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We observed the interference between two prevalent respiratory viruses, respiratory syncytial virus (RSV) and influenza A virus (IAV) (H1N1), and characterized its molecular underpinnings in alveolar epithelial cells (A549). We found that RSV induces higher levels of interferon beta (IFN-β) production than IAV and that IFN-β priming confers higher-level protection against infection with IAV than with RSV. Consequently, we focused on the sequential infection scheme of RSV and then IAV. Using A549 wild-type (WT), IFNAR1 knockout (KO), IFNLR1 KO, and IFNAR1-IFNLR1 double-KO cell lines, we found that both IFN-β and IFN-λ are necessary for maximum protection against subsequent infection. Immunostaining revealed that preinfection with RSV partitions the cell population into a subpopulation susceptible to subsequent infection with IAV and an IAV-proof subpopulation. Strikingly, the susceptible cells turned out to be those already compromised and efficiently expressing RSV, whereas the bystander, interferon-primed cells are resistant to IAV infection. Thus, virus-virus exclusion at the cell population level is not realized through direct competition for a shared ecological niche (single cell) but rather is achieved with the involvement of specific cytokines induced by the host's innate immune response.

When infected with a virus, cells may secrete interferons (IFNs) that prompt nearby cells to prepare for upcoming infection. Reciprocally, viral proteins often interfere with IFN synthesis and IFN-induced signaling. We modeled the crosstalk between the propagating virus and the innate immune response using an agent-based stochastic approach. By analyzing immunofluorescence microscopy images we observed that the mutual antagonism between the respiratory syncytial virus (RSV) and infected A549 cells leads to dichotomous responses at the single-cell level and complex spatial patterns of cell signaling states. Our analysis indicates that RSV blocks innate responses at three levels: by inhibition of IRF3 activation, inhibition of IFN synthesis, and inhibition of STAT1/2 activation. In turn, proteins coded by IFN-stimulated (STAT1/2-activated) genes inhibit the synthesis of viral RNA and viral proteins. The striking consequence of these inhibitions is lack of coincidence of viral proteins and IFN expression within single cells. The model enables investigation of the impact of immunostimulatory defective viral particles and signaling network perturbations that could potentially facilitate containment or clearance of the viral infection.

Viral RNA-activated transcription factors IRF3 and NF-κB trigger synthesis of interferons and interleukins. In non-infected bystander cells, the innate immune response is reinforced by secreted interferon β (IFNβ), which induces the expression of interferon-activated genes (ISGs) through activation of STAT1/2. Here, we show that in cells transfected with an analog of viral RNA, poly(I:C), transcriptional activity of STAT1/2 is terminated due to depletion of the IFNβ receptor, IFNAR. We demonstrate that two ISGs, RNase L and PKR, not only hinder replenishment of IFNAR, but also suppress negative regulators of IRF3 and NF-κB, consequently promoting their transcriptional activity. We incorporated these findings into a comprehensive mathematical model of innate immunity. By coupling signaling through the IRF3/NF-κB and the STAT1/2 pathways with activity of RNase L and PKR, the model explains how poly(I:C) switches the transcriptional program from STAT1/2-induced to IRF3/NF-κB-induced, transforming IFNβ-responding cells into IFNβ-secreting cells. Using an ample set of experiments on wild-type and knock-out A549 cell lines for fitting the model, we managed to achieve parameter identifiability.

Omicron, the novel highly mutated SARS-CoV-2 Variant of Concern (VOC, Pango lineage B.1.1.529) was first collected in early November 2021 in South Africa. By the end of November 2021, it had spread and approached fixation in South Africa, and had been detected on all continents. We analyzed the exponential growth of Omicron over four-week periods in the two most populated of South Africa’s provinces, Gauteng and KwaZulu-Natal, arriving at the doubling time estimates of, respectively, 3.3 days (95% CI: 3.2–3.4 days) and 2.7 days (95% CI: 2.3–3.3 days). Similar or even shorter doubling times were observed in other locations: Australia (3.0 days), New York State (2.5 days), UK (2.4 days), and Denmark (2.0 days). Log–linear regression suggests that the spread began in Gauteng around 11 October 2021; however, due to presumable stochasticity in the initial spread, this estimate can be inaccurate. Phylogenetics-based analysis indicates that the Omicron strain started to diverge between 6 October and 29 October 2021. We estimated that the weekly growth of the ratio of Omicron to Delta is in the range of 7.2–10.2, considerably higher than the growth of the ratio of Delta to Alpha (estimated to be in in the range of 2.5–4.2), and Alpha to pre-existing strains (estimated to be in the range of 1.8–2.7). High relative growth does not necessarily imply higher Omicron infectivity. A two-strain SEIR model suggests that the growth advantage of Omicron may stem from immune evasion, which permits this VOC to infect both recovered and fully vaccinated individuals. As we demonstrated within the model, immune evasion is more concerning than increased transmissibility, because it can facilitate larger epidemic outbreaks.

