including gauge theoretic formulations, statistical physics-inspired methods, dynamical population models, and variational principles such as the Free Energy Principle, address important aspects of this problem but do not fully specify the physical conditions and thermodynamic costs under which self-organizing behavior occurs. Here, we introduce Dynamic Resource Theory (DRT) as a general physical framework for describing self-organization under constrained resource availability. DRT formalizes complexity as a physical property of self-organizing systems arising from coupled mechanisms of resource allocation and dynamic reallocation of internal resources. This framework provides a thermodynamic and variational account of how stability is preserved while adaptive reconfiguration remains possible, consistent with stationary action and thermodynamic constraints. DRT is formulated within a gauge theoretic setting and directly incorporates the energetic costs associated with maintaining structure and enabling system-level reconfiguration. Within DRT, baseline resource allocation preserves system stability, while internal and external demands perturb the system, driving self-organization through dynamic resource reallocation across a coupled free energy landscape without assuming subsystem separability. We then develop Neural Resource Theory (NRT) and Cognitive Resource Theory (CRT) as principled specializations of DRT, illustrating how this structure is instantiated in resource constrained neuronal and cognitive systems. We conclude by discussing the broader implications of DRT for understanding how complexity, emergence, and adaptive capacity arise over time through thermodynamically permissible reallocation processes across scales.

AO_SCPLOWBSTRACTC_SCPLOWOncolytic viruses provide cancer therapy using replication-competent viruses that selectively infect and lyse tumour cells. Their tumour-specific replication also enables the delivery of targeted, virus-encoded gene products, such as enzymes that activate prodrugs. This dual functionality offers the potential for synergistic effects by combining direct oncolysis with localised drug activation. The interplay between infection, replication, lysis, and gene product delivery remains poorly understood. Here, we introduce a spatially structured, multi-patch model of cancer cells infected by an oncolytic virus engineered to deliver a prodrug-activating enzyme. The spatial system is first represented as a microscopic model and subsequently reduced via spectral dimension reduction techniques. This reduction yields an ordinary differential equation model for a set of coarse-grained variables, which we analyze both without the transgene (OV model) and with the transgene (TOV model). For each case, we compute the basic reproduction number, R0, which determines the conditions for viral spread. Both models exhibit three regimes via transcritical bifurcations: (i) R0 < 0, extinction of both cancer and infected cells; (ii) 0 < R0 [&le;] 1, persistence of cancer cells only; and (iii) R0 > 1, coexistence as a stable node or as a focus. The TOV model, as a difference form the OV model, can undergo periodic oscillations arising from a Hopf-Andronov bifurcation. Notably, oscillation amplitudes can be controlled such that cancer cells largely decrease when drug-induced death is stronger in non-infected cells than in infected ones, enabling effective cancer cells killing while maintaining viral replication and prodrug activation. The qualitative behaviour of the coarse-grained model is shown to be preserved in both the microscopic and spatially explicit models.

The aim of this paper is to model homeless accommodation settings to investigate how vaccination mitigates the outbreaks, highlighting the importance of vaccination in vulnerable settings. We estimate the daily per capita contact rate with wider community, the internal transmission rate, and the achieved vaccine coverage. We present stochastic simulation of the final size of disease outbreaks given choices of internal and external transmission. We conclude that vaccine that has effect in reducing transmission will mitigate the outbreak in homeless hostels but it will have better results when the household population has large vaccination coverage, which may lead to more cost from the health economic perspective.

In mammalian cells, under normal circumstances, the p53 protein exhibits oscillatory dynamics in response to DNA damage and maintains the cells in a cell-cycle-arrested state. Intriguingly, some cells can escape this cell-cycle-arrested state even after prolonged DNA damage, and often undergo mitotic catastrophe. In this context, the precise role of p53 dynamics and its complex interplay with cell-cycle regulation remain poorly understood. Herein, by constructing a comprehensive network model, we have identified crucial crosstalk regulations between the p53 protein and key cell-cycle regulators that enable some cells to escape cell-cycle arrest during prolonged DNA damage. The model further illustrates a probable cellular mechanism underlying mitotic catastrophe and predicts ways to induce it in a therapeutically relevant manner.

