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Documentation of model components, interactions and regulatory rules.

Epithelial-to-mesenchymal transition (EMT) has been associated with cancer cell heterogeneity, plasticity, and metastasis. However, the extrinsic signals supervising these phenotypic transitions remain elusive. To assess how selected microenvironmental signals control cancer-associated phenotypes along the EMT continuum, we defined a logical model of the EMT cellular network that yields qualitative degrees of cell adhesions by adherens junctions and focal adhesions, two features affected during EMT. The model attractors recovered epithelial, mesenchymal, and hybrid phenotypes. Simulations showed that hybrid phenotypes may arise through independent molecular paths involving stringent extrinsic signals. Of particular interest, model predictions and their experimental validations indicated that: (i) stiffening of the extracellular matrix was a prerequisite for cells overactivating FAK_SRC to upregulate SNAIL and acquire a mesenchymal phenotype and (ii) FAK_SRC inhibition of cell–cell contacts through the receptor-type tyrosine-protein phosphatases kappa led to acquisition of a full mesenchymal, rather than a hybrid, phenotype. Altogether, these computational and experimental approaches allow assessment of critical microenvironmental signals controlling hybrid EMT phenotypes and indicate that EMT involves multiple molecular programs.Significance:A multidisciplinary study sheds light on microenvironmental signals controlling cancer cell plasticity along EMT and suggests that hybrid and mesenchymal phenotypes arise through independent molecular paths.

Supplementary Methods

Supplementary Figures S1-S8

Epithelial-to-mesenchymal transition (EMT) has been associated with cancer cell heterogeneity, plasticity, and metastasis. However, the extrinsic signals supervising these phenotypic transitions remain elusive. To assess how selected microenvironmental signals control cancer-associated phenotypes along the EMT continuum, we defined a logical model of the EMT cellular network that yields qualitative degrees of cell adhesions by adherens junctions and focal adhesions, two features affected during EMT. The model attractors recovered epithelial, mesenchymal, and hybrid phenotypes. Simulations showed that hybrid phenotypes may arise through independent molecular paths involving stringent extrinsic signals. Of particular interest, model predictions and their experimental validations indicated that: (i) stiffening of the extracellular matrix was a prerequisite for cells overactivating FAK_SRC to upregulate SNAIL and acquire a mesenchymal phenotype and (ii) FAK_SRC inhibition of cell–cell contacts through the receptor-type tyrosine-protein phosphatases kappa led to acquisition of a full mesenchymal, rather than a hybrid, phenotype. Altogether, these computational and experimental approaches allow assessment of critical microenvironmental signals controlling hybrid EMT phenotypes and indicate that EMT involves multiple molecular programs. Significance: A multidisciplinary study sheds light on microenvironmental signals controlling cancer cell plasticity along EMT and suggests that hybrid and mesenchymal phenotypes arise through independent molecular paths.

In this paper, a logical-based mathematical model of the cellular pathways involved in the COVID-19 infection has been developed to study various drug treatments (single or in combination), in different illness scenarios, providing insights into their mechanisms of action. Drug simulations suggest that the effects of single drugs are limited, or depending on the scenario counterproductive, whereas better results appear combining different treatments. Specifically, the combination of the anti-inflammatory Baricitinib and the anti-viral Remdesivir showed significant benefits while a stronger efficacy emerged from the triple combination of Baricitinib, Remdesivir, and the corticosteroid Dexamethasone. Together with a sensitivity analysis, we performed an analysis of the mechanisms of the drugs to reveal their impact on molecular pathways.

RNA vaccines represent a milestone in the history of vaccinology. They provide several advantages over more traditional approaches to vaccine development, showing strong immunogenicity and an overall favorable safety profile. While preclinical testing has provided some key insights on how RNA vaccines interact with the innate immune system, their mechanism of action appears to be fragmented amid the literature, making it difficult to formulate new hypotheses to be tested in clinical settings and ultimately improve this technology platform. Here, we propose a systems biology approach, based on the combination of literature mining and mechanistic graphical modeling, to consolidate existing knowledge around mRNA vaccines mode of action and enhance the translatability of preclinical hypotheses into clinical evidence. A Natural Language Processing (NLP) pipeline for automated knowledge extraction retrieved key biological evidences that were joined into an interactive mechanistic graphical model representing the chain of immune events induced by mRNA vaccines administration. The achieved mechanistic graphical model will help the design of future experiments, foster the generation of new hypotheses and set the basis for the development of mathematical models capable of simulating and predicting the immune response to mRNA vaccines.