Omicron, the novel highly mutated SARS-CoV-2 Variant of Concern (VOC, Pango lineage B.1.1.529), was first collected in early November 2021 in South Africa. By the end of November 2021, it had spread and approached fixation in South Africa, and had been detected on all continents. We analyzed the exponential growth of Omicron over the four-week periods in two most populated South Africa’s provinces, Gauteng and KwaZulu-Natal, arriving at the doubling time estimates of respectively 3.3 days [95% CI: 3.2–3.4 days] and 2.7 days [95% CI: 2.3–3.3 days]. Similar or even shorter doubling times were observed in other locations: Australia (3.0 days), New York State (2.5 days), UK (2.4 days), and Denmark (2.0 days). Log– linear regression suggests that the spread began in Gauteng around October 11, 2021, however, due to presumable stochasticity in the initial spread, this estimate can be inaccurate. Phylogenetics-based analysis indicates that the Omicron strain started to diverge in between October 6 and October 29, 2021. We estimated that the weekly growth of the ratio of Omicron to Delta is in the range 7.2–10.2, considerably higher than the growth of the ratio of Delta to Alpha (estimated to be in in the range 2.5–4.2), and Alpha to pre-existing strains (estimated to be in the range of 1.8–2.7). High relative growth does not necessarily imply higher Omicron infectivity. A two-strain SEIR model suggests that the growth advantage of Omicron may stem from immune evasion, which permits this VOC to infect both the recovered and the fully vaccinated individuals. As we demonstrated within the model, immune evasion is more concerning than increased transmissibility, because it can facilitate larger epidemic outbreaks.

We observed the interference between two prevalent respiratory viruses, respiratory syncytial virus (RSV) and influenza A virus (IAV, H1N1), and characterized its molecular underpinnings in alveolar epithelial cells (A549). We found that RSV induces higher interferon (IFN) {beta} production than IAV and that IFN{beta} priming confers higher protection against infection with IAV than with RSV. Consequently, we focused on the sequential infection scheme: RSV-then-IAV. Using the A549 WT, IFNAR1 KO, IFNLR1 KO, and IFNAR1-IFNLR1 double KO cell lines we found that both IFN{beta} and IFN{lambda} are necessary for maximum protection against subsequent infection. Immunostaining revealed that preinfection with RSV partitions the cell population into a subpopulation susceptible to subsequent infection with IAV and an IAV-proof subpopulation. Strikingly, the susceptible cells turned out to be those already compromised and efficiently expressing RSV, whereas the bystander, interferon-primed cells are resistant to IAV infection. Thus, the virus-virus exclusion at the cell population level is not realized through a direct competition for a shared ecological niche (single cell) but rather achieved with the involvement of specific cytokines induced within the host innate immune response. Author summaryAfter being challenged with a pathogen, infected cells warn bystander cells about the potential threat by synthesizing and secreting cytokines, especially interferons. In this way, the not yet infected but warned cells are given an opportunity to reinforce their defense mechanisms before they encounter the pathogen replicating in the infected cells whose defense mechanisms have been overcome. Consequently, cell population is partitioned into the cells that may be more prone to infection with another pathogen and the cells that may be expected to be resistant to another pathogen. By studying at the single-cell level the sequential infection with two prevalent respiratory viruses, respiratory syncytial virus (RSV) and influenza A virus (IAV), we showed that the interferon-mediated resistance induced by infection with RSV protects non-infected cells from infection with IAV. The cells compromised by RSV turned out however to be susceptible to invasion of IAV. This demonstrates that, even in the absence of within-cell viral competition, the innate immune response can induct viral interference between primary infection with RSV and secondary infection with IAV.

The Variant of Concern (VOC)-202012/01 (also known as B.1.1.7) is a rapidly growing lineage of SARS-CoV-2. In January 2021, VOC-202012/01 constituted about 80% of SARS-CoV-2 genomes sequenced in England and was present in 27 out of 29 countries that reported at least 50 viral genomes. As this strain will likely spread globally towards fixation, it is important to monitor its molecular evolution. Based on GISAID data we systematically estimated growth rates of mutations acquired by the VOC lineage to find that L18F substitution in viral spike protein has initiated a substrain characterized by replicative advantage of 1.70 [95% CI: 1.56–1.96] in relation to the remaining VOC-202012/01 substrains. The L18F mutation is of significance because when recently analyzed in the context of the South African strain 501Y.V2 it has been found to compromise binding of neutralizing antibodies. We additionally indicate three mutations that were acquired by VOC-202012/01 in the receptor binding motif of spike, specifically E484K, F490S, and S494P, that may also give rise to escape mutants. Such mutants may hinder efficiency of existing vaccines and expand in response to the increasing after-infection or vaccine-induced seroprevalence.

Two important signalling pathways of NF-κB and ERK transmit merely 1 bit of information about the level of extracellular stimulation. It is thus unclear how such systems can coordinate complex cell responses to external cues. We analyse information transmission in the MAPK/ERK pathway that converts both constant and pulsatile EGF stimulation into pulses of ERK activity. Based on an experimentally verified computational model, we demonstrate that, when input consists of sequences of EGF pulses, transmitted information increases nearly linearly with time. Thus, pulse-interval transcoding allows more information to be relayed than the amplitude–amplitude transcoding considered previously for the ERK and NF-κB pathways. Moreover, the information channel capacity C, or simply bitrate, is not limited by the bandwidth B = 1/ τ , where τ ≈ 1 h is the relaxation time. Specifically, when the input is provided in the form of sequences of short binary EGF pulses separated by intervals that are multiples of τ / n (but not shorter than τ ), then for n = 2, C ≈ 1.39 bit h −1 ; and for n = 4, C ≈ 1.86 bit h −1 . The capability to respond to random sequences of EGF pulses enables cells to propagate spontaneous ERK activity waves across tissue.

