Biology subjects

Jia, C.

Publications and source records attributed to Jia, C..

At least 19 recordsLinked to original sources

bioRxiv2026

Dynamical stability and accuracy of moment closure approximations for bursty gene expression with nonlinear degradation

Moment-closure methods provide a widely used approach for approximating low-order statistics of stochastic biochemical reaction networks, but the resulting closed equations may exhibit physically meaningless dynamics. Here, we systematically investigate the stability of second-order moment-closure approximations for a bursty gene expression model with nonlinear protein degradation. We consider the Gaussian, log-normal, and negative-binomial closures. By analyzing the resulting dynamical systems, we show that the Gaussian closure fails the proposed stability criterion for all parameter values, whereas both the log-normal and negative-binomial closures possess a unique physically accessible fixed point and are stable if and only if kB(1 + 2B) [≥] 1, where B is the mean burst size and k is the dimensionless protein synthesis rate. Moreover, this condition is automatically satisfied when the steady-state mean protein copy number is at least one, suggesting that it is mild in biologically relevant regimes. Numerical comparisons over a broad parameter range further show that the negative-binomial closure is the most accurate, while the Gaussian closure is the least accurate. We further develop higher-order negative-binomial moment-closure schemes and demonstrate that increasing the closure order substantially improves predictive accuracy. These results highlight the importance of considering dynamical stability, in addition to numerical accuracy, when assessing moment-closure approximations.

systems biology↗

bioRxiv2026

TomatoPGFM: A graph-conditioned foundation model for tomato pangenomes

Most genomic foundation models are pretrained on independent linear assemblies and therefore do not explicitly represent population-level segment sharing or local graph connectivity. We developed TomatoPGFM, a graph-conditioned model pretrained on 54.65 Gb of sequence from 66 tomato (Solanum spp.) accessions. Sequence tokens were conditioned on pangenome node attributes and local adjacency, and the model was optimised using masked language modelling and graph-feature reconstruction. To evaluate model responses to graph-conditioned input, we compared aligned, shuffled and disabled graph inputs in 25,000 windows from the training panel. Sequence-aligned graph input produced lower masked language modelling loss than graph-off at all five curriculum stages in both training-panel strata, while the shuffled perturbation generally yielded intermediate losses. We then assessed sequence-only transfer in Solanum sitiens LA1974 and S. lycopersicum MicroTom, neither of which was used for graph construction or pretraining. Frozen-probe AUROC values for gene-versus-intergenic and coding-sequence-versus-intergenic classification ranged from 0.8489 to 0.9593. TomatoPGFM produced higher AUROC point estimates than DNABERT-2 in all four comparisons. Enabling the zero-feature GraphAdapter pathway with adjacency messaging disabled changed throughput by less than 1% at 512-2,048 positions under the tested configuration. Together, these results show that TomatoPGFM responds consistently to sequence-aligned pangenome context in training-panel sequences and provides informative sequence representations for genic-region classification in accessions excluded from graph construction and pretraining.

bioinformatics↗

bioRxiv2025

The conserved NUS-1/DHDDS complex links N-glycosylation to lipid and lysosomal homeostasis in C. elegans

N-glycosylation, driven by the cis-prenyltransferase (cis-PT) complex, a NUS1 and DHDDS heterotetramer, is vital for proteome integrity. Despite being linked to severe congenital disorders of glycosylation (CDGs), the systemic role of NUS1/DHDDS remains elusive. Here, we characterize the conserved C. elegans cis-PT complex and uncover a critical crosstalk with global lipid metabolism. cis-PT deficiency induces catastrophic ER stress, global glycoprotein defects, and developmental failure. Mechanistically, NUS-1 physically interacts with the core oligosaccharyltransferase (OST) complex, directly coupling substrate synthesis to N-glycan transfer. Loss of NUS-1 or DHDDS causes systemic lipopenia, lysosomal dysfunction, and cholesterol sequestration, resulting from impaired N-glycosylation of key regulatory glycoproteins like SCAP. Utilizing CDG-associated CRISPR models, we resolve the molecular basis for cis-PT dysfunction, identifying interface disruption and catalytic impairment as distinct disease etiologies. These findings collectively reveal a critical and previously unappreciated crosstalk between protein glycosylation and global lipid metabolism, establishing a robust system to explore CDG pathology and therapeutic strategies.