The multistep development of cancer involves the cooperation between multiple molecular lesions, as well as complex interactions between cancer cells and the surrounding tumour microenvironment. The search for these synergistic interactions using experimental models made tremendous contributions to our understanding of oncogenesis. Yet, these approaches remain labour intensive and challenging. To tackle such a hurdle, an integrative, multidisciplinary effort is required. In this article, we highlight the use of logical computational models combined to experimental validations as an effective approach to identify cooperative mechanisms and therapeutic strategies in the context of cancer biology. In silico models overcome limitations of reductionist approaches by capturing tumour complexity, and by generating powerful testable hypotheses. We review representative examples of logical models reported in the literature and their validation. We then provide further analyses of our logical model of Epithelium to Mesenchymal Transition (EMT), searching for additional cooperative interactions involving inputs from the tumour microenvironment and gain of function mutations in NOTCH.

The ventricular action potential (AP) is subserved by an interdependent system of voltage-gated ion channels and pumps that both alter and respond (directly or indirectly) to the dynamic transmembrane potential (Δψm(t)) via voltage-dependent state transitions governing inward and outward ion currents. The native dynamic inward-outward current balance is subject to disruption caused by acquired or inherited loss or gain of function in one or more ion channels or pumps. Building on our previous work, we used a modified version of the O’Hara-Rudy (ORd) model of the undiseased human ventricular cardiomyocyte to study the pro-arrhythmic effects of three types of arrhythmia-inducing perturbations in midmyocytes (M cells): Blockade of the human ether-a-go-go related gene (hERG) K+ channel introduced via a Markov state binding model.Mutation-induced voltage shifts in hERG channel gating, resulting in faster inactivation or slowed recovery of both phosphorylated and non-phosphorylated forms of the channel (known as LQT2 syndrome).Mutation-induced voltage shifts in Nav1.5 gating, resulting in slowed late inactivation of the phosphorylated and non-phosphorylated forms of the channel (known as LQT3 syndrome).We studied the relationships between ion current anomalies and AP morphology as a function of cycle length (CL) and perturbation type/level. The results are summarized as follows: AP duration (APD) is governed directly by Kir2.1 activation (IK1), which is delayed when repolarization is slowed by abnormal net inward tipping of the dynamic inward-outward current balance (reflected in decreased d(Δψm(t))/dt during the late AP repolarization phase). In the case of hERG blockade by non-trappable compounds, the perturbation level consists of the dynamic fractional occupancy of the channel, which is governed by blocker kon relative to the rate of channel opening, pharmacokinetic exposure, and koff (in that order).Arrhythmia progresses from prolonged paced APs → atypical APs (spontaneous and paced) → self-sustaining oscillations. Abrupt transitions between these regimes occur at CL- and perturbation-specific thresholds (denoted as T1, T2, and T3, respectively), whereas intra-regime progression proceeds in a graded fashion toward the subsequent threshold. APD and d(Δψm(t))/dt during the late repolarization phase varied significantly across the 200 APs of our simulations near the T1 threshold at CL = 1/35 min, reflecting increasing instability of the AP generation system.Arrhythmic APs exhibit highly variable cycle-to-cycle morphologies, depending on the perturbation level, type, and phasing between the underlying ion channel states and pacing cycle.Atypical APs may be triggered by typical or atypical depolarizations prior to the T3 threshold, depending on perturbation type/level and phasing relative to CL: APD/CL resides outside of the Goldilocks zone: APD/CL → 1 at shorter CL and/or longer APD, resulting in pro-arrhythmic “collisions” between successive paced APs (APi and APj) within a given cardiomyocyte. We studied this scenario at 60 and 80 beats per minute (BPM), equating to CL = 1/60 and 1/80 min.APD/CL < 1 at longer CL results in spontaneous atypical depolarizations within prolonged paced APs at elevated takeoff Δψm(t) and increased channel phosphorylation levels. We studied this scenario at CL = 1/35 min.APD and d(Δψm(t))/dt during the late repolarization phase become increasingly variable over successive APs on approach to the T1 threshold, which is the possible source of short-long-short sequences observed in the ECG preceding torsades de pointes arrhythmia (TdP).All atypical depolarizations are solely Cav1.2 (ICa,L)-driven (Δψm(t) falls within the Nav1.5 inactivation window), whereas typical depolarizations are Nav1.5 (INa) + ICa,L-driven. Atypical depolarization versus typical repolarization occurrences are determined by the faster of Cav1.2 and Kir2.1 (IK1) activation (where IK1 becomes increasingly dampened as the minimum Δψm(t) drifts above the Kir2.1 activation window).Cav1.2 inactivation gates reset to the open position (accompanied by recovery) synchronously with channel closing under control conditions, generating a small ICa,L window current in the process. This current grows toward a depolarizing spike when the lag time between recovery and closing grows above a threshold level.APs undergo damped oscillatory Cav1.2 recovery/re-inactivation cycles above the T3 threshold, which are refreshed by subsequent pacing signals (nodal or reentrant in origin).

