A variational approach to the stochastic aspects of cellular signal transduction

Cellular signaling networks have evolved to cope with intrinsic fluctuations, coming from the small numbers of constituents, and the environmental noise. Stochastic chemical kinetics equations govern the way biochemical networks process noisy signals. The essential difficulty associated with the master equation approach to solving the stochastic chemical kinetics problem is the enormous number of ordinary differential equations involved. In this work, we show how to achieve tremendous reduction in the dimensionality of specific reaction cascade dynamics by solving variationally an equivalent quantum field theoretic formulation of stochastic chemical kinetics. The present formulation avoids cumbersome commutator computations in the derivation of evolution equations, making more transparent the physical significance of the variational method. We propose novel time-dependent basis functions which work well over a wide range of rate parameters. We apply the new basis functions to describe stochastic signaling in several enzymatic cascades and compare the results so obtained with those from alternative solution techniques. The variational ansatz gives probability distributions that agree well with the exact ones, even when fluctuations are large and discreteness and nonlinearity are important. A numerical implementation of our technique is many orders of magnitude more efficient computationally compared with the traditional Monte Carlo simulation algorithms or the Langevin simulations.Comment: 15 pages, 11 figure

A Minimal Model of Signaling Network Elucidates Cell-to-Cell Stochastic Variability in Apoptosis

Signaling networks are designed to sense an environmental stimulus and adapt to it. We propose and study a minimal model of signaling network that can sense and respond to external stimuli of varying strength in an adaptive manner. The structure of this minimal network is derived based on some simple assumptions on its differential response to external stimuli. We employ stochastic differential equations and probability distributions obtained from stochastic simulations to characterize differential signaling response in our minimal network model. We show that the proposed minimal signaling network displays two distinct types of response as the strength of the stimulus is decreased. The signaling network has a deterministic part that undergoes rapid activation by a strong stimulus in which case cell-to-cell fluctuations can be ignored. As the strength of the stimulus decreases, the stochastic part of the network begins dominating the signaling response where slow activation is observed with characteristic large cell-to-cell stochastic variability. Interestingly, this proposed stochastic signaling network can capture some of the essential signaling behaviors of a complex apoptotic cell death signaling network that has been studied through experiments and large-scale computer simulations. Thus we claim that the proposed signaling network is an appropriate minimal model of apoptosis signaling. Elucidating the fundamental design principles of complex cellular signaling pathways such as apoptosis signaling remains a challenging task. We demonstrate how our proposed minimal model can help elucidate the effect of a specific apoptotic inhibitor Bcl-2 on apoptotic signaling in a cell-type independent manner. We also discuss the implications of our study in elucidating the adaptive strategy of cell death signaling pathways.Comment: 9 pages, 6 figure

Evolution of Robustness to Noise and Mutation in Gene Expression Dynamics

Phenotype of biological systems needs to be robust against mutation in order to sustain themselves between generations. On the other hand, phenotype of an individual also needs to be robust against fluctuations of both internal and external origins that are encountered during growth and development. Is there a relationship between these two types of robustness, one during a single generation and the other during evolution? Could stochasticity in gene expression have any relevance to the evolution of these robustness? Robustness can be defined by the sharpness of the distribution of phenotype; the variance of phenotype distribution due to genetic variation gives a measure of `genetic robustness' while that of isogenic individuals gives a measure of `developmental robustness'. Through simulations of a simple stochastic gene expression network that undergoes mutation and selection, we show that in order for the network to acquire both types of robustness, the phenotypic variance induced by mutations must be smaller than that observed in an isogenic population. As the latter originates from noise in gene expression, this signifies that the genetic robustness evolves only when the noise strength in gene expression is larger than some threshold. In such a case, the two variances decrease throughout the evolutionary time course, indicating increase in robustness. The results reveal how noise that cells encounter during growth and development shapes networks' robustness to stochasticity in gene expression, which in turn shapes networks' robustness to mutation. The condition for evolution of robustness as well as relationship between genetic and developmental robustness is derived through the variance of phenotypic fluctuations, which are measurable experimentally.Comment: 25 page

