Intrinsic noise in gene regulatory networks

Exploring the central dogma through the lens of gene expression noise

Over the past two decades, cell-to-cell heterogeneity has garnered increasing attention due to its critical role in both developmental and pathological processes. This growing interest has been driven, in part, by the advancements in live-cell and single-molecule imaging techniques. These techniques have provided mechanistic insights into how processes, transcription in particular, contribute to gene expression noise and, ultimately, cell-to-cell heterogeneity. More recently, however, research has expanded to explore how downstream steps in the central dogma influence gene expression noise. In this review, we mostly examine the impact of transcriptional processes on the generation of gene expression noise but also discuss how post-transcriptional mechanisms modulate noise and its propagation to the protein level. This evaluation emphasizes the need for further investigation into how processes beyond transcription shape gene expression noise, highlighting unanswered questions that remain in the field.

Progressive Deactivation of Hydroxylases Controls Hypoxia-Inducible Factor-1α-Coordinated Cellular Adaptation to Graded Hypoxia

Graded hypoxia is a common microenvironment in malignant solid tumors. As a central regulator in the hypoxic response, hypoxia-inducible factor-1 (HIF-1) can induce multiple cellular processes including glycolysis, angiogenesis, and necroptosis. How cells exploit the HIF-1 pathway to coordinate different processes to survive hypoxia remains unclear. We developed an integrated model of the HIF-1α network to elucidate the mechanism of cellular adaptation to hypoxia. By numerical simulations and bifurcation analysis, we found that HIF-1α is progressively activated with worsening hypoxia due to the sequential deactivation of the hydroxylases prolyl hydroxylase domain enzymes and factor inhibiting HIF (FIH). Bistable switches control the activation and deactivation processes. As a result, glycolysis, immunosuppression, angiogenesis, and necroptosis are orderly elicited in aggravating hypoxia. To avoid the excessive accumulation of lactic acid during glycolysis, HIF-1α induces monocarboxylate transporter and carbonic anhydrase 9 sequentially to export intracellular hydrogen ions, facilitating tumor cell survival. HIF-1α-induced miR-182 facilitates vascular endothelial growth factor production to promote angiogenesis under moderate hypoxia. The imbalance between accumulation and removal of lactic acid in severe hypoxia may result in acidosis and induce cell necroptosis. In addition, the deactivation of FIH results in the destabilization of HIF-1α in anoxia. Collectively, HIF-1α orchestrates the adaptation of tumor cells to hypoxia by selectively inducing its targets according to the severity of hypoxia. Our work may provide clues for tumor therapy by targeting the HIF-1 pathway.

Local nearby bifurcations lead to synergies in critical slowing down: The case of mushroom bifurcations

The behavior of nonlinear systems near critical transitions has significant implications for stability, transients, and resilience in complex systems. Transient times, τ, become extremely long near phase transitions (or bifurcations) in a phenomenon known as critical slowing down, and are observed in electronic circuits, circuit quantum electrodynamics, ecosystems, and gene regulatory networks. Critical slowing down typically follows universal laws of the form τ∼|μ-μ_{c}|^{β}, with μ being the control parameter and μ_{c} its critical value. For instance, β=-1/2 close to saddle-node bifurcations. Despite intensive research on slowing down phenomena for single bifurcations, both local and global, the behavior of transients when several bifurcations are close to each other remains unknown. Here, we investigate transients near two saddle-node bifurcations merging into a transcritical one. Using a nonlinear gene-regulatory model and a normal form exhibiting a mushroom bifurcation diagram we show, both analytically and numerically, a synergistic, i.e., nonadditive, lengthening of transients due to coupled ghost effects and transcritical slowing down. We also show that intrinsic and extrinsic noise play opposite roles in the slowing down of the transition, allowing us to control the timing of the transition without compromising the precision of timing. This establishes molecular strategies to generate genetic timers with transients much larger than the typical timescales of the reactions involved.

Challenges and opportunities for digital twins in precision medicine from a complex systems perspective

Digital twins (DTs) in precision medicine are increasingly viable, propelled by extensive data collection and advancements in artificial intelligence (AI), alongside traditional biomedical methodologies. We argue that including mechanistic simulations that produce behavior based on explicitly defined biological hypotheses and multiscale mechanisms is beneficial. It enables the exploration of diverse therapeutic strategies and supports dynamic clinical decision-making through insights from network science, quantitative biology, and digital medicine.

Exact distributions of threshold crossing times of proteins under post-transcriptional regulation by small RNAs

The timings of several cellular events like cell lysis, cell division, or pore formation in endosomes are regulated by the time taken for the relevant proteins to cross a threshold in number or concentration. Since protein synthesis is stochastic, the threshold crossing time is a first passage problem. The exact distributions of these first passage processes have been obtained recently for unregulated and autoregulated genes. Many proteins are however regulated by post-transcriptional regulation, controlled by small noncoding RNAs (sRNAs). Certain mathematical models of gene expression with post-transcriptional sRNA regulation have been recently exactly mapped to models without sRNA regulation. Utilizing this mapping and the exact distributions, we calculate exact results on fluctuations (full distribution, all cumulants, and characteristic times) of protein threshold crossing times in the presence of sRNA regulation. We derive two interesting predictions from these exact results. We show that the size of the fluctuation of the threshold crossing times have a nonmonotonic U-shaped behavior as a function of the rates of binding and unbinding of the sRNA-mRNA complex. Thus there are optimal parameters that minimize noise. Furthermore, the fluctuations in models with sRNA regulation may be higher or lower compared to the model without regulation, depending on the mean protein burst size.

Machine learning based analysis of single-cell data reveals evidence of subject-specific single-cell gene expression profiles in acute myeloid leukaemia patients and healthy controls

Acute Myeloid Leukaemia (AML) is characterized by uncontrolled growth of immature myeloid cells, disrupting normal blood production. Treatment typically involves chemotherapy, targeted therapy, and stem cell transplantation but many patients develop chemoresistance, leading to poor outcomes due to the disease's high heterogeneity. In this study, we used publicly available single-cell RNA sequencing data and machine learning to classify AML patients and healthy, monocytes, dendritic and progenitor cells population. We found that gene expression profiles of AML patients and healthy controls can be classified at the individual level with high accuracy (>70 %) when using progenitor cells, suggesting the existence of subject-specific single cell transcriptomics profiles. The analysis also revealed molecular determinants of patient heterogeneity (e.g. TPSD1, CT45A1, and GABRA4) which could support new strategies for patient stratification and personalized treatment in leukaemia.

