Stochastic mechanisms in gene expression

What Is a Digital Twin? Experimental Design for a Data-Centric Machine Learning Perspective in Health

The idea of a digital twin has recently gained widespread attention. While, so far, it has been used predominantly for problems in engineering and manufacturing, it is believed that a digital twin also holds great promise for applications in medicine and health. However, a problem that severely hampers progress in these fields is the lack of a solid definition of the concept behind a digital twin that would be directly amenable for such big data-driven fields requiring a statistical data analysis. In this paper, we address this problem. We will see that the term 'digital twin', as used in the literature, is like a Matryoshka doll. For this reason, we unstack the concept via a data-centric machine learning perspective, allowing us to define its main components. As a consequence, we suggest to use the term Digital Twin System instead of digital twin because this highlights its complex interconnected substructure. In addition, we address ethical concerns that result from treatment suggestions for patients based on simulated data and a possible lack of explainability of the underling models.

Universal structural requirements for maximal robust perfect adaptation in biomolecular networks

Adaptation is a running theme in biology. It allows a living system to survive and thrive in the face of unpredictable environments by maintaining key physiological variables at their desired levels through tight regulation. When one such variable is maintained at a certain value at the steady state despite perturbations to a single input, this property is called robust perfect adaptation (RPA). Here we address and solve the fundamental problem of maximal RPA (maxRPA), whereby, for a designated output variable, RPA is achieved with respect to perturbations in virtually all network parameters. In particular, we show that the maxRPA property imposes certain structural constraints on the network. We then prove that these constraints are fully characterized by simple linear algebraic stoichiometric conditions which differ between deterministic and stochastic descriptions of the dynamics. We use our results to derive a new internal model principle (IMP) for biomolecular maxRPA networks, akin to the celebrated IMP in control theory. We exemplify our results through several known biological examples of robustly adapting networks and construct examples of such networks with the aid of our linear algebraic characterization. Our results reveal the universal requirements for maxRPA in all biological systems, and establish a foundation for studying adaptation in general biomolecular networks, with important implications for both systems and synthetic biology.

Preexisting Heterogeneity of Inducible Nitric Oxide Synthase Expression Drives Differential Growth of Mycobacterium tuberculosis in Macrophages

Mycobacterium tuberculosis infection is initiated by the inhalation and implantation of bacteria in the lung alveoli, where they are phagocytosed by macrophages. Even a single bacterium may be sufficient to initiate infection. Thereafter, the clinical outcome is highly variable between individuals, ranging from sterilization to active disease, for reasons that are not well understood. Here, we show that the rate of intracellular bacterial growth varies markedly between individual macrophages, and this heterogeneity is driven by cell-to-cell variation of inducible nitric oxide synthase (iNOS) activity. At the single-cell level, iNOS expression fluctuates over time, independent of infection or activation with gamma interferon. We conclude that chance encounters between individual bacteria and host cells randomly expressing different levels of an antibacterial gene can determine the outcome of single-cell infections, which may explain why some exposed individuals clear the bacteria while others develop progressive disease. IMPORTANCE In this report, we demonstrate that fluctuations in the expression of antimicrobial genes can define how single host cells control bacterial infections. We show that preexisting cell-to-cell variation in the expression of a single gene, that for inducible nitric oxide synthase, is sufficient to explain why some macrophages kill intracellular M. tuberculosis while others fail to control bacterial replication, possibly leading to disease progression. We introduce the concept that chance encounters between heterogeneous bacteria and host cells can determine the outcome of a host-pathogen interaction. This concept is particularly relevant for all the infectious diseases in which the number of interacting pathogens and host cells is small at some point during the infection.

Comprehensive characterization of Cysteine-rich protein-coding genes of Giardia lamblia and their role during antigenic variation

Giardia lamblia encodes several families of cysteine-rich proteins, including the Variant-specific Surface Proteins (VSPs) involved in the process of antigenic variation. Their characteristics, definition and relationships are still controversial. An exhaustive analysis of the Cys-rich families including organization, features, evolution and levels of expression was performed, by combining pattern searches and predictions with massive sequencing techniques. Thus a new classification for Cys-rich proteins, genes and pseudogenes that better describes their involvement in Giardia's biology is presented. Moreover, three novel characteristics exclusive to the VSP genes, comprising an Initiator element/Kozak-like sequence, an extended polyadenylation signal and a unique pattern of mutually exclusive transcript accumulation is presented as well as the finding that High Cysteine Membrane Proteins, upregulated under stress, may protect the parasite during VSP switching. These results allow better interpretation of previous reports providing the basis for further studies of the biology of this early-branching eukaryote.

Fixed and Distributed Gene Expression Time Delays in Reaction-Diffusion Systems

Time delays, modelling the process of intracellular gene expression, have been shown to have important impacts on the dynamics of pattern formation in reaction-diffusion systems. In particular, past work has shown that such time delays can shrink the Turing space, thereby inhibiting patterns from forming across large ranges of parameters. Such delays can also increase the time taken for pattern formation even when Turing instabilities occur. Here, we consider reaction-diffusion models incorporating fixed or distributed time delays, modelling the underlying stochastic nature of gene expression dynamics, and analyse these through a systematic linear instability analysis and numerical simulations for several sets of different reaction kinetics. We find that even complicated distribution kernels (skewed Gaussian probability density functions) have little impact on the reaction-diffusion dynamics compared to fixed delays with the same mean delay. We show that the location of the delay terms in the model can lead to changes in the size of the Turing space (increasing or decreasing) as the mean time delay, [Formula: see text], is increased. We show that the time to pattern formation from a perturbation of the homogeneous steady state scales linearly with [Formula: see text], and conjecture that this is a general impact of time delay on reaction-diffusion dynamics, independent of the form of the kinetics or location of the delayed terms. Finally, we show that while initial and boundary conditions can influence these dynamics, particularly the time-to-pattern, the effects of delay appear robust under variations of initial and boundary data. Overall, our results help clarify the role of gene expression time delays in reaction-diffusion patterning, and suggest clear directions for further work in studying more realistic models of pattern formation.

Frequency spectra and the color of cellular noise

The invention of the Fourier integral in the 19th century laid the foundation for modern spectral analysis methods. This integral decomposes a temporal signal into its frequency components, providing deep insights into its generating process. While this idea has precipitated several scientific and technological advances, its impact has been fairly limited in cell biology, largely due to the difficulties in connecting the underlying noisy intracellular networks to the frequency content of observed single-cell trajectories. Here we develop a spectral theory and computational methodologies tailored specifically to the computation and analysis of frequency spectra of noisy intracellular networks. Specifically, we develop a method to compute the frequency spectrum for general nonlinear networks, and for linear networks we present a decomposition that expresses the frequency spectrum in terms of its sources. Several examples are presented to illustrate how our results provide frequency-based methods for the design and analysis of noisy intracellular networks.