cell biology↗

bioRxiv2025

DeepADR: Multi-modal Prediction of Adverse Drug Reaction Frequency by Integrating Early-Stage Drug Discovery Information via Kolmogorov-Arnold Networks

Adverse drug reactions (ADRs) are a major cause of clinical trial failure and post-market withdrawal, posing significant risks to public health and impeding drug development. While computational methods offer an alternative to costly preclinical testing, existing models often fail with novel compounds by requiring pre-existing information such as drug-ADR associations or by inadequately integrating diverse data sources. Here, we introduce DeepADR, a multi-modal deep learning framework for predicting both the occurrence and frequency of ADRs using early-stage, readily available data. DeepADR integrates chemical structures and biological target profiles with semantic representations of ADR terms derived from a large language model. These heterogeneous parameters are fused using a Kolmogorov-Arnold Network (KAN), which effectively models complex, non-linear cross-modal interactions to capture underlying toxicological mechanisms. Our model outperforms existing methods in predicting both ADR occurrence and frequency, demonstrating robust generalization to new chemical entities. By effectively integrating chemical, biological, and semantic datasets, DeepADR provides a powerful, scalable tool for the early-stage safety assessment and candidate prioritization. This framework not only facilitates the prioritization of safer drug candidates but also offers a methodology for predicting the toxicity of other hazardous materials, holding significant promise for advancing public health.

bioinformatics↗

bioRxiv2025

Human ribosome interactions reframe neomycin toxicity

Aminoglycosides such as neomycin are clinically limited by toxicity, commonly attributed to the inhibition of mitoribosomes. Here, we re-evaluate this mechanism by integrating Cryo-EM and functional assays to assess neomycins binding potential in vitro with its cellular engagement and functional consequences. Cryo-EM revealed extensive multi-site binding of neomycin on both human mitochondrial and cytosolic ribosomes in vitro, including conserved regions of the decoding center. In contrast, ribosomes isolated from neomycin-treated cells show markedly remodeled occupancy patterns, with no detectable neomycin bound to the mitoribosomes and reduced occupancy at a subset of cytosolic ribosome sites. However, neomycin remained functionally active in cells, inducing widespread stop-codon readthrough while having minimal effects on global mitochondrial and cytosolic protein synthesis. These findings reveal a disconnect between structural binding potential and cellular target engagement and identify disruption of translational fidelity, rather than global translational inhibition, as a major cellular consequence of neomycin exposure.

biochemistry↗

bioRxiv2025

Spectral theory of stochastic gene expression: a Hilbert space framework

A survey of the literature reveals notable discrepancies among the purported exact results for the spectra of stochastic gene expression models. For self-repressing gene circuits, previous studies ([Phys. Rev. Lett. 99, 108103 (2007)], [Phys. Rev. E 83,062902 (2011)], [J. Chem. Phys. 160, 074105 (2024)], and [bioRxiv 2025.02.05.635946 (2025)]) have provided different exact solutions for the eigenvalues of the generator matrix. In this work, we propose a unified Hilbert space framework for the spectral theory of stochastic gene expression. Based on this framework, we analytically derive the spectra for models of constitutive, bursty, and autoregulated gene expression. The eigenvalues and eigenvectors obtained are then used to construct an exact spectral representation of the time-dependent distribution of gene product numbers. The spectral gap between the zero eigenvalue and the first nonzero eigenvalue, which reflects the relaxation rate of the system towards its steady state, is then compared with the prediction of the deterministic model, and we find that deterministic modeling fails to capture the relaxation rate when autoregulation is strong. In particular, our results demonstrate that for infinite-dimensional operators such as in stochastic gene expression models, many conclusions in linear algebra do not apply, and one must rely on the modern theory of functional analysis.

molecular biology↗

bioRxiv2025

Social Exclusion Amplifies Behavioral Responses to Physical Pain via Insular Neuromodulation