Two important signaling pathways of NF-κB and ERK transmit merely one bit of information about the level of extracellular stimulation. It is thus unclear how such systems can coordinate complex cell responses to external cues. Here, we analyze information transmission in the MAPK/ERK pathway that features relaxation oscillations and responds to EGF by pulses of activated ERK. Based on an experimentally verified computational model of the MAPK/ERK pathway, we demonstrate that when input sequences of EGF pulses are transcoded to output sequences of ERK activity pulses, transmitted information increases nearly linearly with time. Moreover, the information channel capacity C (defined as the upper limit of information that can be transmitted over a sufficiently long time t, divided by t), is not limited by the bandwidth B = 1/τ, where τ ≈ 1 hour is the relaxation time. Specifically, when input is provided in the form of sequences of short binary EGF pulses separated by varying intervals that are multiples of τ/n (but are not shorter than τ), then for n = 2, C ≈ 1.39 bit/hour; and for n = 4, C ≈ 1.86 bit/hour. We hypothesize that the primary mode of operation of the MAPK pathway is to translate extracellular growth factor “bursts” into precisely timed intracellular ERK “spikes” of a predefined amplitude. Such pulse-interval transcoding allows to relay more information than the amplitude–amplitude transcoding considered previously for the ERK and NF-κB pathways.Author summaryTo coordinate their actions, cells communicate with each other by sending, receiving, and interpreting cytokine signals. Cells recognize chemical identity of signaling molecules and process quantitative and temporal properties of stimulation: amplitude, duration, or frequency. Previous studies indicated that the MAPK pathway transmits about one bit of information about the amplitude (concentration) of a stimulating cytokine, EGF. Sending more information may be enabled by temporal signal modulation. Here, we use the conceptual framework of information theory to support a hypothesis that the MAPK pathway, analyzed as a noisy information channel, reaches maximum information transmission rate when receiving sequences of EGF pulses that are transcoded to sequences of activity pulses of an effector kinase of the pathway, ERK. Since the pathway resetting time is about 1 hour, one could expect that—when sending EGF pulses of “0” or “1” amplitude every hour—the pathway is able transmit up to 1 bit per hour. We show, however, that when EGF pulses are separated by intervals that are not shorter than 1 hour and are multiples of 15 min (60, 75, 90 min, etc.), information rate can be nearly 2 bits per hour. We hypothesize that high information rate is necessary to control cell proliferation and motility.

In bistable reaction-diffusion systems, transitions between stable states typically occur on timescales orders of magnitude longer than the chemical equilibration time. Estimation of transition rates within explicit Brownian dynamics simulations is computationally prohibitively costly. We present a method that exploits a single trajectory, generated by a prior simulation of diffusive motions of molecules, to sample chemical kinetic processes on timescales several orders of magnitude longer than the duration of the diffusive trajectory. In this approach, we "loop" the diffusive trajectory by transferring chemical states of the molecules from the last to the first time step of the trajectory. Trajectory looping can be applied to enhance sampling of rare events in biochemical systems in which the number of reacting molecules is constant, as in cellular signal transduction pathways. As an example, we consider a bistable system of autophosphorylating kinases, for which we calculate state-to-state transition rates and traveling wave velocities. We provide an open-source implementation of the method.

The NF-κB pathway is known to transmit merely 1 bit of information about stimulus level. We combined experimentation with mathematical modeling to elucidate how information about TNF concentration is turned into a binary decision. Using Kolmogorov-Smirnov distance, we quantified the cell’s ability to discern 8 TNF concentrations at each step of the NF-κB pathway, to find that input discernibility decreases as signal propagates along the pathway. Discernibility of low TNF concentrations is restricted by noise at the TNF receptor level, whereas discernibility of high TNF concentrations it is restricted by saturation/depletion of downstream signaling components. Consequently, signal discernibility is highest between 0.03 and 1 ng/ml TNF. Simultaneous exposure to TNF or LPS and a translation inhibitor, cycloheximide, leads to prolonged NF-κB activation and a marked increase of transcript levels of NF-κB inhibitors, IκBα and A20. The impact of cycloheximide becomes apparent after the first peak of nuclear NF-κB translocation, meaning that the NF-κB network not only relays 1 bit of information to coordinate the all-or-nothing expression of early genes, but also over a longer time course integrates information about other stimuli. The NF-κB system should be thus perceived as a feedback-controlled decision-making module rather than a simple information transmission channel.

Downstream of growth factor receptors and of the guanine triphosphatase (GTPase) RAS, heterodimers of the serine/threonine kinases BRAF and RAF1 are critical upstream kinases and activators of the mitogen-activated protein kinase (MAPK) module containing the mitogen-activated and extracellular signal-regulated kinase kinase (MEK) and their targets, the extracellular signal-regulated kinase (ERK) family. Either direct or scaffold protein-mediated interactions among the components of the ERK module (the MAPKKKs BRAF and RAF1, MEK, and ERK) facilitate signal transmission. RAF1 also has essential functions in the control of tumorigenesis and migration that are mediated through its interaction with the kinase ROKα, an effector of the GTPase RHO and regulator of cytoskeletal rearrangements. We combined mutational and kinetic analysis with mathematical modeling to show that the interaction of RAF1 with ROKα is coordinated with the role of RAF1 in the ERK pathway. We found that the phosphorylated form of RAF1 that interacted with and inhibited ROKα was generated during the interaction of RAF1 with the ERK module. This mechanism adds plasticity to the ERK pathway, enabling signal diversification at the level of both ERK and RAF. Furthermore, by connecting ERK activation with the regulation of ROKα and cytoskeletal rearrangements by RAF1, this mechanism has the potential to precisely coordinate the proper timing of proliferation with changes in cell shape, adhesion, or motility.