Effects of thermal acclimation on the proteome of the planarian Crenobia alpina from an alpine freshwater spring

Species' acclimation capacity and their ability to maintain molecular homeostasis outside ideal temperature ranges will partly predict their success following climate change-induced thermal regime shifts. Theory predicts that ectothermic organisms from thermally stable environments have muted plasticity, and that these species may be particularly vulnerable to temperature increases. Whether such species retained or lost acclimation capacity remains largely unknown. We studied proteome changes in the planarian Crenobia alpina, a prominent member of cold-stable alpine habitats that is considered to be a cold-adapted stenotherm. We found that the species' critical thermal maximum (CT_max) is above its experienced habitat temperatures and that different populations exhibit differential CT_max acclimation capacity, whereby an alpine population showed reduced plasticity. In a separate experiment, we acclimated C. alpina individuals from the alpine population to 8, 11, 14 or 17°C over the course of 168 h and compared their comprehensively annotated proteomes. Network analyses of 3399 proteins and protein set enrichment showed that while the species' proteome is overall stable across these temperatures, protein sets functioning in oxidative stress response, mitochondria, protein synthesis and turnover are lower in abundance following warm acclimation. Proteins associated with an unfolded protein response, ciliogenesis, tissue damage repair, development and the innate immune system were higher in abundance following warm acclimation. Our findings suggest that this species has not suffered DNA decay (e.g. loss of heat-shock proteins) during evolution in a cold-stable environment and has retained plasticity in response to elevated temperatures, challenging the notion that stable environments necessarily result in muted plasticity.

Summary: The proteome of an alpine Crenobia alpina population shows plasticity in response to acclimation to warmer temperatures.

CellDynaMo–stochastic reaction-diffusion-dynamics model: Application to search-and-capture process of mitotic spindle assembly

We introduce a Stochastic Reaction-Diffusion-Dynamics Model (SRDDM) for simulations of cellular mechanochemical processes with high spatial and temporal resolution. The SRDDM is mapped into the CellDynaMo package, which couples the spatially inhomogeneous reaction-diffusion master equation to account for biochemical reactions and molecular transport within the Langevin Dynamics (LD) framework to describe dynamic mechanical processes. This computational infrastructure allows the simulation of hours of molecular machine dynamics in reasonable wall-clock time. We apply SRDDM to test performance of the Search-and-Capture of mitotic spindle assembly by simulating, in three spatial dimensions, dynamic instability of elastic microtubules anchored in two centrosomes, movement and deformations of geometrically realistic centromeres with flexible kinetochores and chromosome arms. Furthermore, the SRDDM describes the mechanics and kinetics of Ndc80 linkers mediating transient attachments of microtubules to the chromosomal kinetochores. The rates of these attachments and detachments depend upon phosphorylation states of the Ndc80 linkers, which are regulated in the model by explicitly accounting for the reactions of Aurora A and B kinase enzymes undergoing restricted diffusion. We find that there is an optimal rate of microtubule-kinetochore detachments which maximizes the accuracy of the chromosome connections, that adding chromosome arms to kinetochores improve the accuracy by slowing down chromosome movements, that Aurora A and kinetochore deformations have a small positive effect on the attachment accuracy, and that thermal fluctuations of the microtubules increase the rates of kinetochore capture and also improve the accuracy of spindle assembly.

The CellDynaMo package models, in 3D, any cellular subsystem where sufficient detail of the macromolecular players and the kinetics of relevant reactions are available. The package is based on the Stochastic Reaction-Diffusion-Dynamics model that combines the stochastic description of chemical kinetics, Brownian diffusion-based description of molecular transport, and Langevin dynamics-based representation of mechanical processes most pertinent to the system. We apply the model to test the Search-and-Capture mechanism of mitotic spindle assembly. We find that there is an optimal rate of microtubule-kinetochore detachments which maximizes the accuracy of chromosome connections, that chromosome arms improve the attachment accuracy by slowing down chromosome movements, that Aurora A kinase and kinetochore deformations have small positive effects on the accuracy, and that thermal fluctuations of the microtubules increase the rates of kinetochore capture and also improve the accuracy.

A computational model of stem cells' decision-making mechanism to maintain tissue homeostasis and organization in the presence of stochasticity

The maintenance of multi-cellular developed tissue depends on the proper cell production rate to replace the cells destroyed by the programmed process of cell death. The stem cell is the main source of producing cells in a developed normal tissue. It makes the stem cell the lead role in the scene of a fully formed developed tissue to fulfill its proper functionality. By focusing on the impact of stochasticity, here, we propose a computational model to reveal the internal mechanism of a stem cell, which generates the right proportion of different types of specialized cells, distribute them into their right position, and in the presence of intercellular reactions, maintain the organized structure in a homeostatic state. The result demonstrates that the spatial pattern could be harassed by the population geometries. Besides, it clearly shows that our model with progenitor cells able to recover the stem cell presence could retrieve the initial pattern appropriately in the case of injury. One of the fascinating outcomes of this project is demonstrating the contradictory roles of stochasticity. It breaks the proper boundaries of the initial spatial pattern in the population. While, on the flip side of the coin, it is the exact factor that provides the demanded non-genetic diversity in the tissue. The remarkable characteristic of the introduced model as the stem cells' internal mechanism is that it could control the overall behavior of the population without need for any external factors.

Discrete Biochemical Systems Theory

Almost every biomedical systems analysis requires early decisions regarding the choice of the most suitable representations to be used. De facto the most prevalent choice is a system of ordinary differential equations (ODEs). This framework is very popular because it is flexible and fairly easy to use. It is also supported by an enormous array of stand-alone programs for analysis, including many distinct numerical solvers that are implemented in the main programming languages. Having selected ODEs, the modeler must then choose a mathematical format for the equations. This selection is not trivial as nearly unlimited options exist and there is seldom objective guidance. The typical choices include ad hoc representations, default models like mass-action or Lotka-Volterra equations, and generic approximations. Within the realm of approximations, linear models are typically successful for analyses of engineered systems, but they are not as appropriate for biomedical phenomena, which often display nonlinear features such as saturation, threshold effects or limit cycle oscillations, and possibly even chaos. Power-law approximations are simple but overcome these limitations. They are the key ingredient of Biochemical Systems Theory (BST), which uses ODEs exclusively containing power-law representations for all processes within a model. BST models cover a vast repertoire of nonlinear responses and, at the same time, have structural properties that are advantageous for a wide range of analyses. Nonetheless, as all ODE models, the BST approach has limitations. In particular, it is not always straightforward to account for genuine discreteness, time delays, and stochastic processes. As a new option, we therefore propose here an alternative to BST in the form of discrete Biochemical Systems Theory (dBST). dBST models have the same generality and practicality as their BST-ODE counterparts, but they are readily implemented even in situations where ODEs struggle. As a case study, we illustrate dBST applied to the dynamics of the aryl hydrocarbon receptor (AhR), a signal transduction system that simultaneously involves time delays and stochasticity.

RNase E and HupB dynamics foster mycobacterial cell homeostasis and fitness

RNA turnover is a primary source of gene expression variation, in turn promoting cellular adaptation. Mycobacteria leverage reversible mRNA stabilization to endure hostile conditions. Although RNase E is essential for RNA turnover in several species, its role in mycobacterial single-cell physiology and functional phenotypic diversification remains unexplored. Here, by integrating live-single-cell and quantitative-mass-spectrometry approaches, we show that RNase E forms dynamic foci, which are associated with cellular homeostasis and fate, and we discover a versatile molecular interactome. We show a likely interaction between RNase E and the nucleoid-associated protein HupB, which is particularly pronounced during drug treatment and infection, where phenotypic diversity increases. Disruption of RNase E expression affects HupB levels, impairing Mycobacterium tuberculosis growth homeostasis during treatment, intracellular replication, and host spread. Our work lays the foundation for targeting the RNase E and its partner HupB, aiming to undermine M. tuberculosis cellular balance, diversification capacity, and persistence.