The "Pain Overlap Theory" (1) proposes that the experience of social pain overlaps with and amplifies the experience of physical pain by sharing parts of the same underlying processing systems (2-6). In humans, the insular cortex has been implicated in this overlap of physical and social pain, but a mechanistic link has not been made (2,4,5,7-9). To determine whether social pain can subsequently impact responses to nociceptive stimuli via convergent electrical signals (spikes) or convergent chemical signals (neuromodulators), we designed a novel Social Exclusion paradigm termed the Fear of Missing Out (FOMO) Task which facilitates a mechanistic investigation in mice. We found that socially-excluded mice display more severe responses to physical pain, disrupted valence encoding, and impaired neural representations of nociceptive stimuli. We performed a systematic biosensor panel and found that endocannabinoid and oxytocin signaling in the insular cortex have opposing responses during trials where mice were attending or not attending to the Social Exclusion events respectively, demonstrating distinct neuromodulatory substrates that underpin different states of Social Exclusion. We also found that intra-insular blockade of oxytocin signaling increased the response to physical pain following Social Exclusion. Together these findings suggest Social Exclusion effectively alters physical pain perception using neuromodulatory signaling in the insular cortex.

neuroscience↗

bioRxiv2025

Ancient DNA Reveals Hominoid Evolution: Intermediate DNA Sequences and Advances in Molecular Paleontology

AbstractFossils and ancient crude pottery vessels function as physical "DNA containers," preserving oriDNA (original, in situ DNA) and accumulating eDNA (environmental DNA) over time. Ancient DNA (aDNA) serves as molecular fossils, chronicling evolutionaryhistory. Using "nano-affinitybead technology", we extracted and sequenced DNAfrom Lycoptera fossils in the Jehol region and a "round-bellied jar (Jar)" from the Erlitou period in Guangwu Town, yielding 236,545 primate sequences from the fossils and 86,908 from the pottery. We observed that the AFF value of DNA sequences negatively corre lates with species divergence time1, offering a quantitative measure of DNA preservation and host divergence. Some fragments distinct from modern genomic sequences, termed "intermediate DNAsequences" (IDS), have been identified. Many IDS exhibit an upper age limit, preserving characteristics of the last common ancestor (LCA) of the Hominidae and offering molecular insights into "Darwins puzzle". Among IDS, the SRRA subtype (Sequence Reversal and Rearrangement), identified in mRNA-coding exonic sequences, arises from the incorporation of a complementary antisense strand upstream of the sense strand, either adjacent to it or separated bya sequence interval. This introduces a novel post-transcriptional regulatory mechanism at the mRNA level, driven by SRRA, which presets hairpin structures and Indels in the UTR or CDS of exonic sequences, modulating gene variation. We propose: "SRRAs played a critical trial-and-error role in early Hominidae evolution, facilitating adaptive genomic changes, with some SRRA sequences later excised from exons", positioning SRRAas an evolutionary "genetic switch". Additionally, seven species -specific fragments (SSFs) of non-human primates (NHPs) linked to Asian Homo erectus were identified in the fossils, and pottery DNA reveale d sequences from tropical species (e.g., zebrass, oil palms), providing evidence of climate-driven local extinction and supporting paleo-ecological and paleo-environmental reconstruction. This method of analyzing aDNA from non-skeletal materials opens new avenues in paleontology, archaeology, and geology, guiding the tracing of ancient migration patterns and fossil searches. DNAfragments preserved within "DNA containers " exhibit an "old-few, new-many" turnover pattern, with many aDNA fragments displaying non-deamination. This evidence challenges prevailing perspectives, the authenticity criteria for aDNA, and the capabilities and scope of the traditional research method, necessitating a thorough reevaluation of the relevant knowledge framework. Furthermore, this study opens new opportunities for frontier research.

paleontology↗

bioRxiv2025

Evolutionary responses and genomic consequences of polyploidization in natural populations of Orychophragmus

Polyploidization has occurred throughout the tree of life and is particularly common in plants. Despite its ubiquity, our understanding of the short- and long-term effects and consequences of genome doubling in natural populations remains incomplete. In this study, we identified a novel ploidy-variable species system within the ornamental and industrial oilseed genus Orychophragmus (Brassicaceae), which comprises six species, including diploid and tetraploid cytotypes of O. taibaiensis. By integrating population-scale genomic and transcriptomic datasets across the species in this genus, we constructed a robust phylogenetic framework and investigated the divergence and demographic history of O. taibaiensis in comparison to its relatives. Specifically, we characterized the geographical distribution patterns of diploids and tetraploids in natural populations of O. taibaiensis, confirmed the autopolyploid origin of tetraploids, and inferred their origin time relative to diploid counterparts. Our findings further revealed that, following genome doubling, tetraploids accumulated a higher genetic load of deleterious mutations, likely due to relaxed purifying selection facilitated by allelic redundancy. Additionally, genome doubling was associated with pronounced changes in gene expression patterns, with differentially expressed genes evolving under relaxed selective constraints. These results highlight that the initial masking of deleterious mutations, changes in expression regulation, and divergent efficacy of selection likely all contribute to shaping the establishment and evolutionary potential of polyploids.