Summary Rule-based modeling is a powerful approach for studying biomolecular site dynamics. Here, we present SPATKIN, a general-purpose simulator for rule-based modeling in two spatial dimensions. The simulation algorithm is a lattice-based method that tracks Brownian motion of individual molecules and the stochastic firing of rule-defined reaction events. Because rules are used as event generators, the algorithm is network-free, meaning that it does not require to generate the complete reaction network implied by rules prior to simulation. In a simulation, each molecule (or complex of molecules) is taken to occupy a single lattice site that cannot be shared with another molecule (or complex). SPATKIN is capable of simulating a wide array of membrane-associated processes, including adsorption, desorption and crowding. Models are specified using an extension of the BioNetGen language, which allows to account for spatial features of the simulated process. Availability and implementation The C ++ source code for SPATKIN is distributed freely under the terms of the GNU GPLv3 license. The source code can be compiled for execution on popular platforms (Windows, Mac and Linux). An installer for 64-bit Windows and a macOS app are available. The source code and precompiled binaries are available at the SPATKIN Web site (http://pmbm.ippt.pan.pl/software/spatkin). Supplementary information Supplementary data are available at Bioinformatics online.

We formulated a computational model for a MAPK signaling cascade downstream of the EGF receptor to investigate how interlinked positive and negative feedback loops process EGF signals into ERK pulses of constant amplitude but dose-dependent duration and frequency. A positive feedback loop involving RAS and SOS, which leads to bistability and allows for switch-like responses to inputs, is nested within a negative feedback loop that encompasses RAS and RAF, MEK, and ERK that inhibits SOS via phosphorylation. This negative feedback, operating on a longer time scale, changes switch-like behavior into oscillations having a period of 1 hour or longer. Two auxiliary negative feedback loops, from ERK to MEK and RAF, placed downstream of the positive feedback, shape the temporal ERK activity profile but are dispensable for oscillations. Thus, the positive feedback introduces a hierarchy among negative feedback loops, such that the effect of a negative feedback depends on its position with respect to the positive feedback loop. Furthermore, a combination of the fast positive feedback involving slow-diffusing membrane components with slower negative feedbacks involving faster diffusing cytoplasmic components leads to local excitation/global inhibition dynamics, which allows the MAPK cascade to transmit paracrine EGF signals into spatially non-uniform ERK activity pulses.

Background Importins and exportins influence gene expression by enabling nucleocytoplasmic shuttling of transcription factors. A key transcription factor of innate immunity, NF-κB, is sequestered in the cytoplasm by its inhibitor, IκBα, which masks nuclear localization sequence of NF-κB. In response to TNFα or LPS, IκBα is degraded, which allows importins to bind NF-κB and shepherd it across nuclear pores. NF-κB nuclear activity is terminated when newly synthesized IκBα enters the nucleus, binds NF-κB and exportin which directs the complex to the cytoplasm. Although importins/exportins are known to regulate spatiotemporal kinetics of NF-κB and other transcription factors governing innate immunity, the mechanistic details of these interactions have not been elucidated and mathematically modelled. Results Based on our quantitative experimental data, we pursue NF-κB system modelling by explicitly including NF-κB–importin and IκBα–exportin binding to show that the competition between importins and IκBα enables NF-κB nuclear translocation despite high levels of IκBα. These interactions reduce the effective relaxation time and allow the NF-κB regulatory pathway to respond to recurrent TNFα pulses of 45-min period, which is about twice shorter than the characteristic period of NF-κB oscillations. By stochastic simulations of model dynamics we demonstrate that randomly appearing, short TNFα pulses can be converted to essentially digital pulses of NF-κB activity, provided that intervals between input pulses are not shorter than 1 h. Conclusions By including interactions involving importin-α and exportin we bring the modelling of spatiotemporal kinetics of transcription factors to a more mechanistic level. Basing on the analysis of the pursued model we estimated the information transmission rate of the NF-κB pathway as 1 bit per hour. Reviewers This article was reviewed by Marek Kimmel, James Faeder and William Hlavacek. Electronic supplementary material The online version of this article (doi:10.1186/s13062-016-0164-z) contains supplementary material.