Cellular function depends on heterogeneousdynamicintra-, inter-, and supramolecular structure-function relationships. However, the specific mechanisms by which cellular function is transduced from molecular systems, and by which cellular dysfunction arises from molecular dysfunction are poorly understood. We proposed previously that cellular function manifests as a molecular form of analog computing, in which specific time-dependent state transition fluxes within sets of molecular species (“molecular differential equations” (MDEs)) are sped and slowed in response to specific perturbations (inputs). In this work, we offer a theoretical treatment of the molecular mechanisms underlying cellular analog computing (which we refer to as “biodynamics”), focusing primarily on non-equilibrium (dynamic) intermolecular state transitions that serve as the principal means by which MDE systems are solved (the molecular equivalent of mathematical “integration”). Under these conditions, bound state occupancy is governed bykonandkoff, together with the rates of binding partner buildup and decay. Achieving constant fractional occupancy over time depends on: 1) equivalence between konand the rate of binding site buildup); 2) equivalence betweenkoffand the rate of binding site decay; and 3) free ligand concentration relative tokoff/k0n(n · Kd, where n is the fold increase in binding partner concentration needed to achieve a given fractional occupancy). Failure to satisfy these conditions results in fractional occupancy well below that corresponding to n · Kd. The implications of biodynamics for cellular function/dysfunction and drug discovery are discussed.

The system (PTTRS) formed by typical 2-Cys peroxiredoxins (Prx), thioredoxin (Trx), Trx reductase (TrxR), and sulfiredoxin (Srx) is central in antioxidant protection and redox signaling in the cytoplasm of eukaryotic cells. Understanding how the PTTRS integrates these functions requires tracing phenotypes to molecular properties, which is non-trivial. Here we analyze this problem based on a model that captures the PTTRS’ conserved features. We have mapped the conditions that generate each distinct response to H2O2 supply rates (vsup), and estimated the parameters for thirteen human cell types and for Saccharomyces cerevisiae. The resulting composition-to-phenotype map yielded the following experimentally testable predictions. The PTTRS permits many distinct responses including ultra-sensitivity and hysteresis. However, nearly all tumor cell lines showed a similar response characterized by limited Trx-S- depletion and a substantial but self-limited gradual accumulation of hyperoxidized Prx at high vsup. This similarity ensues from strong correlations between the TrxR, Srx and Prx activities over cell lines, which contribute to maintain the Prx-SS reduction capacity in slight excess over the maximal steady state Prx-SS production. In turn, in erythrocytes, hepatocytes and HepG2 cells high vsup depletes Trx-S- and oxidizes Prx mainly to Prx-SS. In all nucleated human cells the Prx-SS reduction capacity defined a threshold separating two different regimes. At sub-threshold vsup the cytoplasmic H2O2 concentration is determined by Prx, nM-range and spatially localized, whereas at supra-threshold vsup it is determined by much less active alternative sinks and μM-range throughout the cytoplasm. The yeast shows a distinct response where the Prx Tsa1 accumulates in sulfenate form at high vsup. This is mainly due to an exceptional stability of Tsa1's sulfenate. The implications of these findings for thiol redox regulation and cell physiology are discussed. All estimates were thoroughly documented and provided, together with analytical approximations for system properties, as a resource for quantitative redox biology., Graphical abstract fx1, Highlights • A simple model maps cells’ protein composition to responses to H2O2 supply. • Most human cell lines are predicted to show a similar response to H2O2. • This similarity is due to protein concentrations being correlated over cell lines. • The yeast is predicted to show a response that is distinct from human cells’. • Capacity for PrxSS reduction sets a threshold separating distinct signaling regimes.