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Single mycobacterial cells exhibit phenotypic variation in RNase E expression

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RNase E is implicated in the maintenance of mycobacterial cell growth homeostasis

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RNase E and HupB show a functional interplay in single mycobacterial cells

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RNase E-HupB disruption impairs Mycobacterium tuberculosis fate under drug and in macrophages

Lentiviral Nef Proteins Differentially Govern the Establishment of Viral Latency

Despite the clinical importance of latent human immunodeficiency virus type 1 (HIV-1) infection, our understanding of the biomolecular processes involved in HIV-1 latency control is still limited. This study was designed to address whether interactions between viral proteins, specifically HIV Nef, and the host cell could affect latency establishment. The study was driven by three reported observations. First, early reports suggested that human immunodeficiency virus type 2 (HIV-2) infection in patients produces a lower viral RNA/DNA ratio than HIV-1 infection, potentially indicating an increased propensity of HIV-2 to produce latent infection. Second, Nef, an early viral gene product, has been shown to alter the activation state of infected cells in a lentiviral lineage-dependent manner. Third, it has been demonstrated that the ability of HIV-1 to establish latent infection is a function of the activation state of the host cell at the time of infection. Based on these observations, we reasoned that HIV-2 Nef may have the ability to promote latency establishment. We demonstrate that HIV-1 latency establishment in T cell lines and primary T cells is indeed differentially modulated by Nef proteins. In the context of an HIV-1 backbone, HIV-1 Nef promoted active HIV-1 infection, while HIV-2 Nef strongly promoted latency establishment. Given that Nef represents the only difference in these HIV-1 vectors and is known to interact with numerous cellular factors, these data add support to the idea that latency establishment is a host cell-virus interaction phenomenon, but they also suggest that the HIV-1 lineage may have evolved mechanisms to counteract host cell suppression. IMPORTANCE Therapeutic attempts to eliminate the latent HIV-1 reservoir have failed, at least in part due to our incomplete biomolecular understanding of how latent HIV-1 infection is established and maintained. We here address the fundamental question of whether all lentiviruses actually possess a similar capacity to establish latent infections or whether there are differences between the lentiviral lineages driving differential latency establishment that could be exploited to develop improved latency reversal agents. Research investigating the viral RNA/DNA ratio in HIV-1 and HIV-2 patients could suggest that HIV-2 indeed has a much higher propensity to establish latent infections, a trait that we found, at least in part, to be attributable to the HIV-2 Nef protein. Reported Nef-mediated effects on host cell activation thus also affect latency establishment, and HIV-1 vectors that carry different lentiviral nef genes should become key tools to develop a better understanding of the biomolecular basis of HIV-1 latency establishment.

Parameter inference for stochastic biochemical models from perturbation experiments parallelised at the single cell level

Understanding and characterising biochemical processes inside single cells requires experimental platforms that allow one to perturb and observe the dynamics of such processes as well as computational methods to build and parameterise models from the collected data. Recent progress with experimental platforms and optogenetics has made it possible to expose each cell in an experiment to an individualised input and automatically record cellular responses over days with fine time resolution. However, methods to infer parameters of stochastic kinetic models from single-cell longitudinal data have generally been developed under the assumption that experimental data is sparse and that responses of cells to at most a few different input perturbations can be observed. Here, we investigate and compare different approaches for calculating parameter likelihoods of single-cell longitudinal data based on approximations of the chemical master equation (CME) with a particular focus on coupling the linear noise approximation (LNA) or moment closure methods to a Kalman filter. We show that, as long as cells are measured sufficiently frequently, coupling the LNA to a Kalman filter allows one to accurately approximate likelihoods and to infer model parameters from data even in cases where the LNA provides poor approximations of the CME. Furthermore, the computational cost of filtering-based iterative likelihood evaluation scales advantageously in the number of measurement times and different input perturbations and is thus ideally suited for data obtained from modern experimental platforms. To demonstrate the practical usefulness of these results, we perform an experiment in which single cells, equipped with an optogenetic gene expression system, are exposed to various different light-input sequences and measured at several hundred time points and use parameter inference based on iterative likelihood evaluation to parameterise a stochastic model of the system.

A multiscale cell-based model of tumor growth for chemotherapy assessment and tumor-targeted therapy through a 3D computational approach

OBJECTIVES

Computational modeling of biological systems is a powerful tool to clarify diverse processes contributing to cancer. The aim is to clarify the complex biochemical and mechanical interactions between cells, the relevance of intracellular signaling pathways in tumor progression and related events to the cancer treatments, which are largely ignored in previous studies.

MATERIALS AND METHODS

A three-dimensional multiscale cell-based model is developed, covering multiple time and spatial scales, including intracellular, cellular, and extracellular processes. The model generates a realistic representation of the processes involved from an implementation of the signaling transduction network.

RESULTS

Considering a benign tumor development, results are in good agreement with the experimental ones, which identify three different phases in tumor growth. Simulating tumor vascular growth, results predict a highly vascularized tumor morphology in a lobulated form, a consequence of cells' motile behavior. A novel systematic study of chemotherapy intervention, in combination with targeted therapy, is presented to address the capability of the model to evaluate typical clinical protocols. The model also performs a dose comparison study in order to optimize treatment efficacy and surveys the effect of chemotherapy initiation delays and different regimens.

CONCLUSIONS

Results not only provide detailed insights into tumor progression, but also support suggestions for clinical implementation. This is a major step toward the goal of predicting the effects of not only traditional chemotherapy but also tumor-targeted therapies.

The evolution of mechanisms to produce phenotypic heterogeneity in microorganisms

In bacteria and other microorganisms, the cells within a population often show extreme phenotypic variation. Different species use different mechanisms to determine how distinct phenotypes are allocated between individuals, including coordinated, random, and genetic determination. However, it is not clear if this diversity in mechanisms is adaptive-arising because different mechanisms are favoured in different environments-or is merely the result of non-adaptive artifacts of evolution. We use theoretical models to analyse the relative advantages of the two dominant mechanisms to divide labour between reproductives and helpers in microorganisms. We show that coordinated specialisation is more likely to evolve over random specialisation in well-mixed groups when: (i) social groups are small; (ii) helping is more "essential"; and (iii) there is a low metabolic cost to coordination. We find analogous results when we allow for spatial structure with a more detailed model of cellular filaments. More generally, this work shows how diversity in the mechanisms to produce phenotypic heterogeneity could have arisen as adaptations to different environments.

Diversity of synaptic protein complexes as a function of the abundance of their constituent proteins: A modeling approach

The postsynaptic density (PSD) is a dense protein network playing a key role in information processing during learning and memory, and is also indicated in a number of neurological disorders. Efforts to characterize its detailed molecular organization are encumbered by the large variability of the abundance of its constituent proteins both spatially, in different brain areas, and temporally, during development, circadian rhythm, and also in response to various stimuli. In this study we ran large-scale stochastic simulations of protein binding events to predict the presence and distribution of PSD complexes. We simulated the interactions of seven major PSD proteins (NMDAR, AMPAR, PSD-95, SynGAP, GKAP, Shank3, Homer1) based on previously published, experimentally determined protein abundance data from 22 different brain areas and 42 patients (altogether 524 different simulations). Our results demonstrate that the relative ratio of the emerging protein complexes can be sensitive to even subtle changes in protein abundances and thus explicit simulations are invaluable to understand the relationships between protein availability and complex formation. Our observations are compatible with a scenario where larger supercomplexes are formed from available smaller binary and ternary associations of PSD proteins. Specifically, Homer1 and Shank3 self-association reactions substantially promote the emergence of very large protein complexes. The described simulations represent a first approximation to assess PSD complex abundance, and as such, use significant simplifications. Therefore, their direct biological relevance might be limited but we believe that the major qualitative findings can contribute to the understanding of the molecular features of the postsynapse.