The innate immune system processes pathogen-induced signals into cell fate decisions. How information is turned to decision remains unknown. By combining stochastic mathematical modelling and experimentation, we demonstrate that feedback interactions between the IRF3, NF-κB and STAT pathways lead to switch-like responses to a viral analogue, poly(I:C), in contrast to pulse-like responses to bacterial LPS. Poly(I:C) activates both IRF3 and NF-κB, a requirement for induction of IFNβ expression. Autocrine IFNβ initiates a JAK/STAT-mediated positive-feedback stabilising nuclear IRF3 and NF-κB in first responder cells. Paracrine IFNβ, in turn, sensitises second responder cells through a JAK/STAT-mediated positive feedforward pathway that upregulates the positive-feedback components: RIG-I, PKR and OAS1A. In these sensitised cells, the ‘live-or-die’ decision phase following poly(I:C) exposure is shorter—they rapidly produce antiviral responses and commit to apoptosis. The interlinked positive feedback and feedforward signalling is key for coordinating cell fate decisions in cellular populations restricting pathogen spread., Innate immunity combines intra- and intercellular signalling to develop responses that limit pathogen spread. Here the authors analyse feedback and feedforward loops connecting IRF3, NF-κB and STAT pathways, and suggest they allow coordinating cell fate decisions in cellular populations in response to the virus-mimicking agent poly(I:C).

f ),Zdzislaw Wisniowski a ),Kinga Salapa a a ) 1 ) a The three-dimensional structures of a set ofnever born proteins� (NBP, random amino acid sequence proteins with no significant homology with known proteins) were predicted using two methods: Rosetta and the one based on thefuzzy-oil-drop� (FOD) model. More than 3000 different random amino acid sequences have been generated, filtered against the non redundant protein sequence data base, to remove sequences with significant homology with known proteins, and subjected to three- dimensional structure prediction. Comparison between Rosetta and FOD predictions allowed to select the ten top (highest structural similarity) and the ten bottom (the lowest structural similarity) structures from the ranking list organized according to the RMS-D value. The selected structures were taken for detailed analysis to define the scale of structural accordance and discrepancy between the two methods. The structural similarity measurements revealed discrepancies between structures generated on the basis of the two methods. Their potential biological function appeared to be quite different as well. The ten bottom structures appeared to beunfoldablefor the FOD model. Some aspects of the general characteristics of the NBPs are also discussed. The calculations were performed on the EUChinaGRID grid platform to test the performance of this infrastructure for massive protein structure predictions. Introduction. - The search for techniques aimed at the generation of new proteins for pharmacological and biotechnological applications is widely developed nowadays (1 - 3). This involves the selection of proteins of desirable activity among those present in Nature, as well as the production of new polypeptide compounds resulting from libraries of peptides with random amino acid sequences (4) (5). The final aim of these

We investigate the kinetics of the ubiquitous phosphorylation-dephosphorylation cycle on biological membranes by means of kinetic Monte Carlo simulations on the triangular lattice. We establish the dependence of effective macroscopic reaction rate coefficients as well as the steady-state phosphorylated substrate fraction on the diffusion coefficient and concentrations of opposing enzymes: kinases and phosphatases. In the limits of zero and infinite diffusion, the numerical results agree with analytical predictions; these two limits give the lower and the upper bound for the macroscopic rate coefficients, respectively. In the zero-diffusion limit, which is important in the analysis of dense systems, phosphorylation and dephosphorylation reactions can convert only these substrates which remain in contact with opposing enzymes. In the most studied regime of nonzero but small diffusion, a contribution linearly proportional to the diffusion coefficient appears in the reaction rate. In this regime, the presence of opposing enzymes creates inhomogeneities in the (de)phosphorylated substrate distributions: The spatial correlation function shows that enzymes are surrounded by clouds of converted substrates. This effect becomes important at low enzyme concentrations, substantially lowering effective reaction rates. Effective reaction rates decrease with decreasing diffusion and this dependence is more pronounced for the less-abundant enzyme. Consequently, the steady-state fraction of phosphorylated substrates can increase or decrease with diffusion, depending on relative concentrations of both enzymes. Additionally, steady states are controlled by molecular crowders which, mostly by lowering the effective diffusion of reactants, favor the more abundant enzyme.

Accumulating data indicate that cancer stem cells contribute to tumor chemoresistance and their persistence alters clinical outcome. Our previous study has shown that ovarian cancer may be initiated by ovarian cancer initiating cells (OCIC) characterized by surface antigen CD44 and c-KIT (CD117). It has been experimentally demonstrated that a microRNA, namely miR-193a, targets c-KIT mRNA for degradation and could play a crucial role in ovarian cancer development. How miR-193a is regulated is poorly understood and the emerging picture is complex. To unravel this complexity, we propose a mathematical model to explore how estrogen-mediated up-regulation of another target of miR-193a, namely E2F6, can attenuate the function of miR-193a in two ways, one through a competition of E2F6 and c-KIT transcripts for miR-193a, and second by binding of E2F6 protein, in association with a polycomb complex, to the promoter of miR-193a to down-regulate its transcription. Our model predicts that this bimodal control increases the expression of c-KIT and that the second mode of epigenetic regulation is required to generate a switching behavior in c-KIT and E2F6 expressions. Additional analysis of the TCGA ovarian cancer dataset demonstrates that ovarian cancer patients with low expression of EZH2, a polycomb-group family protein, show positive correlation between E2F6 and c-KIT. We conjecture that a simultaneous EZH2 inhibition and anti-estrogen therapy can constitute an effective combined therapeutic strategy against ovarian cancer.