molecular biology↗

bioRxiv2025

Separable Dorsal Raphe Dopamine Projections mediate the Facets of Loneliness-like state

Affiliative social connections facilitate well-being and survival in numerous species. Engaging in social interactions requires positive or negative motivational drive, elicited through coordinated activity across neural circuits. However, the identity, interconnectivity, and functional encoding of social information within these circuits remains poorly understood. Here, we focus on downstream projections of dorsal raphe nucleus (DRN) dopamine neurons (DRNDAT), which we previously implicated in social motivation alongside an aversive affective state. We show that three prominent DRNDAT projections - to the bed nucleus of the stria terminalis (BNST), central amygdala (CeA), and posterior basolateral amygdala (BLP) - play separable roles in behavior, despite substantial collateralization. Photoactivation of the DRNDAT-CeA projection promoted social behavior and photostimulation of the DRNDAT-BNST projection promoted exploratory behavior, while the DRNDAT-BLP projection supported place avoidance, suggesting a negative affective state. Downstream regions showed diverse receptor expression, poising DRNDAT neurons to act through dopamine, neuropeptide, and glutamate transmission. Furthermore, we show ex vivo that the effect of DRNDAT photostimulation on downstream neuron excitability depended on region and baseline cell properties, resulting in excitatory responses in BNST cells and diverse responses in CeA and BLP. Finally, in vivo microendoscopic cellular-resolution recordings in the CeA with DRNDAT photostimulation revealed a correlation between social behavior and neurons excited by social stimuli- suggesting that increased dopamine tone may recruit different CeA neurons to social ensembles. Collectively, these circuit features may facilitate a coordinated, but flexible, response in the presence of social stimuli that can be flexibly guided based on the internal social homeostatic need state of the individual.

neuroscience↗

bioRxiv2024

Effective Markovian dynamics method of solving non-Markovian dynamics of stochastic gene expression

Experiments have shown that over 10% of proteins are degraded non-exponentially. Gene expression models for non-exponentially degraded proteins are notoriously difficult to solve since the underlying stochastic dynamics is non-Markovian. Here we develop an effective Markovian dynamics (EMD) method which converts a large class of non-Markovian models into effective Markovian ones so that they have the same mRNA and protein distributions at any fixed time. Using the EMD approach, we analytically solve some classical gene expression models with non-exponential or delayed protein decay, whose exact distributions are previously unknown and fail to be obtained using conventional queueing theory. Our theory successfully explains why non-exponentially degraded proteins on average have smaller mRNA-protein correlation than exponentially degraded proteins, and it predicts that bimodality is significantly enhanced in the presence of delayed protein degradation.

biochemistry↗

bioRxiv2024

Predicting Future Development of Stress-Induced Anhedonia From Cortical Dynamics and Facial Expression

The current state of mental health treatment for individuals diagnosed with major depressive disorder leaves billions of individuals with first-line therapies that are ineffective or burdened with undesirable side effects. One major obstacle is that distinct pathologies may currently be diagnosed as the same disease and prescribed the same treatments. The key to developing antidepressants with ubiquitous efficacy is to first identify a strategy to differentiate between heterogeneous conditions. Major depression is characterized by hallmark features such as anhedonia and a loss of motivation (1, 2), and it has been recognized that even among inbred mice raised under identical housing conditions, we observe heterogeneity in their susceptibility and resilience to stress (3). Anhedonia, a condition identified in multiple neuropsychiatric disorders, is described as the inability to experience pleasure and is linked to anomalous medial prefrontal cortex (mPFC) activity (4). The mPFC is responsible for higher order functions (5-8), such as valence encoding; however, it remains unknown how mPFC valence-specific neuronal population activity is affected during anhedonic conditions. To test this, we implemented the unpredictable chronic mild stress (CMS) protocol (9-11) in mice and examined hedonic behaviors following stress and ketamine treatment. We used unsupervised clustering to delineate individual variability in hedonic behavior in response to stress. We then performed in vivo 2-photon calcium imaging to longitudinally track mPFC valence-specific neuronal population dynamics during a Pavlovian discrimination task. Chronic mild stress mice exhibited a blunted effect in the ratio of mPFC neural population responses to rewards relative to punishments after stress that rebounds following ketamine treatment. Also, a linear classifier revealed that we can decode susceptibility to chronic mild stress based on mPFC valence-encoding properties prior to stress-exposure and behavioral expression of susceptibility. Lastly, we used a markerless pose tracking computer vision tool, SLEAP (31), to predict whether a mouse would become resilient or susceptible based on facial expressions during a Pavlovian discrimination task. These results indicate that mPFC valence encoding properties and behavior are predictive of anhedonic states. Altogether, these experiments point to the need for increased granularity in the measurement of both behavior and neural activity, as these factors can predict the predisposition to stress-induced anhedonia.