DeepCME: A deep learning framework for computing solution statistics of the chemical master equation

Stochastic models of biomolecular reaction networks are commonly employed in systems and synthetic biology to study the effects of stochastic fluctuations emanating from reactions involving species with low copy-numbers. For such models, the Kolmogorov's forward equation is called the chemical master equation (CME), and it is a fundamental system of linear ordinary differential equations (ODEs) that describes the evolution of the probability distribution of the random state-vector representing the copy-numbers of all the reacting species. The size of this system is given by the number of states that are accessible by the chemical system, and for most examples of interest this number is either very large or infinite. Moreover, approximations that reduce the size of the system by retaining only a finite number of important chemical states (e.g. those with non-negligible probability) result in high-dimensional ODE systems, even when the number of reacting species is small. Consequently, accurate numerical solution of the CME is very challenging, despite the linear nature of the underlying ODEs. One often resorts to estimating the solutions via computationally intensive stochastic simulations. The goal of the present paper is to develop a novel deep-learning approach for computing solution statistics of high-dimensional CMEs by reformulating the stochastic dynamics using Kolmogorov's backward equation. The proposed method leverages superior approximation properties of Deep Neural Networks (DNNs) to reliably estimate expectations under the CME solution for several user-defined functions of the state-vector. This method is algorithmically based on reinforcement learning and it only requires a moderate number of stochastic simulations (in comparison to typical simulation-based approaches) to train the "policy function". This allows not just the numerical approximation of various expectations for the CME solution but also of its sensitivities with respect to all the reaction network parameters (e.g. rate constants). We provide four examples to illustrate our methodology and provide several directions for future research.

Noise distorts the epigenetic landscape and shapes cell-fate decisions

The Waddington epigenetic landscape has become an iconic representation of the cellular differentiation process. Recent single-cell transcriptomic data provide new opportunities for quantifying this originally conceptual tool, offering insight into the gene regulatory networks underlying cellular development. While many methods for constructing the landscape have been proposed, by far the most commonly employed approach is based on computing the landscape as the negative logarithm of the steady-state probability distribution. Here, we use simple models to highlight the complexities and limitations that arise when reconstructing the potential landscape in the presence of stochastic fluctuations. We consider how the landscape changes in accordance with different stochastic systems and show that it is the subtle interplay between the deterministic and stochastic components of the system that ultimately shapes the landscape. We further discuss how the presence of noise has important implications for the identifiability of the regulatory dynamics from experimental data. A record of this paper's transparent peer review process is included in the supplemental information.

Inferring gene regulatory networks from single-cell RNA-seq temporal snapshot data requires higher-order moments

Single-cell RNA sequencing (scRNA-seq) has become ubiquitous in biology. Recently, there has been a push for using scRNA-seq snapshot data to infer the underlying gene regulatory networks (GRNs) steering cellular function. To date, this aspiration remains unrealized due to technical and computational challenges. In this work we focus on the latter, which is under-represented in the literature. We took a systemic approach by subdividing the GRN inference into three fundamental components: data pre-processing, feature extraction, and inference. We observed that the regulatory signature is captured in the statistical moments of scRNA-seq data and requires computationally intensive minimization solvers to extract it. Furthermore, current data pre-processing might not conserve these statistical moments. Although our moment-based approach is a didactic tool for understanding the different compartments of GRN inference, this line of thinking—finding computationally feasible multi-dimensional statistics of data—is imperative for designing GRN inference methods.

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Single-cell RNA-seq temporal snapshot data for detecting regulation

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Challenges in data pre-processing, feature extraction, and network inference for GRNs

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Encoding of regulatory information in higher-order raw moments

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Non-linear least-squares inference for temporal scRNA-seq snapshot data

Single-cell RNA sequencing (scRNA-seq) has become ubiquitous in biology. Recently, there has been a push for using scRNA-seq snapshot data to infer the underlying gene regulatory networks (GRNs) steering cellular function. A recent benchmark of 12 GRN methods demonstrated that the algorithms struggled to predict the ground-truth GRNs and speculated that the low performance was due to the insufficient resolution in the scRNA-seq data. Rather than proposing another method, this paper focuses on how to decompose a GRN problem into three subproblems (pre-processing, feature extraction, and inference), so that the gene regulatory information is preserved in each step. Subsequently, we discuss how to best approach each of the three subproblems.

Quantitative control of noise in mammalian gene expression by dynamic histone regulation

Fluctuation ('noise') in gene expression is critical for mammalian cellular processes. Numerous mechanisms contribute to its origins, yet the mechanisms behind large fluctuations that are induced by single transcriptional activators remain elusive. Here, we probed putative mechanisms by studying the dynamic regulation of transcriptional activator binding, histone regulator inhibitors, chromatin accessibility, and levels of mRNAs and proteins in single cells. Using a light-induced expression system, we showed that the transcriptional activator could form an interplay with dual functional co-activator/histone acetyltransferases CBP/p300. This interplay resulted in substantial heterogeneity in H3K27ac, chromatin accessibility, and transcription. Simultaneous attenuation of CBP/p300 and HDAC4/5 reduced heterogeneity in the expression of endogenous genes, suggesting that this mechanism is universal. We further found that the noise was reduced by pulse-wide modulation of transcriptional activator binding possibly as a result of alternating the epigenetic states. Our findings suggest a mechanism for the modulation of noise in synthetic and endogenous gene expression systems.

Different Patterns of mRNA Nuclear Retention during Meiotic Prophase in Larch Microsporocytes

Recent studies show a crucial role of post-transcriptional processes in the regulation of gene expression. Our research has shown that mRNA retention in the nucleus plays a significant role in such regulation. We studied larch microsporocytes during meiotic prophase, characterized by pulsatile transcriptional activity. After each pulse, the transcriptional activity is silenced, but the transcripts synthesized at this time are not exported immediately to the cytoplasm but are retained in the cell nucleus and especially in Cajal bodies, where non-fully-spliced transcripts with retained introns are accumulated. Analysis of the transcriptome of these cells and detailed analysis of the nuclear retention and transport dynamics of several mRNAs revealed two main patterns of nuclear accumulation and transport. The majority of studied transcripts followed the first one, consisting of a more extended retention period and slow release to the cytoplasm. We have shown this in detail for the pre-mRNA and mRNA encoding RNA pol II subunit 10. In this pre-mRNA, a second (retained) intron is posttranscriptionally spliced at a precisely defined time. Fully mature mRNA is then released into the cytoplasm, where the RNA pol II complexes are produced. These proteins are necessary for transcription in the next pulse to occur.mRNAs encoding translation factors and SERRATE followed the second pattern, in which the retention period was shorter and transcripts were rapidly transferred to the cytoplasm. The presence of such a mechanism in various cell types from a diverse range of organisms suggests that it is an evolutionarily conserved mechanism of gene regulation.