Stress-Induced Constraint on Expression Noise of Essential Genes in E. coli

Gene expression is an inherently noisy process that is constrained by natural selection. Yet the condition dependence of constraint on expression noise remains unclear. Here, we address this problem by studying constraint on expression noise of E. coli genes in eight diverse growth conditions. In particular, we use variation in expression noise as an analog for constraint, examining its relationships to expression level and to the number of regulatory inputs from transcription factors across and within conditions. We show that variation in expression noise is negatively associated with expression level, implicating constraint to minimize expression noise of highly expressed genes. However, this relationship is condition dependent, with the strongest constraint observed when E. coli are grown in the presence of glycerol or ciprofloxacin, which result in carbon or antibiotic stress, respectively. In contrast, we do not observe evidence of constraint on expression noise of highly regulated genes, suggesting that highly expressed and highly regulated genes represent distinct classes of genes. Indeed, we find that essential genes are often highly expressed but not highly regulated, with elevated expression noise in glycerol and ciprofloxacin conditions. Thus, our findings support the hypothesis that selective constraint on expression noise is condition dependent in E. coli, illustrating how it may play a critical role in ensuring expression stability of essential genes in unstable environments.

Network structure and fluctuation data improve inference of metabolic interaction strengths with the inverse Jacobian

Based on high-throughput metabolomics data, the recently introduced inverse differential Jacobian algorithm can infer regulatory factors and molecular causality within metabolic networks close to steady-state. However, these studies assumed perturbations acting independently on each metabolite, corresponding to metabolic system fluctuations. In contrast, emerging evidence puts forward internal network fluctuations, particularly from gene expression fluctuations, leading to correlated perturbations on metabolites. Here, we propose a novel approach that exploits these correlations to quantify relevant metabolic interactions. By integrating enzyme-related fluctuations in the construction of an appropriate fluctuation matrix, we are able to exploit the underlying reaction network structure for the inverse Jacobian algorithm. We applied this approach to a model-based artificial dataset for validation, and to an experimental breast cancer dataset with two different cell lines. By highlighting metabolic interactions with significantly changed interaction strengths, the inverse Jacobian approach identified critical dynamic regulation points which are confirming previous breast cancer studies.

Plausible, robust biological oscillations through allelic buffering

Biological oscillators can specify time- and dose-dependent functions via dedicated control of their oscillatory dynamics. However, how biological oscillators, which recurrently activate noisy biochemical processes, achieve robust oscillations remains unclear. Here, we characterize the long-term oscillations of p53 and its negative feedback regulator Mdm2 in single cells after DNA damage. Whereas p53 oscillates regularly, Mdm2 from a single MDM2 allele exhibits random unresponsiveness to ∼9% of p53 pulses. Using allelic-specific imaging of MDM2 activity, we show that MDM2 alleles buffer each other to maintain p53 pulse amplitude. Removal of MDM2 allelic buffering cripples the robustness of p53 amplitude, thereby elevating p21 levels and cell-cycle arrest. In silico simulations support that allelic buffering enhances the robustness of biological oscillators and broadens their plausible biochemical space. Our findings show how allelic buffering ensures robust p53 oscillations, highlighting the potential importance of allelic buffering for the emergence of robust biological oscillators during evolution. A record of this paper's transparent peer review process is included in the supplemental information.

Sequestration of gene products by decoys enhances precision in the timing of intracellular events

Expressed gene products often interact ubiquitously with binding sites at nucleic acids and macromolecular complexes, known as decoys. The binding of transcription factors (TFs) to decoys can be crucial in controlling the stochastic dynamics of gene expression. Here, we explore the impact of decoys on the timing of intracellular events, as captured by the time taken for the levels of a given TF to reach a critical threshold level, known as the first passage time (FPT). Although nonlinearity introduced by binding makes exact mathematical analysis challenging, employing suitable approximations and reformulating FPT in terms of an alternative variable, we analytically assess the impact of decoys. The stability of the decoy-bound TFs against degradation impacts FPT statistics crucially. Decoys reduce noise in FPT, and stable decoy-bound TFs offer greater timing precision with less expression cost than their unstable counterparts. Interestingly, when both bound and free TFs decay at the same rate, decoy binding does not directly alter FPT noise. We verify these results by performing exact stochastic simulations. These results have important implications for the precise temporal scheduling of events involved in the functioning of biomolecular clocks, development processes, cell-cycle control, and cell-size homeostasis.

Energy Landscape Reveals the Underlying Mechanism of Cancer-Adipose Conversion in Gene Network Models

Cancer is a systemic heterogeneous disease involving complex molecular networks. Tumor formation involves an epithelial-mesenchymal transition (EMT), which promotes both metastasis and plasticity of cancer cells. Recent experiments have proposed that cancer cells can be transformed into adipocytes via a combination of drugs. However, the underlying mechanisms for how these drugs work, from a molecular network perspective, remain elusive. To reveal the mechanism of cancer-adipose conversion (CAC), this study adopts a systems biology approach by combing mathematical modeling and molecular experiments, based on underlying molecular regulatory networks. Four types of attractors are identified, corresponding to epithelial (E), mesenchymal (M), adipose (A) and partial/intermediate EMT (P) cell states on the CAC landscape. Landscape and transition path results illustrate that intermediate states play critical roles in the cancer to adipose transition. Through a landscape control approach, two new therapeutic strategies for drug combinations are identified, that promote CAC. These predictions are verified by molecular experiments in different cell lines. The combined computational and experimental approach provides a powerful tool to explore molecular mechanisms for cell fate transitions in cancer networks. The results reveal underlying mechanisms of intermediate cell states that govern the CAC, and identified new potential drug combinations to induce cancer adipogenesis.

A modified variational approach to noisy cell signaling

Signaling in cells is full of noise and, hence, described with stochastic biochemical models. Thus, an efficient computation algorithm for these fluctuating reactions is much needed. Apart from the very popular Monte Carlo simulation, methods based on probability distributions are frequently desired due to their analytical tractability and possible numerical advantages in diverse circumstances, among which the variational approach is the most notable. In this paper, new basis functions are proposed to better depict possibly complex distribution profiles, and an extra regularization scheme is supplied to the variational equation to remove occasional degeneracy-induced singularities during the evolution. The new extension is applied to four typical biochemical reaction models and restores the Gillespie results accurately but with greatly reduced simulation time. This modified variational approach is expected to work in a wide range of cell signaling networks.

Translation regulation by RNA stem-loops can reduce gene expression noise

BACKGROUND

Stochastic modelling plays a crucial role in comprehending the dynamics of intracellular events in various biochemical systems, including gene-expression models. Cell-to-cell variability arises from the stochasticity or noise in the levels of gene products such as messenger RNA (mRNA) and protein. The sources of noise can stem from different factors, including structural elements. Recent studies have revealed that the mRNA structure can be more intricate than previously assumed.