neuroscience↗

bioRxiv2024

Superimposed inhibitory surrounds underlying Saliency-based Stimulus Selection in avian Midbrain isthmi pars magnocellularis

In the avian midbrain network, bottom-up spatial attention is directed by saliency-based stimulus selection. However, it remains unclear whether the isthmi pars magnocellularis (Imc), the first site in the midbrain network to represent stimulus selection, can represent stimulus salience and what is the mechanism by which the midbrain network computes salience. Here, we used two separate translational motion stimuli as the main stimulation protocols and conducted in vivo electrophysiological experiments in the pigeons Imc. By combining bio-plausible model validation, we found two types of inhibitory surrounds of the Imc neuron receptive field, homogenous inhibitory surrounds (HIS) and non-homogenous inhibitory surrounds (non-HIS), and elucidated the mechanism by which both arise. While HIS is local and depends on stimulus feature similarity, which can be used to compute stimulus saliency, non-HIS is global and doesnt depend on stimulus feature similarity, which can be used to compute stimulus selection. Moreover, the superimposition of HIS and non-HIS modulates the neural response of Imc. The two inhibitory surrounds of Imc identified in this study more clearly elucidate the full process of achieving bottom-up stimulus selection based on saliency in the midbrain network and show that Imc is a nucleus that can represent both stimulus saliency and stimulus selection.

neuroscience↗

bioRxiv2024

Avian-restrict Salmonella transition to endemicity is accompanied by localized resistome adaptation

Bacterial regional demonstration after global dissemination is an essential pathway for selecting distinct finesses. However, the evolution of the resistome during the transition to endemicity remains unaddressed. Using the most comprehensive whole-genome sequencing dataset of Salmonella enterica serovar Gallinarum (S. Gallinarum) collected from 15 countries, including 45 newly recovered samples from two related local regions, we established the relationship among avian-specific pathogen genetic profiles and localization patterns. Initially, we revealed the international transmission and evolutionary history of S. Gallinarum to recent endemicity through phylogenetic analysis conducted using a spatiotemporal Bayesian framework. Our findings indicate that the independent acquisition of the resistome via the mobilome, primarily through plasmids and transposons shapes a unique antimicrobial resistance profile among different lineages. Notably, the mobilome-resistome combination among distinct lineages exhibits a geographical-specific manner, further supporting a localized endemic mobilome-driven process. Collectively, this study elucidates resistome adaptation in the endemic transition of an avian-specific pathogen, likely driven by the localized farming style, and provides valuable insights for targeted interventions.

microbiology↗

bioRxiv2024

The m6A Reader ECT1 Mediates Seed Germination via the DAG2-ECT1-PHYB Regulatory Cascade in Arabidopsis

The N6-methyladenosine (m6A) RNA modification, a significant epitranscriptomic mark, is integral to plant growth and development. m6A reader proteins are capable of recognizing m6A modifications to impact RNA metabolic and biological processes. Here, we discovered ECT1 as an m6A reader protein that directly binds to the m6A site and plays a role in positively regulating seed germination in the context of gibberellins (GAs). ECT1 undergoes m6A modification to ensure its own stability and engages in self-interaction to enhance its protein stability. Moreover, ECT1 establishes a regulatory circuit with DAG2, which has been reported to play a positive regulatory role in GA-mediated seed germination. We found that DAG2 directly binds to the ECT1 promoter to control its transcription. ECT1 modulates the mRNA stability of DAG2. Furthermore, we identified PHYB, which encodes a key photoreceptor controlling GA-regulated seed germination, as a common downstream target of DAG2 and ECT1. DAG2 and ECT1 regulate the expression of PHYB at the transcriptional and post-transcriptional levels, respectively. ECT1 binds directly to PHYB, thereby influencing its stability. While DAG2 binds to the PHYB promoter to regulate its transcription. Together, these results unveil that ECT1 participates in the m6A signaling pathway through complex and multifaceted molecular mechanisms, broadening the spectrum of m6A reader functions and deepening our insight into the m6A signaling network in Arabidopsis.