Rule-based modeling of biochemical systems with BioNetGen

Totowa, NJ. Please cite this article when referencing BioNetGen in future publications. Rule-based modeling involves the representation of molecules as structured objects and molecular interactions as rules for transforming the attributes of these objects. The approach is notable in that it allows one to systematically incorporate site-specific details about proteinprotein interactions into a model for the dynamics of a signal-transduction system, but the method has other applications as well, such as following the fates of individual carbon atoms in metabolic reactions. The consequences of protein-protein interactions are difficult to specify and track with a conventional modeling approach because of the large number of protein phosphoforms and protein complexes that these interactions potentially generate. Here, we focus on how a rule-based model is specified in the BioNetGen language (BNGL) and how a model specification is analyzed using the BioNetGen software tool. We also discuss new developments in rule-based modeling that should enable the construction and analyses of comprehensive models for signal transduction pathways and similarly large-scale models for other biochemical systems. Key Words: Computational systems biology; mathematical modeling; combinatorial complexity; software; formal languages; stochastic simulation; ordinary differential equations; protein-protein interactions; signal transduction; metabolic networks. 1

Dedifferentiated early postnatal lung myofibroblasts redifferentiate in adult disease

Alveolarization ensures sufficient lung surface area for gas exchange, and during bulk alveolarization in mice (postnatal day [P] 4.5–14.5), alpha-smooth muscle actin (SMA)+ myofibroblasts accumulate, secrete elastin, and lay down alveolar septum. Herein, we delineate the dynamics of the lineage of early postnatal SMA+ myofibroblasts during and after bulk alveolarization and in response to lung injury. SMA+ lung myofibroblasts first appear at ∼ P2.5 and proliferate robustly. Lineage tracing shows that, at P14.5 and over the next few days, the vast majority of SMA+ myofibroblasts downregulate smooth muscle cell markers and undergo apoptosis. Of note, ∼8% of these dedifferentiated cells and another ∼1% of SMA+ myofibroblasts persist to adulthood. Single cell RNA sequencing analysis of the persistent SMA− cells and SMA+ myofibroblasts in the adult lung reveals distinct gene expression profiles. For instance, dedifferentiated SMA− cells exhibit higher levels of tissue remodeling genes. Most interestingly, these dedifferentiated early postnatal myofibroblasts re-express SMA upon exposure of the adult lung to hypoxia or the pro-fibrotic drug bleomycin. However, unlike during alveolarization, these cells that re-express SMA do not proliferate with hypoxia. In sum, dedifferentiated early postnatal myofibroblasts are a previously undescribed cell type in the adult lung and redifferentiate in response to injury

Quantification of Cytokeratin 5 mRNA Expression in the Circulation of Healthy Human Subjects and after Lung Transplantation

Circulating epithelial progenitor cells are important for repair of the airway epithelium in a mouse model of tracheal transplantation. We therefore hypothesized that circulating epithelial progenitor cells would also be present in normal human subjects and could be important for repair of the airway after lung injury. As lung transplantation is associated with lung injury, which is severe early on and exacerbated during episodes of infection and rejection, we hypothesized that circulating epithelial progenitor cell levels could predict clinical outcome following lung transplantation.Quantitative Real Time PCR was performed to determine peripheral blood mRNA levels of cytokeratin 5, a previously characterized marker of circulating epithelial progenitor cells. Cytokeratin 5 levels were evaluated in healthy human subjects, in lung transplant recipients immediately post-transplant and serially thereafter, and in heart transplant recipients. All normal human subjects examined expressed cytokeratin 5 in their buffy coat in amounts that were not significantly influenced by age or gender. There was a profound, statistically significant decrease in cytokeratin 5 mRNA expression levels in lung transplant patients compared to healthy human subjects (p = 3.1x10(-13)) and to heart transplant recipients. There was a moderate negative correlation between improved circulating cytokeratin 5 mRNA levels in lung transplant recipients with recovering lung function, as measured by improved FEV1 values (rho = -0.39).Levels of cytokeratin 5 mRNA, a proxy marker for circulating epithelial progenitor cells, inversely correlated with disease status in lung transplant recipients. It may therefore serve as a biomarker of the clinical outcome of lung transplant patients and potentially other patients with airway injury