NF-κB is a key transcription factor that regulates innate immune response. Its activity is tightly controlled by numerous feedback loops, including two negative loops mediated by NF-κB inducible inhibitors, IκBα and A20, which assure oscillatory responses, and by positive feedback loops arising due to the paracrine and autocrine regulation via TNFα, IL-1 and other cytokines. We study the NF-κB system of interlinked negative and positive feedback loops, combining bifurcation analysis of the deterministic approximation with stochastic numerical modeling. Positive feedback assures the existence of limit cycle oscillations in unstimulated wild-type cells and introduces bistability in A20-deficient cells. We demonstrated that cells of significant autocrine potential, i.e., cells characterized by high secretion of TNFα and its receptor TNFR1, may exhibit sustained cytoplasmic-nuclear NF-κB oscillations which start spontaneously due to stochastic fluctuations. In A20-deficient cells even a small TNFα expression rate qualitatively influences system kinetics, leading to long-lasting NF-κB activation in response to a short-pulsed TNFα stimulation. As a consequence, cells with impaired A20 expression or increased TNFα secretion rate are expected to have elevated NF-κB activity even in the absence of stimulation. This may lead to chronic inflammation and promote cancer due to the persistent activation of antiapoptotic genes induced by NF-κB. There is growing evidence that A20 mutations correlate with several types of lymphomas and elevated TNFα secretion is characteristic of many cancers. Interestingly, A20 loss or dysfunction also leaves the organism vulnerable to septic shock and massive apoptosis triggered by the uncontrolled TNFα secretion, which at high levels overcomes the antiapoptotic action of NF-κB. It is thus tempting to speculate that some cancers of deregulated NF-κB signaling may be prone to the pathogen-induced apoptosis.

Ovarian cancer is one of the most lethal cancers in the female reproductive system. Our previous study has shown that ovarian cancer may be initiated by ovarian cancer initiating cells (OCIC) characterized by the surface antigen CD44 and c-KIT (CD117). Previous study also suggested that long term treatment of estrogen such as hormonal replacement therapy (HRT) may increase the risk of ovarian cancer, however the role of estrogen in ovarian carcinogenesis is still controversial. To unravel this complexity, we propose a mathematical model to explore how the ER signaling pathway contribute to c-KIT expression during ovarian carcinogenesis: one through a ceRNA competition of an ER target,E2F6 and c-KIT for their targeted miRNA, miR-193a; second by binding of E2F6 protein, in association with the polycomb complex, to the promoter of miR-193a to downregulate miR-193a transcription by epigenetic modifications. Our model found that epigenetic silencing of miR-193a generates a bistable switching of c-KIT during ovarian carcinogenesis based on the level of EZH2. To confirm our results, we performed ectopic expression of miR-193a and 3’UTR luciferase in ovarian cancer cell lines and confirmed that E2F6 and c-KIT are the targets of miR-193a. Importantly, treatment of E2 or bisphenol A (BPA) resulted in the up-regulation of E2F6 and c-kit mRNA in IOSE cells in which no or low methylation at the promoter CpG island of miR-193a was found. On the contrary, promoter hypermethylation of miR193a could be observed in miR-193a-underexpressed CP70 ovarian cancer cells but not in HeyC2 cells which showed similar expression level of miR-193a as in IOSE cells. Treatment of demethylating agent (5azaDC) or EZH2 inhibitor (GSK343) resulted in a reexpression of miR-193a in CP70 ovarian cancer cells. Overexpression of miR-193a inhibited tumor growth in vitro and in an animal model. Further ChIP-PCR assay also found that open chromatin mark H3K4me3 was enriched in the promoter region of miR-193a in HeyC2 but not in CP70 cells. On the contrary, repressive chromatin marks H3K9me3 and H3K27me3 were only enriched in CP70 cells. Clinically, ovarian cancer patients (n = 109) with higher promoter methylation of miR-193a were associated with poor survival (p>0.05). Additional analysis of the TCGA ovarian cancer dataset demonstrated that ovarian cancer patients with low expression of EZH2, a polycomb-group protein, showed positive correlation (p Citation Format: Frank Hsueh-Che Cheng, Baltazar D. Aguda, Hon-Yi Lin, Je-Chiang Tsai, Marek Kochanczyk, Ru-Inn Lin, Jora M. J. Lin, Gary C. W. Chen, Cheng-Chang Chang, Hung-Cheng Lai, Kenneth P. Nephew, Tzy-Wei Hwang, Michael W. Y. Chan. Bistable switching of c-KIT by estrogen-mediated ceRNA and epigenetic silencing of miR-193a predicts survival in ovarian cancer. [abstract]. In: Proceedings of the 107th Annual Meeting of the American Association for Cancer Research; 2016 Apr 16-20; New Orleans, LA. Philadelphia (PA): AACR; Cancer Res 2016;76(14 Suppl):Abstract nr 950.