A model explaining mRNA level fluctuations based on activity demands and RNA age

Cellular RNA levels typically fluctuate and are influenced by different transcription rates and RNA degradation rates. However, the understanding of the fundamental relationships between RNA abundance, environmental stimuli, RNA activities, and RNA age distributions is incomplete. Furthermore, the rates of RNA degradation and transcription are difficult to measure in transcriptomic experiments in living organisms, especially in studies involving humans. A model based on activity demands and RNA age was developed to explore the mechanisms of RNA level fluctuations. Using single-cell time-series gene expression experimental data, we assessed the transcription rates, RNA degradation rates, RNA life spans, RNA demand, accumulated transcription levels, and accumulated RNA degradation levels. This model could also predict RNA levels under simulation backgrounds, such as stimuli that induce regular oscillations in RNA abundance, stable RNA levels over time that result from long-term shortage of total RNA activity or from uncontrollable transcription, and relationships between RNA/protein levels and metabolic rates. This information contributes to existing knowledge.

Detected cellular RNA levels usually fluctuate. The understanding of the fundamental relationships between RNA level fluctuations, the rates of RNA degradation and transcription, environmental stimuli, RNA activities, and RNA age distributions is incomplete. In the present research, we developed a model based on the demands of RNA (related to intrinsic and/or extrinsic information), RNA age (determines the survival time and biological activity of an RNA), transcription, and RNA degradation to explain the mechanism underlying intracellular RNA level fluctuations. We also explored applicability of the model for analysing dynamic processes between interacting biomolecules, such as the relationship between RNA and protein level fluctuations. Using single-cell time-series gene expression experimental data, we assessed some biological parameters, such as transcription rates, RNA degradation rates, and RNA life spans. This model could also predict RNA levels under simulation backgrounds, such as stimuli that induce regular oscillations in RNA abundance, stable RNA levels over time that result from long-term shortage of total RNA activity or from uncontrollable transcription, and relationships between RNA/protein levels and metabolic rates. This information contributes to existing knowledge and provides a new perspective for future studies.

The essential role of mRNA degradation in understanding and engineering E. coli metabolism

Metabolic engineering strategies are crucial for the development of bacterial cell factories with improved performance. Until now, optimal metabolic networks have been designed based on systems biology approaches integrating large-scale data on the steady-state concentrations of mRNA, protein and metabolites, sometimes with dynamic data on fluxes, but rarely with any information on mRNA degradation. In this review, we compile growing evidence that mRNA degradation is a key regulatory level in E. coli that metabolic engineering strategies should take into account. We first discuss how mRNA degradation interacts with transcription and translation, two other gene expression processes, to balance transcription regulation and remove poorly translated mRNAs. The many reciprocal interactions between mRNA degradation and metabolism are also highlighted: metabolic activity can be controlled by changes in mRNA degradation and in return, the activity of the mRNA degradation machinery is controlled by metabolic factors. The mathematical models of the crosstalk between mRNA degradation dynamics and other cellular processes are presented and discussed with a view towards novel mRNA degradation-based metabolic engineering strategies. We show finally that mRNA degradation-based strategies have already successfully been applied to improve heterologous protein synthesis. Overall, this review underlines how important mRNA degradation is in regulating E. coli metabolism and identifies mRNA degradation as a key target for innovative metabolic engineering strategies in biotechnology.

A forecast for large-scale, predictive biology: Lessons from meteorology

Quantitative systems biology, in which predictive mathematical models are constructed to guide the design of experiments and predict experimental outcomes, is at an exciting transition point, where the foundational scientific principles are becoming established, but the impact is not yet global. The next steps necessary for mathematical modeling to transform biological research and applications, in the same way it has already transformed other fields, is not completely clear. The purpose of this perspective is to forecast possible answers to this question-what needs to happen next-by drawing on the experience gained in another field, specifically meteorology. We review here a number of lessons learned in weather prediction that are directly relevant to biological systems modeling, and that we believe can enable the same kinds of global impact in our field as atmospheric modeling makes today.

Reconstructing an epigenetic landscape using a genetic pulling approach

Cells use genetic switches to shift between alternate stable gene expression states, e.g., to adapt to new environments or to follow a developmental pathway. Conceptually, these stable phenotypes can be considered as attractive states on an epigenetic landscape with phenotypic changes being transitions between states. Measuring these transitions is challenging because they are both very rare in the absence of appropriate signals and very fast. As such, it has proved difficult to experimentally map the epigenetic landscapes that are widely believed to underly developmental networks. Here, we introduce a nonequilibrium perturbation method to help reconstruct a regulatory network's epigenetic landscape. We derive the mathematical theory needed and then use the method on simulated data to reconstruct the landscapes. Our results show that with a relatively small number of perturbation experiments it is possible to recover an accurate representation of the true epigenetic landscape. We propose that our theory provides a general method by which epigenetic landscapes can be studied. Finally, our theory suggests that the total perturbation impulse required to induce a switch between metastable states is a fundamental quantity in developmental dynamics.

Coordination of gene expression noise with cell size: analytical results for agent-based models of growing cell populations

The chemical master equation and the Gillespie algorithm are widely used to model the reaction kinetics inside living cells. It is thereby assumed that cell growth and division can be modelled through effective dilution reactions and extrinsic noise sources. We here re-examine these paradigms through developing an analytical agent-based framework of growing and dividing cells accompanied by an exact simulation algorithm, which allows us to quantify the dynamics of virtually any intracellular reaction network affected by stochastic cell size control and division noise. We find that the solution of the chemical master equation-including static extrinsic noise-exactly agrees with the agent-based formulation when the network under study exhibits stochastic concentration homeostasis, a novel condition that generalizes concentration homeostasis in deterministic systems to higher order moments and distributions. We illustrate stochastic concentration homeostasis for a range of common gene expression networks. When this condition is not met, we demonstrate by extending the linear noise approximation to agent-based models that the dependence of gene expression noise on cell size can qualitatively deviate from the chemical master equation. Surprisingly, the total noise of the agent-based approach can still be well approximated by extrinsic noise models.

A top-down measure of gene-to-gene coordination for analyzing cell-to-cell variability

Recent technological advances, such as single-cell RNA sequencing (scRNA-seq), allow the measurement of gene expression profiles of individual cells. These expression profiles typically exhibit substantial variations even across seemingly homogeneous populations of cells. Two main different sources contribute to this measured variability: actual differences between the biological activity of the cells and technical measurement errors. Analysis of the biological variability may provide information about the underlying gene regulation of the cells, yet distinguishing it from the technical variability is a challenge. Here, we apply a recently developed computational method for measuring the global gene coordination level (GCL) to systematically study the cell-to-cell variability in numerical models of gene regulation. We simulate ‘biological variability’ by introducing heterogeneity in the underlying regulatory dynamic of different cells, while ‘technical variability’ is represented by stochastic measurement noise. We show that the GCL decreases for cohorts of cells with increased ‘biological variability’ only when it is originated from the interactions between the genes. Moreover, we find that the GCL can evaluate and compare—for cohorts with the same cell-to-cell variability—the ratio between the introduced biological and technical variability. Finally, we show that the GCL is robust against spurious correlations that originate from a small sample size or from the compositionality of the data. The presented methodology can be useful for future analysis of high-dimensional ecological and biochemical dynamics.