Cells are occasionally exposed to high H2O2 concentrations, often preceding exposure to other electrophylic compounds. Both H2O2 and these compounds can irreversibly modify protein thiols, with deleterious consequences. Induction of enzymatic defenses against those agents is too slow to avoid significant damage. Cells may solve this conundrum by reversibly "blocking" the thiols once H2O2 concentrations begin to increase. We term this mechanism "anticipatory blocking" because it acts in anticipation of irreversible damage upon detection of early signs of stress. Here we examine the design requirements for the Peroxiredoxin/Thioredoxin/Thioredoxin-Reductase/Protein-Dithiol System (PTTRDS) to effectively integrate H2O2 signaling and anticipatory blocking of protein dithiols as disulfides, and we compared them to the designs found in cells. To that effect, we developed a minimal model of the PTTRDS, and we defined a set of quantitative performance criteria that embody the requirements for (a) efficient scavenging capacity, (b) low NADPH consumption, (c) effective signal propagation, and (d) effective anticipatory blocking. We then sought the design principles (relationships among rate constants and species concentrations) that warrant fulfillment of all these criteria. Experimental data indicates that the design of the PTTRDS in human erythrocytes fulfills these principles and thus accomplishes effective integration between anticipatory blocking, antioxidant protection and redox signaling. A more general analysis suggests that the same principles hold in a wide variety of cell types and organisms. We acknowledge grants PEst-C/SAU/LA0001/2013-2014, PEst-OE/QUI/UI0612/2013, FCOMP-01-0124-FEDER-020978 (PTDC/QUI-BIQ/119657/2010) financed by FEDER through the "Programa Operacional Factores de Competitividade, COMPETE" and by national funds through "FCT, Fundacao para a Ciencia e a Tecnologia".

In human erythrocytes H2O2 is mainly consumed by glutathione peroxidase, catalase and peroxiredoxin 2 (Prx2). Our previous analyses indicate that Prx2's peroxidase activity is subjected to a strong but quickly reversible inhibition (see companion abstract). If this activity is inhibited then the main role of Prx2 cannot be to eliminate H2O2. What functional advantages could then such an inhibition confer?We set up and validated a kinetic model of H2O2 metabolism human erythrocytes that shows quantitative agreement with extensive experimental observations. We then applied it to analyze the behavior of Prx2 and Trx under the H2O2 exposure dynamics that erythrocytes face in circulation. The significance of Prx2 inhibition was assessed by comparing the behavior of this model with that of an otherwise identical model lacking inhibition.Our analysis shows that Prx2 inhibition leads to 25-40% lower NADPH consumption under low to moderately high H2O2 supply (