RESULTS

Here, we focus on the formation of stem-loops and present a reinterpretation of previous data, offering new insights. Our analysis demonstrates that stem-loops that restrict translation have the potential to reduce noise.

CONCLUSIONS

In conclusion, we investigate a structured/generalised version of a stochastic gene-expression model, wherein mRNA molecules can be found in one of their finite number of different states and transition between them. By characterising and deriving non-trivial analytical expressions for the steady-state protein distribution, we provide two specific examples which can be readily obtained from the structured/generalised model, showcasing the model's practical applicability.

Leveraging gene correlations in single cell transcriptomic data

BACKGROUND

Many approaches have been developed to overcome technical noise in single cell RNA-sequencing (scRNAseq). As researchers dig deeper into data-looking for rare cell types, subtleties of cell states, and details of gene regulatory networks-there is a growing need for algorithms with controllable accuracy and fewer ad hoc parameters and thresholds. Impeding this goal is the fact that an appropriate null distribution for scRNAseq cannot simply be extracted from data in which ground truth about biological variation is unknown (i.e., usually).

RESULTS

We approach this problem analytically, assuming that scRNAseq data reflect only cell heterogeneity (what we seek to characterize), transcriptional noise (temporal fluctuations randomly distributed across cells), and sampling error (i.e., Poisson noise). We analyze scRNAseq data without normalization-a step that skews distributions, particularly for sparse data-and calculate p values associated with key statistics. We develop an improved method for selecting features for cell clustering and identifying gene-gene correlations, both positive and negative. Using simulated data, we show that this method, which we call BigSur (Basic Informatics and Gene Statistics from Unnormalized Reads), captures even weak yet significant correlation structures in scRNAseq data. Applying BigSur to data from a clonal human melanoma cell line, we identify thousands of correlations that, when clustered without supervision into gene communities, align with known cellular components and biological processes, and highlight potentially novel cell biological relationships.

CONCLUSIONS

New insights into functionally relevant gene regulatory networks can be obtained using a statistically grounded approach to the identification of gene-gene correlations.

Quantum modeling simulates nutrient effect of bioplastic polyhydroxyalkanoate (PHA) production in Pseudomonas putida

Polyhydroxyalkanoates (PHAs) could be used to make sustainable, biodegradable plastics. However, the precise and accurate mechanistic modeling of PHA biosynthesis, especially medium-chain-length PHA (mcl-PHA), for yield improvement remains a challenge to biology. PHA biosynthesis is typically triggered by nitrogen limitation and tends to peak at an optimal carbon-to-nitrogen (C/N) ratio. Specifically, simulation of the underlying dynamic regulation mechanisms for PHA bioprocess is a bottleneck owing to surfeit model complexity and current modeling philosophies for uncertainty. To address this issue, we proposed a quantum-like decision-making model to encode gene expression and regulation events as hidden layers by the general transformation of a density matrix, which uses the interference of probability amplitudes to provide an empirical-level description for PHA biosynthesis. We implemented our framework modeling the biosynthesis of mcl-PHA in Pseudomonas putida with respect to external C/N ratios, showing its optimization production at maximum PHA production of 13.81% cell dry mass (CDM) at the C/N ratio of 40:1. The results also suggest the degree of P. putida's preference in channeling carbon towards PHA production as part of the bacterium's adaptative behavior to nutrient stress using quantum formalism. Generic parameters (kD, kN and theta θ) obtained based on such quantum formulation, representing P. putida's PHA biosynthesis with respect to external C/N ratios, was discussed. This work offers a new perspective on the use of quantum theory for PHA production, demonstrating its application potential for other bioprocesses.

Molecular models of bidirectional promoter regulation

Approximately 11% of human genes are transcribed by a bidirectional promoter (BDP), defined as two genes with <1 kb between their transcription start sites. Despite their evolutionary conservation and enrichment for housekeeping genes and oncogenes, the regulatory role of BDPs remains unclear. BDPs have been suggested to facilitate gene coregulation and/or decrease expression noise. This review discusses these potential regulatory functions through the context of six prospective underlying mechanistic models: a single nucleosome free region, shared transcription factor/regulator binding, cooperative negative supercoiling, bimodal histone marks, joint activation by enhancer(s), and RNA-mediated recruitment of regulators. These molecular mechanisms may act independently and/or cooperatively to facilitate the coregulation and/or decreased expression noise predicted of BDPs.

Transcriptional determinism and stochasticity contribute to the complexity of autism-associated SHANK family genes

Precision of transcription is critical because transcriptional dysregulation is disease causing. Traditional methods of transcriptional profiling are inadequate to elucidate the full spectrum of the transcriptome, particularly for longer and less abundant mRNAs. SHANK3 is one of the most common autism causative genes. Twenty-four Shank3-mutant animal lines have been developed for autism modeling. However, their preclinical validity has been questioned due to incomplete Shank3 transcript structure. We apply an integrative approach combining cDNA-capture and long-read sequencing to profile the SHANK3 transcriptome in humans and mice. We unexpectedly discover an extremely complex SHANK3 transcriptome. Specific SHANK3 transcripts are altered in Shank3-mutant mice and postmortem brain tissues from individuals with autism spectrum disorder. The enhanced SHANK3 transcriptome significantly improves the detection rate for potential deleterious variants from genomics studies of neuropsychiatric disorders. Our findings suggest that both deterministic and stochastic transcription of the genome is associated with SHANK family genes.

Living in a noisy world-origins of gene expression noise and its impact on cellular decision-making

The expression level of a gene can vary between genetically identical cells under the same environmental condition-a phenomenon referred to as gene expression noise. Several studies have now elucidated a central role of transcription factors in the generation of expression noise. Transcription factors, as the key components of gene regulatory networks, drive many important cellular decisions in response to cellular and environmental signals. Therefore, a very relevant question is how expression noise impacts gene regulation and influences cellular decision-making. In this Review, we summarize the current understanding of the molecular origins of expression noise, highlighting the role of transcription factors in this process, and discuss the ways in which noise can influence cellular decision-making. As advances in single-cell technologies open new avenues for studying expression noise as well as gene regulatory circuits, a better understanding of the influence of noise on cellular decisions will have important implications for many biological processes.