Bistability in cell signalling and its significance in identifying potential drug targets

MOTIVATION

Bistability is one of the salient dynamical features in various all-or-none kinds of decision-making processes. The presence of bistability in a cell signalling network plays a key role in input-output (I/O) relation. Our study is aiming to capture and emphasise the role of motif structure influencing the I/O relation between two nodes in the context of bistability. Here, a model-based analysis is made to investigate the critical conditions responsible for the emergence of different bistable protein-protein interaction (PPI) motifs and their possible applications to find the potential drug targets.

RESULTS

The global sensitivity analysis is used to identify sensitive parameters and their role in maintaining the bistability. Additionally, the bistable switching through hysteresis is explored to develop an understanding of the underlying mechanisms involved in the cell signalling processes, when significant motifs exhibiting bistability have emerged. Further, we elaborate the application of the results by the implication of the emerged PPI motifs to identify potential drug-targets in three cancer networks, which is validated with existing databases. The influence of stochastic perturbations that could hinder desired functionality of any signalling networks is also described here.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

From Bench to Keyboard and Back Again: A Brief History of Lambda Phage Modeling

Cellular decision making is the process whereby cells choose one developmental pathway from multiple possible ones, either spontaneously or due to environmental stimuli. Examples in various cell types suggest an almost inexhaustible plethora of underlying molecular mechanisms. In general, cellular decisions rely on the gene regulatory network, which integrates external signals to drive cell fate choice. The search for general principles of such a process benefits from appropriate biological model systems that reveal how and why certain gene regulatory mechanisms drive specific cellular decisions according to ecological context and evolutionary outcomes. In this article, we review the historical and ongoing development of the phage lambda lysis-lysogeny decision as a model system to investigate all aspects of cellular decision making. The unique generality, simplicity, and richness of phage lambda decision making render it a constant source ofmathematical modeling-aided inspiration across all of biology. We discuss the origins and progress of quantitative phage lambda modeling from the 1950s until today, as well as its possible future directions. We provide examples of how modeling enabled methods and theory development, leading to new biological insights by revealing gaps in the theory and pinpointing areas requiring further experimental investigation. Overall, we highlight the utility of theoretical approaches both as predictive tools, to forecast the outcome of novel experiments, and as explanatory tools, to elucidate the natural processes underlying experimental data.

Measuring and modeling energy and power consumption in living microbial cells with a synthetic ATP reporter

Background

Adenosine triphosphate (ATP) is the main energy carrier in living organisms, critical for metabolism and essential physiological processes. In humans, abnormal regulation of energy levels (ATP concentration) and power consumption (ATP consumption flux) in cells is associated with numerous diseases from cancer, to viral infection and immune dysfunction, while in microbes it influences their responses to drugs and other stresses. The measurement and modeling of ATP dynamics in cells is therefore a critical component in understanding fundamental physiology and its role in pathology. Despite the importance of ATP, our current understanding of energy dynamics and homeostasis in living cells has been limited by the lack of easy-to-use ATP sensors and the lack of models that enable accurate estimates of energy and power consumption related to these ATP dynamics. Here we describe a dynamic model and an ATP reporter that tracks ATP in E. coli over different growth phases.

Results

The reporter is made by fusing an ATP-sensing rrnB P1 promoter with a fast-folding and fast-degrading GFP. Good correlations between reporter GFP and cellular ATP were obtained in E. coli growing in both minimal and rich media and in various strains. The ATP reporter can reliably monitor bacterial ATP dynamics in response to nutrient availability. Fitting the dynamics of experimental data corresponding to cell growth, glucose, acetate, dissolved oxygen, and ATP yielded a mathematical and circuit model. This model can accurately predict cellular energy and power consumption under various conditions. We found that cellular power consumption varies significantly from approximately 0.8 and 0.2 million ATP/s for a tested strain during lag and stationary phases to 6.4 million ATP/s during exponential phase, indicating ~ 8–30-fold changes of metabolic rates among different growth phases. Bacteria turn over their cellular ATP pool a few times per second during the exponential phase and slow this rate by ~ 2–5-fold in lag and stationary phases.

Conclusion

Our rrnB P1-GFP reporter and kinetic circuit model provide a fast and simple way to monitor and predict energy and power consumption dynamics in bacterial cells, which can impact fundamental scientific studies and applied medical treatments in the future.

Temporally regulated cell migration is sensitive to variation in body size

Few studies have measured the robustness to perturbations of the final position of a long-range migrating cell. In the nematode Caenorhabditis elegans, the QR neuroblast migrates anteriorly, while undergoing three division rounds. We study the final position of two of its great-granddaughters, the end of migration of which was previously shown to depend on a timing mechanism. We find that the variance in their final position is similar to that of other long-range migrating neurons. As expected from the timing mechanism, the position of QR descendants depends on body size, which we varied by changing maternal age or using body size mutants. Using a mathematical model, we show that body size variation is partially compensated for. Applying environmental perturbations, we find that the variance in final position increased following starvation at hatching. The mean position is displaced upon a temperature shift. Finally, highly significant variation was found among C. elegans wild isolates. Overall, this study reveals that the final position of these neurons is quite robust to stochastic variation, shows some sensitivity to body size and to external perturbations, and varies in the species.This article has an associated 'The people behind the papers' interview.

Variability in mRNA translation: a random matrix theory approach

The rate of mRNA translation depends on the initiation, elongation, and termination rates of ribosomes along the mRNA. These rates depend on many "local" factors like the abundance of free ribosomes and tRNA molecules in the vicinity of the mRNA molecule. All these factors are stochastic and their experimental measurements are also noisy. An important question is how protein production in the cell is affected by this considerable variability. We develop a new theoretical framework for addressing this question by modeling the rates as identically and independently distributed random variables and using tools from random matrix theory to analyze the steady-state production rate. The analysis reveals a principle of universality: the average protein production rate depends only on the of the set of possible values that the random variable may attain. This explains how total protein production can be stabilized despite the overwhelming stochasticticity underlying cellular processes.

Quantifying information accumulation encoded in the dynamics of biochemical signaling

Cellular responses to environmental changes are encoded in the complex temporal patterns of signaling proteins. However, quantifying the accumulation of information over time to direct cellular decision-making remains an unsolved challenge. This is, in part, due to the combinatorial explosion of possible configurations that need to be evaluated for information in time-course measurements. Here, we develop a quantitative framework, based on inferred trajectory probabilities, to calculate the mutual information encoded in signaling dynamics while accounting for cell-cell variability. We use it to understand NFκB transcriptional dynamics in response to different immune threats, and reveal that some threats are distinguished faster than others. Our analyses also suggest specific temporal phases during which information distinguishing threats becomes available to immune response genes; one specific phase could be mapped to the functionality of the IκBα negative feedback circuit. The framework is generally applicable to single-cell time series measurements, and enables understanding how temporal regulatory codes transmit information over time.