Gata4 Is Required for Formation of the Genital Ridge in Mice

In mammals, both testis and ovary arise from a sexually undifferentiated precursor, the genital ridge, which first appears during mid-gestation as a thickening of the coelomic epithelium on the ventromedial surface of the mesonephros. At least four genes (Lhx9, Sf1, Wt1, and Emx2) have been demonstrated to be required for subsequent growth and maintenance of the genital ridge. However, no gene has been shown to be required for the initial thickening of the coelomic epithelium during genital ridge formation. We report that the transcription factor GATA4 is expressed in the coelomic epithelium of the genital ridge, progressing in an anterior-to-posterior (A-P) direction, immediately preceding an A-P wave of epithelial thickening. Mouse embryos conditionally deficient in Gata4 show no signs of gonadal initiation, as their coelomic epithelium remains a morphologically undifferentiated monolayer. The failure of genital ridge formation in Gata4-deficient embryos is corroborated by the absence of the early gonadal markers LHX9 and SF1. Our data indicate that GATA4 is required to initiate formation of the genital ridge in both XX and XY fetuses, prior to its previously reported role in testicular differentiation of the XY gonadHoward Hughes Medical Institut

Correction to: Differentiation of RPE cells from integration-free iPS cells and their cell biological characterization.

The original article [1] contains an error in the legend of Fig 5 whereby the descriptions for panels 5d and 5e are incorrect; as such, the corrected legend can be viewed below with its respective figure images

Automated Imaging Differentiation for Parkinsonism

Importance: Magnetic resonance imaging (MRI) paired with appropriate disease-specific machine learning holds promise for the clinical differentiation of Parkinson disease (PD), multiple system atrophy (MSA) parkinsonian variant, and progressive supranuclear palsy (PSP). A prospective study is needed to test whether the approach meets primary end points to be considered in a diagnostic workup. Objective: To assess the discriminative performance of Automated Imaging Differentiation for Parkinsonism (AIDP) using 3-T diffusion MRI and support vector machine (SVM) learning. Design, Setting, and Participants: This was a prospective, multicenter cohort study conducted from July 2021 to January 2024 across 21 Parkinson Study Group sites (US/Canada). Included were patients with PD, MSA, and PSP with established criteria and unanimous agreement in the clinical diagnosis among 3 independent, blinded neurologists who specialize in movement disorders. Patients were assigned to a training set or an independent testing set. Exposure: MRI. Main Outcomes and Measures: Area under the receiver operating characteristic curve (AUROC) in the testing set for primary model end points of PD vs atypical parkinsonism, MSA vs PSP, PD vs MSA, and PD vs PSP. AIDP was also paired with antemortem MRI to test against postmortem neuropathology in a subset of autopsy cases. Results: A total of 316 patients were screened and 249 patients (mean [SD] age, 67.8 [7.7] years; 155 male [62.2%]) met inclusion criteria. Of these patients, 99 had PD, 53 had MSA, and 97 had PSP. A retrospective cohort of 396 patients (mean [SD] age, 65.8 [8.9] years; 234 male [59.1%]) was also included. Of these patients, 211 had PD, 98 had MSA, and 87 had PSP. Patients were assigned to the training set (78%; 104 prospective, 396 retrospective) or independent testing set, which included 145 (22%; 60 PD, 27 MSA, 58 PSP) prospective patients (mean age, 67.4 [SD 7.7] years; 95 male [65.5%]). The model was robust in differentiating PD vs atypical parkinsonism (AUROC, 0.96; 95% CI, 0.93-0.99; positive predictive value [PPV], 0.91; negative predictive value [NPV], 0.83), MSA vs PSP (AUROC, 0.98; 95% CI, 0.96-1.00; PPV, 0.98; NPV, 0.81), PD vs MSA (AUROC, 0.98; 95% CI, 0.96-1.00; PPV, 0.97; NPV, 0.97), and PD vs PSP (AUROC, 0.98; 95% CI, 0.96-1.00; PPV, 0.92; NPV, 0.98). AIDP predictions were confirmed neuropathologically in 46 of 49 brains (93.9%). Conclusions and Relevance: This prospective multicenter cohort study of AIDP met its primary end points. Results suggest using AIDP in the diagnostic workup for common parkinsonian syndromes.</p