Understanding underlying physical mechanism reveals early warning indicators and key elements for adaptive infections disease networks

The study of infectious diseases holds significant scientific and societal importance, yet current research on the mechanisms of disease emergence and prediction methods still face challenging issues. This research uses the landscape and flux theoretical framework to reveal the non-equilibrium dynamics of adaptive infectious diseases and uncover its underlying physical mechanism. This allows the quantification of dynamics, characterizing the system with two basins of attraction determined by gradient and rotational flux forces. Quantification of entropy production rates provides insights into the system deviating from equilibrium and associated dissipative costs. The study identifies early warning indicators for the critical transition, emphasizing the advantage of observing time irreversibility from time series over theoretical entropy production and flux. The presence of rotational flux leads to an irreversible pathway between disease states. Through global sensitivity analysis, we identified the key factors influencing infectious diseases. In summary, this research offers valuable insights into infectious disease dynamics and presents a practical approach for predicting the onset of critical transition, addressing existing research gaps.

Evidence for Behavioral Autorepression in Covid-19 Epidemiological Dynamics

It has long been hypothesized that behavioral reactions to epidemic severity autoregulate infection dynamics, for example when susceptible individuals self-sequester based on perceived levels of circulating disease. However, evidence for such 'behavioral autorepression' has remained elusive, and its presence could significantly affect epidemic forecasting and interventions. Here, we analyzed early COVID-19 dynamics at 708 locations over three epidemiological scales (96 countries, 50 US states, and 562 US counties). Signatures of behavioral autorepression were identified through: (i) a counterintuitive mobility-death correlation, (ii) fluctuation-magnitude analysis, and (iii) dynamics of SARS-CoV-2 infection waves. These data enabled calculation of the average behavioral-autorepression strength (i.e., negative feedback 'gain') across different populations. Surprisingly, incorporating behavioral autorepression into conventional models was required to accurately forecast COVID-19 mortality. Models also predicted that the strength of behavioral autorepression has the potential to alter the efficacy of non-pharmaceutical interventions. Overall, these results provide evidence for the long-hypothesized existence of behavioral autorepression, which could improve epidemic forecasting and enable more effective application of non-pharmaceutical interventions during future epidemics.

Significance

Challenges with epidemiological forecasting during the COVID-19 pandemic suggested gaps in underlying model architecture. One long-held hypothesis, typically omitted from conventional models due to lack of empirical evidence, is that human behaviors lead to intrinsic negative autoregulation of epidemics (termed 'behavioral autorepression'). This omission substantially alters model forecasts. Here, we provide independent lines of evidence for behavioral autorepression during the COVID-19 pandemic, demonstrate that it is sufficient to explain counterintuitive data on 'shutdowns', and provides a mechanistic explanation of why early shutdowns were more effective than delayed, high-intensity shutdowns. We empirically measure autorepression strength, and show that incorporating autorepression dramatically improves epidemiological forecasting. The autorepression phenomenon suggests that tailoring interventions to specific populations may be warranted.

Responses of organ precursors to correct and incorrect inductive signals

During embryonic development, the inductive molecules produced by local origins normally arrive at their target tissues in a nondirectional, diffusion manner. The target organ precursor cells must correctly interpret these inductive signals to ensure proper specification/differentiation, which is dependent on two prerequisites: (i) obtaining cell-intrinsic competence; and (ii) receiving correct inductive signals while resisting incorrect ones. Gain of intrinsic competence could avoid a large number of misinductions because the incompetent cells are nonresponsive to inductive signals. However, in cases of different precursor cells with similar competence and located in close proximity, resistance to incorrect inductive signals is essential for accurate determination of cell fate. Here we outline the mechanisms of how organ precursors respond to correct and incorrect inductive signals.

Phase separation provides a mechanism to drive phenotype switching

Phenotypic switching plays a crucial role in cell fate determination across various organisms. Recent experimental findings highlight the significance of protein compartmentalization via liquid-liquid phase separation in influencing such decisions. However, the precise mechanism through which phase separation regulates phenotypic switching remains elusive. To investigate this, we established a mathematical model that couples a phase separation process and a gene expression process with feedback. We used the chemical master equation theory and mean-field approximation to study the effects of phase separation on the gene expression products. We found that phase separation can cause bistability and bimodality. Furthermore, phase separation can control the bistable properties of the system, such as bifurcation points and bistable ranges. On the other hand, in stochastic dynamics, the droplet phase exhibits double peaks within a more extensive phase separation threshold range than the dilute phase, indicating the pivotal role of the droplet phase in cell fate decisions. These findings propose an alternative mechanism that influences cell fate decisions through the phase separation process. As phase separation is increasingly discovered in gene regulatory networks, related modeling research can help build biomolecular systems with desired properties and offer insights into explaining cell fate decisions.

Non-Poissonian Bursts in the Arrival of Phenotypic Variation Can Strongly Affect the Dynamics of Adaptation

Modeling the rate at which adaptive phenotypes appear in a population is a key to predicting evolutionary processes. Given random mutations, should this rate be modeled by a simple Poisson process, or is a more complex dynamics needed? Here we use analytic calculations and simulations of evolving populations on explicit genotype-phenotype maps to show that the introduction of novel phenotypes can be "bursty" or overdispersed. In other words, a novel phenotype either appears multiple times in quick succession or not at all for many generations. These bursts are fundamentally caused by statistical fluctuations and other structure in the map from genotypes to phenotypes. Their strength depends on population parameters, being highest for "monomorphic" populations with low mutation rates. They can also be enhanced by additional inhomogeneities in the mapping from genotypes to phenotypes. We mainly investigate the effect of bursts using the well-studied genotype-phenotype map for RNA secondary structure, but find similar behavior in a lattice protein model and in Richard Dawkins's biomorphs model of morphological development. Bursts can profoundly affect adaptive dynamics. Most notably, they imply that fitness differences play a smaller role in determining which phenotype fixes than would be the case for a Poisson process without bursts.

Contributions of transcriptional noise to leukaemia evolution: KAT2A as a case-study

Transcriptional noise is proposed to participate in cell fate changes, but contributions to mammalian cell differentiation systems, including cancer, remain associative. Cancer evolution is driven by genetic variability, with modulatory or contributory participation of epigenetic variants. Accumulation of epigenetic variants enhances transcriptional noise, which can facilitate cancer cell fate transitions. Acute myeloid leukaemia (AML) is an aggressive cancer with strong epigenetic dependencies, characterized by blocked differentiation. It constitutes an attractive model to probe links between transcriptional noise and malignant cell fate regulation. Gcn5/KAT2A is a classical epigenetic transcriptional noise regulator. Its loss increases transcriptional noise and modifies cell fates in stem and AML cells. By reviewing the analysis of KAT2A-depleted pre-leukaemia and leukaemia models, I discuss that the net result of transcriptional noise is diversification of cell fates secondary to alternative transcriptional programmes. Cellular diversification can enable or hinder AML progression, respectively, by differentiation of cell types responsive to mutations, or by maladaptation of leukaemia stem cells. KAT2A-dependent noise-responsive genes participate in ribosome biogenesis and KAT2A loss destabilizes translational activity. I discuss putative contributions of perturbed translation to AML biology, and propose KAT2A loss as a model for mechanistic integration of transcriptional and translational control of noise and fate decisions. This article is part of a discussion meeting issue 'Causes and consequences of stochastic processes in development and disease'.