Allosteric autoactivation of SOS and its kinetic mechanism

Son of Sevenless (SOS), one of guanine nucleotide exchange factors (GEFs), activates Ras. We discovered that the allosteric domain of SOS yields SOS to proceed a previously unrecognized autoactivation kinetics. Its essential feature is a time-dependent acceleration of SOS feedback activation with a reaction initiator or with the priming of active Ras. Thus, this mechanistic autoactivation feature explains the notion, previously only conjectured, of accelerative SOS activation followed by the priming of active Ras, an action produced by another GEF Ras guanyl nucleotide-releasing protein (RasGRP). Intriguingly, the kinetic transition from gradual RasGRP activation to accelerative SOS activation has been interpreted as an analog to digital conversion; however, from the perspective of autoactivation kinetics, it is a process of straightforward RasGRP-mediated SOS autoactivation. From the viewpoint of allosteric protein cooperativity, SOS autoactivation is a unique time-dependent cooperative SOS activation because it enables an active SOS to accelerate activation of other SOS as a function of time. This time-dependent SOS cooperativity does not belong to the classic steady-state protein cooperativity, which depends on ligand concentration. Although its hysteretic or sigmoid-like saturation curvature is a classic hallmark of steady-state protein cooperativity, its hyperbolic saturation figure typically represents protein noncooperativity. We also discovered that SOS autoactivation perturbs the previously predicted hysteresis of SOS activation in a steady state to produce a hyperbolic saturation curve. We interpret this as showing that SOS allostery elicits, through SOS autoactivation, cooperativity uniquely time-dependent but not ligand concentration dependent.

Effective Biophysical Modeling of Cell Free Transcription and Translation Processes

Transcription and translation are at the heart of metabolism and signal transduction. In this study, we developed an effective biophysical modeling approach to simulate transcription and translation processes. The model, composed of coupled ordinary differential equations, was tested by comparing simulations of two cell free synthetic circuits with experimental measurements generated in this study. First, we considered a simple circuit in which sigma factor 70 induced the expression of green fluorescent protein. This relatively simple case was then followed by a more complex negative feedback circuit in which two control genes were coupled to the expression of a third reporter gene, green fluorescent protein. Many of the model parameters were estimated from previous biophysical studies in the literature, while the remaining unknown model parameters for each circuit were estimated by minimizing the difference between model simulations and messenger RNA (mRNA) and protein measurements generated in this study. In particular, either parameter estimates from published studies were used directly, or characteristic values found in the literature were used to establish feasible ranges for the parameter estimation problem. In order to perform a detailed analysis of the influence of individual model parameters on the expression dynamics of each circuit, global sensitivity analysis was used. Taken together, the effective biophysical modeling approach captured the expression dynamics, including the transcription dynamics, for the two synthetic cell free circuits. While, we considered only two circuits here, this approach could potentially be extended to simulate other genetic circuits in both cell free and whole cell biomolecular applications as the equations governing the regulatory control functions are modular and easily modifiable. The model code, parameters, and analysis scripts are available for download under an MIT software license from the Varnerlab GitHub repository.

Plasticity via feedback reduces the cost of developmental instability

Costs of plasticity are thought to have important physiological and evolutionary consequences. A commonly predicted cost to plasticity is that plastic genotypes are likely to suffer from developmental instability. Adaptive plasticity requires that the developing organism can in some way sense what environment it is in or how well it is performing in that environment. These two information pathways—an “environmental signal” or a “performance signal” that indicates how well a developing phenotype matches the optimum in the current environment—can differ in their consequences for the organism and its evolution. Here, we consider how developmental instability might emerge as a side‐effect of these two distinct mechanisms. Because a performance cue allows a regulatory feedback loop connecting a trait to a feedback signal, we hypothesized that plastic genotypes using a performance signal would be more developmentally robust compared to those using a purely environmental signal. Using a numerical model of a network of gene interactions, we show that plasticity comes at a cost of developmental instability when the plastic response is mediated via an environmental signal, but not when it is mediated via a performance signal. We also show that a performance signal mechanism can evolve even in a constant environment, leading to genotypes preadapted for plasticity to novel environments even in populations without a history of environmental heterogeneity.

Microbial metabolic noise

From the time a cell was first placed under the microscope, it became apparent that identifying two clonal cells that "look" identical is extremely challenging. Since then, cell-to-cell differences in shape, size, and protein content have been carefully examined, informing us of the ultimate limits that hinder two cells from occupying an identical phenotypic state. Here, we present recent experimental and computational evidence that similar limits emerge also in cellular metabolism. These limits pertain to stochastic metabolic dynamics and, thus, cell-to-cell metabolic variability, including the resulting adapting benefits. We review these phenomena with a focus on microbial metabolism and conclude with a brief outlook on the potential relationship between metabolic noise and adaptive evolution. This article is categorized under: Metabolic Diseases > Computational Models Metabolic Diseases > Biomedical Engineering.

Identification of Genes Involved in the Differentiation of R7y and R7p Photoreceptor Cells in Drosophila

The R7 and R8 photoreceptor cells of the Drosophila compound eye mediate color vision. Throughout the majority of the eye, these cells occur in two principal types of ommatidia. Approximately 35% of ommatidia are of the pale type and express Rh3 in R7 cells and Rh5 in R8 cells. The remaining 65% are of the yellow type and express Rh4 in R7 cells and Rh6 in R8 cells. The specification of an R8 cell in a pale or yellow ommatidium depends on the fate of the adjacent R7 cell. However, pale and yellow R7 cells are specified by a stochastic process that requires the genes spineless, tango and klumpfuss. To identify additional genes involved in this process we performed genetic screens using a collection of 480 P{EP} transposon insertion strains. We identified genes in gain of function and loss of function screens that significantly altered the percentage of Rh3 expressing R7 cells (Rh3%) from wild-type. 36 strains resulted in altered Rh3% in the gain of function screen where the P{EP} insertion strains were crossed to a sevEP-GAL4 driver line. 53 strains resulted in altered Rh3% in the heterozygous loss of function screen. 4 strains showed effects that differed between the two screens, suggesting that the effect found in the gain of function screen was either larger than, or potentially masked by, the P{EP} insertion alone. Analyses of homozygotes validated many of the candidates identified. These results suggest that R7 cell fate specification is sensitive to perturbations in mRNA transcription, splicing and localization, growth inhibition, post-translational protein modification, cleavage and secretion, hedgehog signaling, ubiquitin protease activity, GTPase activation, actin and cytoskeletal regulation, and Ser/Thr kinase activity, among other diverse signaling and cell biological processes.

Uncoupling gene expression noise along the central dogma using genome engineered human cell lines

Eukaryotic protein synthesis is an inherently stochastic process. This stochasticity stems not only from variations in cell content between cells but also from thermodynamic fluctuations in a single cell. Ultimately, these inherently stochastic processes manifest as noise in gene expression, where even genetically identical cells in the same environment exhibit variation in their protein abundances. In order to elucidate the underlying sources that contribute to gene expression noise, we quantify the contribution of each step within the process of protein synthesis along the central dogma. We uncouple gene expression at the transcriptional, translational, and post-translational level using custom engineered circuits stably integrated in human cells using CRISPR. We provide a generalized framework to approximate intrinsic and extrinsic noise in a population of cells expressing an unbalanced two-reporter system. Our decomposition shows that the majority of intrinsic fluctuations stem from transcription and that coupling the two genes along the central dogma forces the fluctuations to propagate and accumulate along the same path, resulting in increased observed global correlation between the products.