The p53 transcription factor is a regulator of key cellular processes including DNA repair, cell cycle arrest, and apoptosis. In this theoretical study, we investigate how the complex circuitry of the p53 network allows for stochastic yet unambiguous cell fate decision-making. The proposed Markov chain model consists of the regulatory core and two subordinated bistable modules responsible for cell cycle arrest and apoptosis. The regulatory core is controlled by two negative feedback loops (regulated by Mdm2 and Wip1) responsible for oscillations, and two antagonistic positive feedback loops (regulated by phosphatases Wip1 and PTEN) responsible for bistability. By means of bifurcation analysis of the deterministic approximation we capture the recurrent solutions (i.e., steady states and limit cycles) that delineate temporal responses of the stochastic system. Direct switching from the limit-cycle oscillations to the “apoptotic” steady state is enabled by the existence of a subcritical Neimark—Sacker bifurcation in which the limit cycle loses its stability by merging with an unstable invariant torus. Our analysis provides an explanation why cancer cell lines known to have vastly diverse expression levels of Wip1 and PTEN exhibit a broad spectrum of responses to DNA damage: from a fast transition to a high level of p53 killer (a p53 phosphoform which promotes commitment to apoptosis) in cells characterized by high PTEN and low Wip1 levels to long-lasting p53 level oscillations in cells having PTEN promoter methylated (as in, e.g., MCF-7 cell line)., Author Summary Cancers are diseases of signaling networks. Transcription factor p53 is a pivotal node of a network that integrates a variety of stress signals and governs critical processes of DNA repair, cell cycle arrest, and apoptosis. Somewhat paradoxically, despite the fact that carcinogenesis is prevalently caused by p53 network malfunction, most of our knowledge about p53 signaling is based on cancer or immortalized cell lines. In this paper, we construct a mathematical model of intact p53 network to understand dynamics of non-cancerous cells and then dynamics of cancerous cells by introducing perturbations to the regulatory system. Cell fate decisions are enabled by the presence of interlinked feedback loops which give rise to a rich repertoire of behaviors. We explain and analyze by means of numerical simulations how the dynamical structure of the regulatory system allows for generating unambiguous single-cell fate decisions, also in the case when the cell population splits into an apoptotic and a surviving subpopulation. Perturbation analysis provides an explanation why cancer cell lines known to have vastly diverse expression levels of p53 regulators can exhibit a broad spectrum of responses to DNA damage.

A description of many biological processes requires knowledge of the 3-D structure of proteins and, in particular, the defined active site responsible for biological function. Many proteins, the genes of which have been identified as the result of human genome sequencing, and which were synthesized experimentally, await identification of their biological activity. Currently used methods do not always yield satisfactory results, and new algorithms need to be developed to recognize the localization of active sites in proteins. This paper describes a computational model that can be used to identify potential areas that are able to interact with other molecules (ligands, substrates, inhibitors, etc.). The model for active site recognition is based on the analysis of hydrophobicity distribution in protein molecules. It is shown, based on the analyses of proteins with known biological activity and of proteins of unknown function, that the region of significantly irregular hydrophobicity distribution in proteins appears to be function related., Author Summary We present here a method of defining functional site recognition in proteins. The active site (enzymatic cavity or ligand-binding site) is localized on the basis of hydrophobicity deficiency, which is understood as the difference between empirical (dependent on amino acid positions) and idealized (3-D Gauss function, or Fuzzy Oil Drop model) distribution of hydrophobicity. It is assumed that the localization of amino acids representing a high difference of hydrophobic density reveals the functional site. The analysis of the structure of 33 proteins of known biological activity and of 33 proteins of unknown function (with comparable polypeptide chain lengths) seems to verify the applicability of the method to binding cavity localization. The comparative analysis with other methods oriented on biological function is also presented. The validation of predictability accuracy is shown with respect to the enzyme classes.

Biological signals in cells are transmitted with the use of reaction cycles, such as the phosphorylation-dephosphorylation cycle, in which substrate is modified by antagonistic enzymes. An appreciable share of such reactions takes place in crowded environments of two-dimensional structures, such as plasma membrane or intracellular membranes, and is expected to be diffusion-controlled. In this work, starting from the microscopic bimolecular reaction rate constants and using estimates of the mean first-passage time for an enzyme-substrate encounter, we derive diffusion-dependent effective macroscopic reaction rate coefficients (EMRRC) for a generic reaction cycle. Each EMRRC was found to be half of the harmonic average of the microscopic rate constant (phosphorylation c or dephosphorylation d), and the effective (crowding-dependent) motility divided by a slowly decreasing logarithmic function of the sum of the enzyme concentrations. This implies that when c and d differ, the two EMRRCs scale differently with the motility, rendering the steady-state fraction of phosphorylated substrate molecules diffusion-dependent. Analytical predictions are verified using kinetic Monte Carlo simulations on the two-dimensional triangular lattice at the single-molecule resolution. It is demonstrated that the proposed formulas estimate the steady-state concentrations and effective reaction rates for different sets of microscopic reaction rates and concentrations of reactants, including a non-trivial example where with increasing diffusivity the fraction of phosphorylated substrate molecules changes from 10% to 90%.

Knowledge-based models for protein folding assume that the early-stage structural form of a polypeptide is determined by the backbone conformation, followed by hydrophobic collapse. Side chain–side chain interactions, mostly of hydrophobic character, lead to the formation of the hydrophobic core, which seems to stabilize the structure of the protein in its natural environment. The fuzzy-oil-drop model is employed to represent the idealized hydrophobicity distribution in the protein molecule. Comparing it with the one empirically observed in the protein molecule reveals that they are not in agreement. It is shown in this study that the irregularity of hydrophobic distributions is aim-oriented. The character and strength of these irregularities in the organization of the hydrophobic core point to the specificity of a particular protein’s structure/function. When the location of these irregularities is determined versus the idealized fuzzy-oil-drop, function-related areas in the protein molecule can be identified. The presented model can also be used to identify ways in which protein–protein complexes can possibly be created. Active sites can be predicted for any protein structure according to the presented model with the free prediction server at http://www.bioinformatics.cm-uj.krakow.pl/activesite . The implication based on the model presented in this work suggests the necessity of active presence of ligand during the protein folding process simulation.