Effects of mRNA conformational switching on translational noise in gene circuits

Intragenic translational heterogeneity describes the variation in translation at the level of transcripts for an individual gene. A factor that contributes to this source of variation is the mRNA structure. Both the composition of the thermodynamic ensemble, i.e., the stationary distribution of mRNA structures, and the switching dynamics between those play a role. The effect of the switching dynamics on intragenic translational heterogeneity remains poorly understood. We present a stochastic translation model that accounts for mRNA structure switching and is derived from a Markov model via approximate stochastic filtering. We assess the approximation on various timescales and provide a method to quantify how mRNA structure dynamics contributes to translational heterogeneity. With our approach, we allow quantitative information on mRNA switching from biophysical experiments or coarse-grain molecular dynamics simulations of mRNA structures to be included in gene regulatory chemical reaction network models without an increase in the number of species. Thereby, our model bridges a gap between mRNA structure kinetics and gene expression models, which we hope will further improve our understanding of gene regulatory networks and facilitate genetic circuit design.

Transcriptional Determinism and Stochasticity Contribute to the Complexity of Autism Associated SHANK Family Genes

Precision of transcription is critical because transcriptional dysregulation is disease causing. Traditional methods of transcriptional profiling are inadequate to elucidate the full spectrum of the transcriptome, particularly for longer and less abundant mRNAs. SHANK3 is one of the most common autism causative genes. Twenty-four Shank3 mutant animal lines have been developed for autism modeling. However, their preclinical validity has been questioned due to incomplete Shank3 transcript structure. We applied an integrative approach combining cDNA-capture and long-read sequencing to profile the SHANK3 transcriptome in human and mice. We unexpectedly discovered an extremely complex SHANK3 transcriptome. Specific SHANK3 transcripts were altered in Shank3 mutant mice and postmortem brains tissues from individuals with ASD. The enhanced SHANK3 transcriptome significantly improved the detection rate for potential deleterious variants from genomics studies of neuropsychiatric disorders. Our findings suggest the stochastic transcription of genome associated with SHANK family genes.

Rapid adaptation of cellular metabolic rate to the MicroRNA complements of mammals and its relevance to the evolution of endothermy

The metabolic efficiency of mammalian cells depends on the attenuation of intrinsic translation noise by microRNAs. We devised a metric of cellular metabolic rate (cMR), rMR/Mexp optimally fit to the number of microRNA families (mirFam), that is robust to variation in mass and sensitive to body temperature (Tb), consistent with the heat dissipation limit theory of Speakman and Król (2010). Using mirFam as predictor, an Ornstein-Uhlenbeck process of stabilizing selection, with an adaptive shift at the divergence of Boreoeutheria, accounted for 95% of the variation in cMR across mammals. Branchwise rates of evolution of cMR, mirFam and Tb concurrently increased 6- to 7-fold at the divergence of Boreoeutheria, independent of mass. Cellular MR variation across placental mammals was also predicted by the sum of model conserved microRNA-target interactions, revealing an unexpected degree of integration of the microRNA-target apparatus into the energy economy of the mammalian cell.

Chemical Reaction Models in Synthetic Promoter Design in Bacteria

We discuss the formalism of chemical reaction networks (CRNs) as a computer-aided design interface for using formal methods in engineering living technologies. We set out by reviewing formal methods within a broader view of synthetic biology. Based on published results, we illustrate, step by step, how mathematical and computational techniques on CRNs can be used to study the structural and dynamic properties of the designed systems. As a case study, we use an E. coli two-component system that relays the external inorganic phosphate concentration signal to genetic components. We show how CRN models can scan and explore phenotypic regimes of synthetic promoters with varying detection thresholds, thereby providing a means for fine-tuning the promoter strength to match the specification.

From reinforcement learning to agency: Frameworks for understanding basal cognition

Organisms play, explore, and mimic those around them. Is there a purpose to this behavior? Are organisms just behaving, or are they trying to achieve goals? We believe this is a false dichotomy. To that end, to understand organisms, we attempt to unify two approaches for understanding complex agents, whether evolved or engineered. We argue that formalisms describing multiscale competencies and goal-directedness in biology (e.g., TAME), and reinforcement learning (RL), can be combined in a symbiotic framework. While RL has been largely focused on higher-level organisms and robots of high complexity, TAME is naturally capable of describing lower-level organisms and minimal agents as well. We propose several novel questions that come from using RL/TAME to understand biology as well as ones that come from using biology to formulate new theory in AI. We hope that the research programs proposed in this piece shape future efforts to understand biological organisms and also future efforts to build artificial agents.

Evolution of hierarchy and irreversibility in theoretical cell differentiation model

The process of cell differentiation in multicellular organisms is characterized by hierarchy and irreversibility in many cases. However, the conditions and selection pressures that give rise to these characteristics remain poorly understood. By using a mathematical model, here we show that the network of differentiation potency (differentiation diagram) becomes necessarily hierarchical and irreversible by increasing the number of terminally differentiated states under certain conditions. The mechanisms generating these characteristics are clarified using geometry in the cell state space. The results demonstrate that the hierarchical organization and irreversibility can manifest independently of direct selection pressures associated with these characteristics, instead they appear to evolve as byproducts of selective forces favoring a diversity of differentiated cell types. The study also provides a new perspective on the structure of gene regulatory networks that produce hierarchical and irreversible differentiation diagrams. These results indicate some constraints on cell differentiation, which are expected to provide a starting point for theoretical discussion of the implicit limits and directions of evolution in multicellular organisms.

Flagellar dynamics reveal fluctuations and kinetic limit in the Escherichia coli chemotaxis network

The Escherichia coli chemotaxis network, by which bacteria modulate their random run/tumble swimming pattern to navigate their environment, must cope with unavoidable number fluctuations ("noise") in its molecular constituents like other signaling networks. The probability of clockwise (CW) flagellar rotation, or CW bias, is a measure of the chemotaxis network's output, and its temporal fluctuations provide a proxy for network noise. Here we quantify fluctuations in the chemotaxis signaling network from the switching statistics of flagella, observed using time-resolved fluorescence microscopy of individual optically trapped E. coli cells. This approach allows noise to be quantified across the dynamic range of the network. Large CW bias fluctuations are revealed at steady state, which may play a critical role in driving flagellar switching and cell tumbling. When the network is stimulated chemically to higher activity, fluctuations dramatically decrease. A stochastic theoretical model, inspired by work on gene expression noise, points to CheY activation occurring in bursts, driving CW bias fluctuations. This model also shows that an intrinsic kinetic ceiling on network activity places an upper limit on activated CheY and CW bias, which when encountered suppresses network fluctuations. This limit may also prevent cells from tumbling unproductively in steep gradients.