plant biology↗

bioRxiv2024

Exact switching time distributions for autoregulated gene expression models with mRNA and protein descriptions

In this study, we obtain the exact switching time distributions between the free and bound gene states for a detailed stochastic model of an autoregulatory genetic feedback loop with transcription, translation, mRNA and protein decay, as well as protein-gene interactions. The analytical solution generalizes and corrects the previous ones obtained in [Phys. Rev. Lett. 101, 118104 (2008)] and [Nat. Commun. 9, 3305 (2018)] for a reduced model of an autoregulatory loop that ignores the mRNA dynamics. We find that when the mRNA dynamics is modelled explicitly, the holding time in the free gene state can produce three shapes of steady-state distributions (decaying, bell-shaped, and bimodal). In particular, the detailed model with both mRNA and protein descriptions can produce a distribution shape that the reduced model fails to capture -- the detailed model of a negative (positive) feedback loop can display a bimodal (bell-shaped) holding time distribution, while the reduced model cannot. Interestingly, we also find that an autoregulatory loop can produce a heavy-tailed holding time distribution and the origin of this heavy-tailed phenomenon is clarified using our analytical solution. Finally, we investigate how the distribution shape is affected by the type of feedback, the binding and unbinding rates, and the transcription rates.

systems biology↗

bioRxiv2024

SlSAURs, targeted by SlSTOP1, inhibit SlPP2C.Ds to modulate H+-ATPase and tomato root elongation under aluminum stress

Aluminum (Al) stress, a prevalent constraint in acid soils, is known to inhibit plant growth by inhibiting root elongation through restricted cell expansion. The molecular mechanisms of Al-induced root inhibition, however, are not fully understood. This study aimed to elucidate the role of SlSAUR (Small auxin up-regulated RNA) proteins, which were downstream of the key Al stress-responsive transcription factor SlSTOP1 and its enhancer SlSZP1, in modulating root elongation under Al stress in tomato (Solanum lycopersicum). Our findings demonstrated that tomato lines with SlSAURs knockout exhibited shorter root lengths when subjected to Al stress. Further investigation into the underlying mechanisms revealed that SlSAURs interact with D-clade type 2C protein phosphatases, specifically SlPP2C.Ds. This interaction was pivotal as it suppresses the phosphatase activity, leading to the derepression of SlPP2C.Ds inhibitory effect on H+-ATPase. Consequently, this promoted cell expansion and root elongation under Al stress conditions. Our research significantly contributes to the current understanding of the molecular mechanisms by which Al ions modulate root elongation. The discovery of the SlSAUR-SlPP2C.D interaction and its impact on H+-ATPase activity provides a novel perspective on the adaptive strategies employed by plants to cope with Al toxicity. This knowledge may pave the way for the development of tomato cultivars with enhanced Al stress tolerance, thereby improving crop productivity in acid soils.

plant biology↗

bioRxiv2024

Geometry theory of distribution shapes for autoregulatory gene circuits

In this study, we provide a complete mathematical characterization of the phase diagram of distribution shapes in an extension of the two-state telegraph model of stochastic gene expression in the presence of positive or negative autoregulation. Using the techniques of second-order difference equations and nonlinear discrete dynamical systems, we prove that the feedback loop can only produce three shapes of steady-state protein distributions (decaying, bell-shaped, and bimodal), corresponding to three distinct parameter regions in the phase diagram. The boundaries of the three regions are characterized by two continuous curves, which can be constructed geometrically by the contour lines of a series of ratio operators. Based on the geometric structure of the phase diagram, we then provide some simple and verifiable sufficient and/or necessary conditions for the existence of the bimodal parameter region, as well as the conditions for the steady-state distribution to be decaying, bell-shaped, or bimodal. Finally, we also investigate how the phase diagram is affected by the strength of positive or negative feedback.

biophysics↗