Likelihood-free nested sampling for parameter inference of biochemical reaction networks

The development of mechanistic models of biological systems is a central part of Systems Biology. One major challenge in developing these models is the accurate inference of model parameters. In recent years, nested sampling methods have gained increased attention in the Systems Biology community due to the fact that they are parallelizable and provide error estimates with no additional computations. One drawback that severely limits the usability of these methods, however, is that they require the likelihood function to be available, and thus cannot be applied to systems with intractable likelihoods, such as stochastic models. Here we present a likelihood-free nested sampling method for parameter inference which overcomes these drawbacks. This method gives an unbiased estimator of the Bayesian evidence as well as samples from the posterior. We derive a lower bound on the estimators variance which we use to formulate a novel termination criterion for nested sampling. The presented method enables not only the reliable inference of the posterior of parameters for stochastic systems of a size and complexity that is challenging for traditional methods, but it also provides an estimate of the obtained variance. We illustrate our approach by applying it to several realistically sized models with simulated data as well as recently published biological data. We also compare our developed method with the two most popular other likeliood-free approaches: pMCMC and ABC-SMC. The C++ code of the proposed methods, together with test data, is available at the github web page https://github.com/Mijan/LFNS_paper.

The behaviour of mathematical models of biochemical reactions is governed by model parameters encoding for various reaction rates, molecule concentrations and other biochemical quantities. As the general purpose of these models is to reproduce and predict the true biological response to different stimuli, the inference of these parameters, given experimental observations, is a crucial part of Systems Biology. While plenty of methods have been published for the inference of model parameters, most of them require the availability of the likelihood function and thus cannot be applied to models that do not allow for the computation of the likelihood. Further, most established methods do not provide an estimate of the variance of the obtained estimator. In this paper, we present a novel inference method that accurately approximates the posterior distribution of parameters and does not require the evaluation of the likelihood function. Our method is based on the nested sampling algorithm and approximates the likelihood with a particle filter. We show that the resulting posterior estimates are unbiased and provide a way to estimate not just the posterior distribution, but also an error estimate of the final estimator. We illustrate our method on several stochastic models with simulated data as well as one model of transcription with real biological data.

Fine-tuning Nanog expression heterogeneity in embryonic stem cells by regulating a Nanog transcript-specific microRNA

In embryonic stem cells (ESCs), the transcription factor Nanog maintains the stemness of ESCs despite exhibiting heterogeneous expression patterns under varied culture conditions. Efficient fine-tuning of Nanog expression heterogeneity could enable ESC proliferation and differentiation along specific lineages to be regulated. Herein, by employing a stochastic modeling approach, we show that Nanog expression heterogeneity can be controlled by modulating the regulatory features of a Nanog transcript-specific microRNA, mir-296. We demonstrate how and why the extent of origin-dependent fluctuations in Nanog expression level can be altered by varying either the binding efficiency of the microRNA-mRNA complex or the expression level of mir-296. Moreover, our model makes experimentally feasible and insightful predictions to maneuver Nanog expression heterogeneity explicitly to achieve cell-type-specific differentiation of ESCs.

Stochastic reaction networks in dynamic compartment populations

Many biochemical processes in living systems take place in compartmentalized environments, where individual compartments can interact with each other and undergo dynamic remodeling. Studying such processes through mathematical models poses formidable challenges because the underlying dynamics involve a large number of states, which evolve stochastically with time. Here we propose a mathematical framework to study stochastic biochemical networks in compartmentalized environments. We develop a generic population model, which tracks individual compartments and their molecular composition. We then show how the time evolution of this system can be studied effectively through a small number of differential equations, which track the statistics of the population. Our approach is versatile and renders an important class of biological systems computationally accessible.

Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and typically very challenging to analyze computationally. Recent studies have made progress toward addressing this problem in the context of specific biological systems, but a general and sufficiently effective approach remains lacking. In this work, we propose a mathematical framework based on counting processes that allows us to study dynamic compartment populations with arbitrary interactions and internal biochemistry. We derive an efficient description of the dynamics in terms of differential equations which capture the statistics of the population. We demonstrate the relevance of our approach by analyzing models inspired by different biological processes, including subcellular compartmentalization and tissue homeostasis.

Computer-Aided Whole-Cell Design: Taking a Holistic Approach by Integrating Synthetic With Systems Biology

Computer-aided design (CAD) for synthetic biology promises to accelerate the rational and robust engineering of biological systems. It requires both detailed and quantitative mathematical and experimental models of the processes to (re)design biology, and software and tools for genetic engineering and DNA assembly. Ultimately, the increased precision in the design phase will have a dramatic impact on the production of designer cells and organisms with bespoke functions and increased modularity. CAD strategies require quantitative models of cells that can capture multiscale processes and link genotypes to phenotypes. Here, we present a perspective on how whole-cell, multiscale models could transform design-build-test-learn cycles in synthetic biology. We show how these models could significantly aid in the design and learn phases while reducing experimental testing by presenting case studies spanning from genome minimization to cell-free systems. We also discuss several challenges for the realization of our vision. The possibility to describe and build whole-cells in silico offers an opportunity to develop increasingly automatized, precise and accessible CAD tools and strategies.

A computational model of stem cell molecular mechanism to maintain tissue homeostasis

Stem cells, with their capacity to self-renew and to differentiate to more specialized cell types, play a key role to maintain homeostasis in adult tissues. To investigate how, in the dynamic stochastic environment of a tissue, non-genetic diversity and the precise balance between proliferation and differentiation are achieved, it is necessary to understand the molecular mechanisms of the stem cells in decision making process. By focusing on the impact of stochasticity, we proposed a computational model describing the regulatory circuitry as a tri-stable dynamical system to reveal the mechanism which orchestrate this balance. Our model explains how the distribution of noise in genes, linked to the cell regulatory networks, affects cell decision-making to maintain homeostatic state. The noise effect on tissue homeostasis is achieved by regulating the probability of differentiation and self-renewal through symmetric and/or asymmetric cell divisions. Our model reveals, when mutations due to the replication of DNA in stem cell division, are inevitable, how mutations contribute to either aging gradually or the development of cancer in a short period of time. Furthermore, our model sheds some light on the impact of more complex regulatory networks on the system robustness against perturbations.

Extended Robust Boolean Network of Budding Yeast Cell Cycle

Background:

How to explore the dynamics of transition probabilities between phases of budding yeast cell cycle (BYCC) network based on the dynamics of protein activities that control this network? How to identify the robust structure of protein interactions of BYCC Boolean network (BN)? Budding yeast allows scientists to put experiments into effect in order to discover the intracellular cell cycle regulating structures which are well simulated by mathematical modeling.

Methods:

We extended an available deterministic BN of proteins responsible for the cell cycle to a Markov chain model containing apoptosis besides G1, S, G2, M, and stationary G1. Using genetic algorithm (GA), we estimated the kinetic parameters of the extended BN model so that the subsequent transition probabilities derived using Markov chain model of cell states as normal cell cycle becomes the maximum while the structure of chemical interactions of extended BN of cell cycle becomes more stable.

Results:

Using kinetic parameters optimized by GA, the probability of the subsequent transitions between cell cycle phases is maximized. The relative basin size of stationary G1 increased from 86% to 96.48% while the number of attractors decreased from 7 in the original model to 5 in the extended one. Hence, an increase in the robustness of the system has been achieved.

Conclusion:

The structure of interacting proteins in cell cycle network affects its robustness and probabilities of transitions between different cell cycle phases. Markov chain and BN are good approaches to study the stability and dynamics of the cell cycle network.