Effects of microRNA-mediated negative feedback on gene expression noise

MicroRNAs (miRNAs) are small noncoding RNAs that regulate gene expression post-transcriptionally in eukaryotes by binding with target mRNAs and preventing translation. miRNA-mediated feedback motifs are ubiquitous in various genetic networks that control cellular decision making. A key question is how such a feedback mechanism may affect gene expression noise. To answer this, we have developed a mathematical model to study the effects of a miRNA-dependent negative-feedback loop on mean expression and noise in target mRNAs. Combining analytics and simulations, we show the existence of an expression threshold demarcating repressed and expressed regimes in agreement with earlier studies. The steady-state mRNA distributions are bimodal near the threshold, where copy numbers of mRNAs and miRNAs exhibit enhanced anticorrelated fluctuations. Moreover, variation of negative-feedback strength shifts the threshold locations and modulates the noise profiles. Notably, the miRNA-mRNA binding affinity and feedback strength collectively shape the bimodality. We also compare our model with a direct auto-repression motif, where a gene produces its own repressor. Auto-repression fails to produce bimodal mRNA distributions as found in miRNA-based indirect repression, suggesting the crucial role of miRNAs in creating phenotypic diversity. Together, we demonstrate how miRNA-dependent negative feedback modifies the expression threshold and leads to a broader parameter regime of bimodality compared to the no-feedback case.

Leveraging gene correlations in single cell transcriptomic data

BACKGROUND

Many approaches have been developed to overcome technical noise in single cell RNA-sequencing (scRNAseq). As researchers dig deeper into data-looking for rare cell types, subtleties of cell states, and details of gene regulatory networks-there is a growing need for algorithms with controllable accuracy and fewer ad hoc parameters and thresholds. Impeding this goal is the fact that an appropriate null distribution for scRNAseq cannot simply be extracted from data when ground truth about biological variation is unknown (i.e., usually).

RESULTS

We approach this problem analytically, assuming that scRNAseq data reflect only cell heterogeneity (what we seek to characterize), transcriptional noise (temporal fluctuations randomly distributed across cells), and sampling error (i.e., Poisson noise). We analyze scRNAseq data without normalization-a step that skews distributions, particularly for sparse data-and calculate p-values associated with key statistics. We develop an improved method for selecting features for cell clustering and identifying gene-gene correlations, both positive and negative. Using simulated data, we show that this method, which we call BigSur (Basic Informatics and Gene Statistics from Unnormalized Reads), captures even weak yet significant correlation structures in scRNAseq data. Applying BigSur to data from a clonal human melanoma cell line, we identify thousands of correlations that, when clustered without supervision into gene communities, align with known cellular components and biological processes, and highlight potentially novel cell biological relationships.

CONCLUSIONS

New insights into functionally relevant gene regulatory networks can be obtained using a statistically grounded approach to the identification of gene-gene correlations.

Engineered live bacteria as disease detection and diagnosis tools

Sensitive and minimally invasive medical diagnostics are essential to the early detection of diseases, monitoring their progression and response to treatment. Engineered bacteria as live sensors are being developed as a new class of biosensors for sensitive, robust, noninvasive, and in situ detection of disease onset at low cost. Akin to microrobotic systems, a combination of simple genetic rules, basic logic gates, and complex synthetic bioengineering principles are used to program bacterial vectors as living machines for detecting biomarkers of diseases, some of which cannot be detected with other sensing technologies. Bacterial whole-cell biosensors (BWCBs) can have wide-ranging functions from detection only, to detection and recording, to closed-loop detection-regulated treatment. In this review article, we first summarize the unique benefits of bacteria as living sensors. We then describe the different bacteria-based diagnosis approaches and provide examples of diagnosing various diseases and disorders. We also discuss the use of bacteria as imaging vectors for disease detection and image-guided surgery. We conclude by highlighting current challenges and opportunities for further exploration toward clinical translation of these bacteria-based systems.

Studying stochastic systems biology of the cell with single-cell genomics data

Recent experimental developments in genome-wide RNA quantification hold considerable promise for systems biology. However, rigorously probing the biology of living cells requires a unified mathematical framework that accounts for single-molecule biological stochasticity in the context of technical variation associated with genomics assays. We review models for a variety of RNA transcription processes, as well as the encapsulation and library construction steps of microfluidics-based single-cell RNA sequencing, and present a framework to integrate these phenomena by the manipulation of generating functions. Finally, we use simulated scenarios and biological data to illustrate the implications and applications of the approach.

Heterogeneous off-target impact of ion-channel deletion on intrinsic properties of hippocampal model neurons that self-regulate calcium

How do neurons that implement cell-autonomous self-regulation of calcium react to knockout of individual ion-channel conductances? To address this question, we used a heterogeneous population of 78 conductance-based models of hippocampal pyramidal neurons that maintained cell-autonomous calcium homeostasis while receiving theta-frequency inputs. At calcium steady-state, we individually deleted each of the 11 active ion-channel conductances from each model. We measured the acute impact of deleting each conductance (one at a time) by comparing intrinsic electrophysiological properties before and immediately after channel deletion. The acute impact of deleting individual conductances on physiological properties (including calcium homeostasis) was heterogeneous, depending on the property, the specific model, and the deleted channel. The underlying many-to-many mapping between ion channels and properties pointed to ion-channel degeneracy. Next, we allowed the other conductances (barring the deleted conductance) to evolve towards achieving calcium homeostasis during theta-frequency activity. When calcium homeostasis was perturbed by ion-channel deletion, post-knockout plasticity in other conductances ensured resilience of calcium homeostasis to ion-channel deletion. These results demonstrate degeneracy in calcium homeostasis, as calcium homeostasis in knockout models was implemented in the absence of a channel that was earlier involved in the homeostatic process. Importantly, in reacquiring homeostasis, ion-channel conductances and physiological properties underwent heterogenous plasticity (dependent on the model, the property, and the deleted channel), even introducing changes in properties that were not directly connected to the deleted channel. Together, post-knockout plasticity geared towards maintaining homeostasis introduced heterogenous off-target effects on several channels and properties, suggesting that extreme caution be exercised in interpreting experimental outcomes involving channel knockouts.