Computational models of brain structures impacted by Parkinsons disease are useful for exploring potential therapies. We use the Hindmarsh-Rose neuronal model to simulate synchronized activity in the subthalamic nucleus, capturing key features of the pathological rhythms observed in Parkinsons disease using a relatively small network of 100 neurons. Our model incorporates unidirectional excitatory chemical synapses whose strengths evolve according to a spike-timing-dependent plasticity (STDP) rule. To account for inputs from unmodelled neurons, both uniformly distributed white noise and Poisson noise were explored. White noise produced a single stable state of synchronized neuronal activity whereas Poisson noise resulted in two stable states, one synchronized and one desynchronized. We applied coordinated reset stimulation with a rapidly varying sequence (RVS CR) to examine its ability to reduce neuronal synchrony. The neuronal population was divided into subpopulations representing distinct physical sites of stimulation, as in deep brain stimulation therapy, and phase-shifted stimuli were delivered to each subpopulation in a random sequence. We explored how stimulation frequency and the number of stimulation sites affect the efficacy of RVS CR at desynchronizing the network. We demonstrate that RVS CR efficacy is sensitive to the depression-to-potentiation ratio in the STDP rule, which may be an important parameter to tune when reconciling simulations with experimental data. Numerical simulation of neuronal networks is constrained by computational resources when models demand large networks. This work proposes a model that demonstrates similar utility with a relatively small network, enabling researchers to study pathological neuronal activity and treatments more efficiently.

Stabilizing synaptic plasticity together with the neurons activity has remained a central challenge in theoretical neuroscience since the introduction of Hebbian learning principles. Classical Hebbian learning rules typically lead to unbounded synaptic growth, motivating the development of stabilization mechanisms such as normalization methods, BCM-type learning, synaptic scaling and others. While these approaches can prevent divergence, they can also exhibit different limitations e.g. resulting in too-sparse synaptic configurations or leading to poor scalability with increasing network size. A recently introduced meta-plasticity mechanism, termed annealed linear learning (ALL), dynamically reduces the learning rate as neuronal output increases, thereby preserving stable and interpretable fixed-point behavior of the output. However, the original formulation leads to an irreversible decay of the learning rate, preventing adaptation to changing environmental conditions. To address this, in the present study, we balance learning rate reduction at large outputs with recovery at small outputs and in addition introduce forgetting that gradually reduces synaptic weights. These extensions allow the system to discard outdated representations and adapt to novel input conditions. Analytical investigations demonstrate that the favorable output fixed-point properties of the original ALL framework are preserved under the extended rule. Furthermore, simulations with an artificial agent show that the proposed mechanism enables robust and fast re-learning and adaptation in changing environments.

The c-MYC proto-oncogene regulates cellular proliferation, and its aberrant expression drives a range of human cancers. It also has a bidirectional regulatory relationship with the mammalian core circadian clock, with emerging evidence suggesting that MYC overexpression leads to clock disruption and loss of rhythms. While prior studies have probed MYCs role in clock disruption by overexpressing or mutating the c-MYC gene, our understanding of the endogenous nature of c-MYC is limited. A major gap in knowledge is whether MYC itself is expressed rhythmically and if so, how its timing relates to that of core clock components. To address these shortcomings, we generated a c-MYC reporter and assessed its circadian nature, comparing it to BMAL1 and PER2, and developed a computational model based on these and previous findings to evaluate its role(s). We developed lentiviral constructs for and established a U2OS (common circadian model) reporter cell line expressing luciferase (luc) driven by a human-derived c-MYC promoter sequence. To facilitate comparisons, as part of this work, we also developed a human-sequence derived BMAL1 promoter reporter to more readily recapitulate its behaviors. Using luminometry studies and subsequent data analyses, we demonstrated that the c-MYC promoter oscillated rhythmically in U2OS cells, which possess inherently low levels of c-MYC. Furthermore, we found that c-MYC oscillates out-of-phase relative to BMAL1 and PER2. Using this information, we built a mathematical model to better understand how c-MYCs oscillations at both basal and over-expressed levels affect the clock and vice versa. The model reproduced expected alterations to the core clock resulting from c-MYC overexpression and showed that MYCs role is as a disruptor, although the timing of MYC regulation can minimize its negative impact(s) on circadian timekeeping. This work is the first to assess c-MYCs phase relationships relative to the core clock and to provide evidence for its circadian nature. Author summaryc-MYC is a transcription factor that is highly regulated and plays an important role in cellular proliferation. In cancers, deregulation of c-MYC causes its overexpression, resulting in tumorigenesis. There have been multiple connections demonstrated between MYC and the circadian clock, including the clocks role in MYC expression and that its overexpression can lead to disruptions to the core circadian clock. However, knowledge of the expression patterns of MYC are limited, including whether they occur in a circadian manner. To address this, we developed a c-MYC-luciferase reporter in a human circadian cell model (U2OS). For the first time, we were able to directly assess the rhythmic nature of c-MYC using this tool. Subsequently, we developed a mathematical model to gain insights into the disruptive role of MYC in clock regulation under disease-like conditions and, in turn, the effects of the circadian clock on MYC. We found that c-MYC oscillated in a circadian manner in U2OS cells and that the MYC proteins role is as a disruptor, but its timing can minimize its negative impact(s) on circadian rhythms.