Transitions between steady states of a multi-stable stochastic system in the perfectly mixed chemical reactor are possible only because of stochastic switching. In realistic cellular conditions, where diffusion is limited, transitions between steady states can also follow from the propagation of travelling waves. Here, we study the interplay between the two modes of transition for a prototype bistable system of kinase–phosphatase interactions on the plasma membrane. Within microscopic kinetic Monte Carlo simulations on the hexagonal lattice, we observed that for finite diffusion the behaviour of the spatially extended system differs qualitatively from the behaviour of the same system in the well-mixed regime. Even when a small isolated subcompartment remains mostly inactive, the chemical travelling wave may propagate, leading to the activation of a larger compartment. The activating wave can be induced after a small subdomain is activated as a result of a stochastic fluctuation. Such a spontaneous onset of activity is radically more probable in subdomains characterized by slower diffusion. Our results show that a local immobilization of substrates can lead to the global activation of membrane proteins by the mechanism that involves stochastic fluctuations followed by the propagation of a semi-deterministic travelling wave.

Background Apoptosis is a tightly regulated process: cellular survive-or-die decisions cannot be accidental and must be unambiguous. Since the suicide program may be initiated in response to numerous stress stimuli, signals transmitted through a number of checkpoints have to be eventually integrated. Results In order to analyze possible mechanisms of the integration of multiple pro-apoptotic signals, we constructed a simple model of the Bcl-2 family regulatory module. The module collects upstream signals and processes them into life-or-death decisions by employing interactions between proteins from three subgroups of the Bcl-2 family: pro-apoptotic multidomain effectors, pro-survival multidomain restrainers, and pro-apoptotic single domain BH3-only proteins. Although the model is based on ordinary differential equations (ODEs), it demonstrates that the Bcl-2 family module behaves akin to a Boolean logic gate of the type dependent on levels of BH3-only proteins (represented by Bad) and restrainers (represented by Bcl-xL). A low level of pro-apoptotic Bad or a high level of pro-survival Bcl-xL implies gate AND, which allows for the initiation of apoptosis only when two stress stimuli are simultaneously present: the rise of the p53 killer level and dephosphorylation of kinase Akt. In turn, a high level of Bad or a low level of Bcl-xL implies gate OR, for which any of these stimuli suffices for apoptosis. Conclusions Our study sheds light on possible signal integration mechanisms in cells, and spans a bridge between modeling approaches based on ODEs and on Boolean logic. In the proposed scheme, logic gates switching results from the change of relative abundances of interacting proteins in response to signals and involves system bistability. Consequently, the regulatory system may process two analogous inputs into a digital survive-or-die decision.

Living cells may be considered as biochemical reactors of multiple steady states. Transitions between these states are enabled by noise, or, in spatially extended systems, may occur due to the traveling wave propagation. We analyze a one-dimensional bistable stochastic birth-death process by means of potential and temperature fields. The potential is defined by the deterministic limit of the process, while the temperature field is governed by noise. The stable steady state in which the potential has its global minimum defines the global deterministic attractor. For the stochastic system, in the low noise limit, the stationary probability distribution becomes unimodal, concentrated in one of two stable steady states, defined in this study as the global stochastic attractor. Interestingly, these two attractors may be located in different steady states. This observation suggests that the asymptotic behavior of spatially extended stochastic systems depends on the substrate diffusivity and size of the reactor. We confirmed this hypothesis within kinetic Monte Carlo simulations of a bistable reaction- diffusion model on the hexagonal lattice. In particular, we found that although the kinase-phosphatase system remains inactive in a small domain, the activatory traveling wave may propagate when a larger domain is considered.

Background Well-performing automated protein function recognition approaches usually comprise several complementary techniques. Beside constructing better consensus, their predictive power can be improved by either adding or refining independent modules that explore orthogonal features of proteins. In this work, we demonstrated how the exploration of global atomic distributions can be used to indicate functionally important residues. Results Using a set of carefully selected globular proteins, we parametrized continuous probability density functions describing preferred central distances of individual protein atoms. Relative preferred burials were estimated using mixture models of radial density functions dependent on the amino acid composition of a protein under consideration. The unexpectedness of extraordinary locations of atoms was evaluated in the information-theoretic manner and used directly for the identification of key amino acids. In the validation study, we tested capabilities of a tool built upon our approach, called SurpResi, by searching for binding sites interacting with ligands. The tool indicated multiple candidate sites achieving success rates comparable to several geometric methods. We also showed that the unexpectedness is a property of regions involved in protein-protein interactions, and thus can be used for the ranking of protein docking predictions. The computational approach implemented in this work is freely available via a Web interface at http://www.bioinformatics.org/surpresi. Conclusions Probabilistic analysis of atomic central distances in globular proteins is capable of capturing distinct orientational preferences of amino acids as resulting from different sizes, charges and hydrophobic characters of their side chains. When idealized spatial preferences can be inferred from the sole amino acid composition of a protein, residues located in hydrophobically unfavorable environments can be easily detected. Such residues turn out to be often directly involved in binding ligands or interfacing with other proteins.