Transcriptional Stochasticity as a Key Aspect of HIV-1 Latency

This review summarizes current advances in the role of transcriptional stochasticity in HIV-1 latency, which were possible in a large part due to the development of single-cell approaches. HIV-1 transcription proceeds in bursts of RNA production, which stem from the stochastic switching of the viral promoter between ON and OFF states. This switching is caused by random binding dynamics of transcription factors and nucleosomes to the viral promoter and occurs at several time scales from minutes to hours. Transcriptional bursts are mainly controlled by the core transcription factors TBP, SP1 and NF-κb, the chromatin status of the viral promoter and RNA polymerase II pausing. In particular, spontaneous variability in the promoter chromatin creates heterogeneity in the response to activators such as TNF-α, which is then amplified by the Tat feedback loop to generate high and low viral transcriptional states. This phenomenon is likely at the basis of the partial and stochastic response of latent T cells from HIV-1 patients to latency-reversing agents, which is a barrier for the development of shock-and-kill strategies of viral eradication. A detailed understanding of the transcriptional stochasticity of HIV-1 and the possibility to precisely model this phenomenon will be important assets to develop more effective therapeutic strategies.

Evaluating single-cell variability in proteasomal decay

Gene expression is a stochastic process that leads to variability in mRNA and protein abundances even within an isogenic population of cells grown in the same environment. This variation, often called gene-expression noise, has typically been attributed to transcriptional and translational processes while ignoring the contributions of protein decay variability across cells. Here we estimate the single-cell protein decay rates of two degron GFPs in Saccharomyces cerevisiae using time-lapse microscopy. We find substantial cell-to-cell variability in the decay rates of the degron GFPs. We evaluate cellular features that explain the variability in the proteasomal decay and find that the amount of 20s catalytic beta subunit of the proteasome marginally explains the observed variability in the degron GFP half-lives. We propose alternate hypotheses that might explain the observed variability in the decay of the two degron GFPs. Overall, our study highlights the importance of studying the kinetics of the decay process at single-cell resolution and that decay rates vary at the single-cell level, and that the decay process is stochastic. A complex model of decay dynamics must be included when modeling stochastic gene expression to estimate gene expression noise.

Theoretical and computational tools to model multistable gene regulatory networks

The last decade has witnessed a surge of theoretical and computational models to describe the dynamics of complex gene regulatory networks, and how these interactions can give rise to multistable and heterogeneous cell populations. As the use of theoretical modeling to describe genetic and biochemical circuits becomes more widespread, theoreticians with mathematical and physical backgrounds routinely apply concepts from statistical physics, non-linear dynamics, and network theory to biological systems. This review aims at providing a clear overview of the most important methodologies applied in the field while highlighting current and future challenges. It also includes hands-on tutorials to solve and simulate some of the archetypical biological system models used in the field. Furthermore, we provide concrete examples from the existing literature for theoreticians that wish to explore this fast-developing field. Whenever possible, we highlight the similarities and differences between biochemical and regulatory networks and 'classical' systems typically studied in non-equilibrium statistical and quantum mechanics.

Out-of-equilibrium gene expression fluctuations in the presence of extrinsic noise

Cell-to-cell variability in protein concentrations is strongly affected by extrinsic noise, especially for highly expressed genes. Extrinsic noise can be due to fluctuations of several possible cellular factors connected to cell physiology and to the level of key enzymes in the expression process. However, how to identify the predominant sources of extrinsic noise in a biological system is still an open question. This work considers a general stochastic model of gene expression with extrinsic noise represented as fluctuations of the different model rates, and focuses on the out-of-equilibrium expression dynamics. Combining analytical calculations with stochastic simulations, we characterize how extrinsic noise shapes the protein variability during gene activation or inactivation, depending on the prevailing source of extrinsic variability, on its intensity and timescale. In particular, we show that qualitatively different noise profiles can be identified depending on which are the fluctuating parameters. This indicates an experimentally accessible way to pinpoint the dominant sources of extrinsic noise using time-coarse experiments.

The minimal intrinsic stochasticity of constitutively expressed eukaryotic genes is sub-Poissonian

Gene expression inherently gives rise to stochastic variation ("noise") in the production of gene products. Minimizing noise is crucial for ensuring reliable cellular functions. However, noise cannot be suppressed below a certain intrinsic limit. For constitutively expressed genes, this limit is typically assumed to be Poissonian noise, wherein the variance in mRNA numbers is equal to their mean. Here, we demonstrate that several cell division genes in fission yeast exhibit mRNA variances significantly below this limit. The reduced variance can be explained by a gene expression model incorporating multiple transcription and mRNA degradation steps. Notably, in this sub-Poissonian regime, distinct from Poissonian or super-Poissonian regimes, cytoplasmic noise is effectively suppressed through a higher mRNA export rate. Our findings redefine the lower limit of eukaryotic gene expression noise and uncover molecular requirements for achieving ultralow noise, which is expected to be important for vital cellular functions.

Bacterial Replication Initiation as Precision Control by Protein Counting

Balanced biosynthesis is the hallmark of bacterial cell physiology, where the concentrations of stable proteins remain steady. However, this poses a conceptual challenge to modeling the cell-cycle and cell-size controls in bacteria, as prevailing concentration-based eukaryote models are not directly applicable. In this study, we revisit and significantly extend the initiator-titration model, proposed 30 years ago, and we explain how bacteria precisely and robustly control replication initiation based on the mechanism of protein copy-number sensing. Using a mean-field approach, we first derive an analytical expression of the cell size at initiation based on three biological mechanistic control parameters for an extended initiator-titration model. We also study the stability of our model analytically and show that initiation can become unstable in multifork replication conditions. Using simulations, we further show that the presence of the conversion between active and inactive initiator protein forms significantly represses initiation instability. Importantly, the two-step Poisson process set by the initiator titration step results in significantly improved initiation synchrony with C V ~ 1 / N scaling rather than the standard 1 / N scaling in the Poisson process, where N is the total number of initiators required for initiation. Our results answer two long-standing questions in replication initiation: (i) Why do bacteria produce almost two orders of magnitude more DnaA, the master initiator proteins, than required for initiation? (ii) Why does DnaA exist in active (DnaA-ATP) and inactive (DnaA-ADP) forms if only the active form is competent for initiation? The mechanism presented in this work provides a satisfying general solution to how the cell can achieve precision control without sensing protein concentrations, with broad implications from evolution to the design of synthetic cells.