H2O2 elimination in human erythrocytes is mainly carried out by catalase (Cat), glutathione peroxidase (GPx1) and the more recently discovered peroxiredoxin 2 (Prx2). However, the contribution of Prx2 to H2O2 consumption is still unclear. Prx2's high reactivity with H2O2 (kPrx2=10×10(7) M(-1)s(-1), kCat =7×10(7) M(-1)s(-1), kGPx1 =4×10(7) M(-1)s(-1)) and high abundance ([Prx2]= 570µM, [Cat]= 32µM, [GPx1]= 1µM) suggest that under low H2O2 supply rates it should consume >99% of the H2O2. However, extensive evidence indicates that in intact erythrocytes Prx2 contributes no more than Cat to H2O2 consumption. In order for this to be attained, Prx2's effective rate constant with H2O2would have to be just ~10(5) M(-1)s(-1), much lower than that determined in multiple experiments with the purified proteins. Nevertheless, nearly all Prx2 is oxidized within 1min of exposing erythrocytes to a H2O2 bolus, which is inconsistent with an irreversible inhibition. A mathematical model of the H2O2 metabolism in human erythrocytes [Benfeitas et al. (2014) Free Radic. Biol. Med.] where Prx2 either has a low kPrx2 or is subject to a strong (>99%) but readily reversible inhibition achieves quantitative agreement with detailed experimental observations of the responses of the redox status of Prx2 in human erythrocytes and suggests functional advantages of this design (see companion abstract). By contrast, a variant where Prx2 is fully active with kPrx2=10(8) M(-1)s(-1) shows important qualitative discrepancies. Altogether, these results suggest that Prx2's peroxidase activity is strongly inhibited in human erythrocytes. We acknowledge fellowship SFRH/BD/51199/2010, grants PEst-C/SAU/LA0001/2013-2014, PEst-OE/QUI/UI0612/2013, PEst-OE/QUI/UI0313/2014, and FCOMP-01-0124-FEDER-020978 (PTDC/QUI-BIQ/119657/2010) co-financed by FEDER through the COMPETE program and by FCT.

Hydrogen peroxide (H 2 O 2 ) metabolism in human erythrocytes has been thoroughly investigated, but unclear points persist. By integrating the available data into a mathematical model that accurately represents the current understanding and comparing computational predictions to observations we sought to (a) identify inconsistencies in present knowledge, (b) propose resolutions, and (c) examine their functional implications. The systematic confrontation of computational predictions with experimental observations of the responses of intact erythrocytes highlighted the following important discrepancy. The high rate constant (10 7 –10 8 M −1 s −1 ) for H 2 O 2 reduction determined for purified peroxiredoxin II (Prx2) and the high abundance of this protein indicate that under physiological conditions it consumes practically all the H 2 O 2 . However, this is inconsistent with extensive evidence that Prx2’s contribution to H 2 O 2 elimination is comparable to that of catalase. Models modified such that Prx2’s effective peroxidase activity is just 10 5 M −1 s −1 agree near quantitatively with extensive experimental observations. This low effective activity is probably due to a strong but readily reversible inhibition of Prx2’s peroxidatic activity in intact cells, implying that the main role of Prx2 in human erythrocytes is not to eliminate peroxide substrates. Simulations of the responses to physiological H 2 O 2 stimuli highlight that a design combining abundant Prx2 with a low effective peroxidase activity spares NADPH while improving potential signaling properties of the Prx2/thioredoxin/thioredoxin reductase system.

Fluorescent signals are widely used in life sciences to investigate cellular behaviors. Using a fluorometer is a reliable approach to measure the amount of a specific fluorescent radiation emitted by a cellular population. On the other hand, measuring fluorescent signals at the single-cell level requires the use of properly equipped microscopes to acquire images for further analysis. Here we present a digital image processing (DIP) approach to analyze these images. More in detail, a DIP system was developed to analyze photographic images of fluorescent Escherichia coli expressing a Green Fluorescent Protein (GFP). This system includes stages of noise filtering, uneven illumination correction, segmentation, detection of cell aggregates and measurement of the level of fluorescence of the selected cells. To accomplish this task, well established DIP algorithms for the different functions were adapted to the specific conditions of the experiment under study. In the results section, images are presented that reveal the behavior of the algorithms employed, as well as the calculated distribution of single cell fluorescence. In regard of the adequate selection of valid cells (i.e. deletion of aggregates), the system effectiveness was evaluated through comparison to the results obtained by human analysis, and expressed quantitatively. An assessment on the perspectives of further improvements to the developed system is finally proposed.