Sequestration of histidine kinases by non-cognate response regulators establishes a threshold level of stimulation for bacterial two-component signaling

Bacterial two-component systems (TCSs) consist of a sensor histidine kinase (HK) that perceives a specific signal, and a cognate response regulator (RR) that modulates the expression of target genes. Positive autoregulation improves TCS sensitivity to stimuli, but may trigger disproportionately large responses to weak signals, compromising bacterial fitness. Here, we combine experiments and mathematical modelling to reveal a general design that prevents such disproportionate responses: phosphorylated HKs (HK~Ps) can be sequestered by non-cognate RRs. We study five TCSs of Mycobacterium tuberculosis and find, for all of them, non-cognate RRs that show higher affinity than cognate RRs for HK~Ps. Indeed, in vitro assays show that HK~Ps preferentially bind higher affinity non-cognate RRs and get sequestered. Mathematical modelling indicates that this sequestration would introduce a 'threshold' stimulus strength for eliciting responses, thereby preventing responses to weak signals. Finally, we construct tunable expression systems in Mycobacterium bovis BCG to show that higher affinity non-cognate RRs suppress responses in vivo.

Predicting attractors from spectral properties of stylized gene regulatory networks

How the architecture of gene regulatory networks shapes gene expression patterns is an open question, which has been approached from a multitude of angles. The dominant strategy has been to identify nonrandom features in these networks and then argue for the function of these features using mechanistic modeling. Here we establish the foundation of an alternative approach by studying the correlation of network eigenvectors with synthetic gene expression data simulated with a basic and popular model of gene expression dynamics: Boolean threshold dynamics in signed directed graphs. We show that eigenvectors of the network adjacency matrix can predict collective states (attractors). However, the overall predictive power depends on details of the network architecture, namely the fraction of positive 3-cycles, in a predictable fashion. Our results are a set of statistical observations, providing a systematic step towards a further theoretical understanding of the role of network eigenvectors in dynamics on graphs.

A Noise-Tolerating Gene Association Network Uncovering an Oncogenic Regulatory Motif in Lymphoma Transcriptomics

In cancer genomics research, gene expressions provide clues to gene regulations implicating patients' risk of survival. Gene expressions, however, fluctuate due to noises arising internally and externally, making their use to infer gene associations, hence regulation mechanisms, problematic. Here, we develop a new regression approach to model gene association networks while considering uncertain biological noises. In a series of simulation experiments accounting for varying levels of biological noises, the new method was shown to be robust and perform better than conventional regression methods, as judged by a number of statistical measures on unbiasedness, consistency and accuracy. Application to infer gene associations in germinal-center B cells led to the discovery of a three-by-two regulatory motif gene expression and a three-gene prognostic signature for diffuse large B-cell lymphoma.

Quantifying Information of Dynamical Biochemical Reaction Networks

A large number of complex biochemical reaction networks are included in the gene expression, cell development, and cell differentiation of in vivo cells, among other processes. Biochemical reaction-underlying processes are the ones transmitting information from cellular internal or external signaling. However, how this information is measured remains an open question. In this paper, we apply the method of information length, based on the combination of Fisher information and information geometry, to study linear and nonlinear biochemical reaction chains, respectively. Through a lot of random simulations, we find that the amount of information does not always increase with the length of the linear reaction chain; instead, the amount of information varies significantly when this length is not very large. When the length of the linear reaction chain reaches a certain value, the amount of information hardly changes. For nonlinear reaction chains, the amount of information changes not only with the length of this chain, but also with reaction coefficients and rates, and this amount also increases with the length of the nonlinear reaction chain. Our results will help to understand the role of the biochemical reaction networks in cells.

Studying stochastic systems biology of the cell with single-cell genomics data

Recent experimental developments in genome-wide RNA quantification hold considerable promise for systems biology. However, rigorously probing the biology of living cells requires a unified mathematical framework that accounts for single-molecule biological stochasticity in the context of technical variation associated with genomics assays. We review models for a variety of RNA transcription processes, as well as the encapsulation and library construction steps of microfluidics-based single-cell RNA sequencing, and present a framework to integrate these phenomena by the manipulation of generating functions. Finally, we use simulated scenarios and biological data to illustrate the implications and applications of the approach.

Inference on autoregulation in gene expression with variance-to-mean ratio

Some genes can promote or repress their own expressions, which is called autoregulation. Although gene regulation is a central topic in biology, autoregulation is much less studied. In general, it is extremely difficult to determine the existence of autoregulation with direct biochemical approaches. Nevertheless, some papers have observed that certain types of autoregulations are linked to noise levels in gene expression. We generalize these results by two propositions on discrete-state continuous-time Markov chains. These two propositions form a simple but robust method to infer the existence of autoregulation from gene expression data. This method only needs to compare the mean and variance of the gene expression level. Compared to other methods for inferring autoregulation, our method only requires non-interventional one-time data, and does not need to estimate parameters. Besides, our method has few restrictions on the model. We apply this method to four groups of experimental data and find some genes that might have autoregulation. Some inferred autoregulations have been verified by experiments or other theoretical works.

Coupling dynamics of 2D Notch-Delta signalling

Understanding pattern formation driven by cell-cell interactions has been a significant theme in cellular biology for many years. In particular, due to their implications within many biological contexts, lateral-inhibition mechanisms present in the Notch-Delta signalling pathway led to an extensive discussion between biologists and mathematicians. Deterministic and stochastic models have been developed as a consequence of this discussion, some of which address long-range signalling by considering cell protrusions reaching non-neighbouring cells. The dynamics of such signalling systems reveal intricate properties of the coupling terms involved in these models. In this work, we investigate the advantages and drawbacks of a single-parameter long-range signalling model across diverse scenarios. By employing linear and multi-scale analyses, we discover that pattern selection is not only partially explained but also depends on nonlinear effects that extend beyond the scope of these analytical techniques.

Leveraging developmental landscapes for model selection in Boolean gene regulatory networks

Boolean models are a well-established framework to model developmental gene regulatory networks (DGRNs) for acquisition of cellular identities. During the reconstruction of Boolean DGRNs, even if the network structure is given, there is generally a large number of combinations of Boolean functions that will reproduce the different cell fates (biological attractors). Here we leverage the developmental landscape to enable model selection on such ensembles using the relative stability of the attractors. First we show that previously proposed measures of relative stability are strongly correlated and we stress the usefulness of the one that captures best the cell state transitions via the mean first passage time (MFPT) as it also allows the construction of a cellular lineage tree. A property of great computational importance is the insensitivity of the different stability measures to changes in noise intensities. That allows us to use stochastic approaches to estimate the MFPT and thereby scale up the computations to large networks. Given this methodology, we revisit different Boolean models of Arabidopsis thaliana root development, showing that a most recent one does not respect the biologically expected hierarchy of cell states based on relative stabilities. We therefore developed an iterative greedy algorithm that searches for models which satisfy the expected hierarchy of cell states and found that its application to the root development model yields many models that meet this expectation. Our methodology thus provides new tools that can enable reconstruction of more realistic and accurate Boolean models of DGRNs.