Abstract Motivated by the spatiotemporal waves of MAPK/ERK activity, crucial for long-range communication in regenerating tissues, we investigated stochastic homoclinic fronts propagating through channels formed by directly interacting cells. We evaluated the efficiency of long-range communication in these channels by examining the rate of information transmission. Our study identified the stochastic phenomena that reduce this rate: front propagation failure, new front spawning, and variability in the front velocity. We found that a trade-off between the frequencies of propagation failures and new front spawning determines the optimal channel width (which geometrically determines the front length). The optimal frequency of initiating new waves is determined by a trade-off between the input information rate (higher with more frequent initiation) and the fidelity of information transmission (lower with more frequent initiation). Our analysis provides insight into the relative timescales of intra- and intercellular processes necessary for successful wave propagation. Author Summary In biological tissues, traveling waves of cellular activity are observed in the process of wound healing when they coordinate cell replication and collective migration. These waves can carry information over long distances. However, random effects on the single-cell level can affect wave propagation and disrupt information flow. In this paper, using a numerical model we classified these stochastic events and quantified the maximum range and frequency of such waves and their capacity to carry information. We discovered that most effective transmission occurs in relatively narrow channels (formed by directly interacting cells), and that the refractory time, in which a cell is resistant to activation by neighboring cells, must be long with respect to the time needed for cell activation. The optimal time intervals between the initiated waves are of order of few refractory times (depending on channel length).
Abstract Resolving practical nonidentifiability of computational models typically requires either additional data or non-algorithmic model reduction, which frequently results in models containing parameters lacking direct interpretation. Here, instead of reducing models, we explore an alternative, Bayesian approach, and quantify predictive power of non-identifiable models. Considering an example biochemical signalling cascade model as well as its mechanical analog, we demonstrate that by measuring a single variable in response to a properly chosen stimulation protocol, the dimensionality of the parameter space is reduced, which allows for prediction of its trajectory in response to different stimulation protocols even if all model parameters remain unidentified. Successive measurements of remaining variables further constrain model parameters and enable more predictions. We analyse potential pitfalls of the proposed approach that can arise when the investigated model is oversimplified, incorrect, or when the training protocol is inadequate. The main advantage of the suggested iterative approach is that the predictive power of the model can be assessed and practically utilised at each step.
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 a 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.
Motivated by the spatiotemporal waves of MAPK/ERK activity, crucial for long-range communication in regenerating tissues, we investigated stochastic homoclinic fronts propagating through channels formed by directly interacting cells. We evaluated the efficiency of long-range communication in these channels by examining the rate of information transmission. Our study identified the stochastic phenomena that reduce this rate: front propagation failure, new front spawning, and variability in the front velocity. We found that a trade-off between the frequencies of propagation failures and new front spawning determines the optimal channel width (which geometrically determines the front length). The optimal frequency of initiating new waves is determined by a trade-off between the input information rate (higher with more frequent initiation) and the fidelity of information transmission (lower with more frequent initiation). Our analysis provides insight into the relative timescales of intra- and intercellular processes necessary for successful wave propagation.
Abstract 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 summary To 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.
The novel SARS-CoV-2 Variant of Concern (VOC)-202012/01 (also known as B.1.1.7), first collected in United Kingdom on 20 September 2020, is a rapidly growing lineage that in January 2021 constituted 86% of all SARS-CoV-2 genomes sequenced in England. The VOC has been detected in 40 out of 46 countries that reported at least 50 genomes in January 2021. We have estimated that the replicative advantage of the VOC is in the range 1.83–2.18 [95% CI: 1.71–2.40] with respect to the 20A.EU1 variant that dominated in England in November 2020, and in range 1.65–1.72 [95% CI: 1.46–2.04] in Wales, Scotland, Denmark, and USA. As the VOC strain will likely spread globally towards fixation, it is important to monitor its molecular evolution. We have estimated growth rates of expanding mutations acquired by the VOC lineage to find that the L18F substitution in spike has initiated a fast growing VOC substrain. The L18F substitution is of significance because it has been found to compromise binding of neutralizing antibodies. Of concern are immune escape mutations acquired by the VOC: E484K, F490S, S494P (in the receptor binding motif of spike) and Q677H, Q675H (in the proximity of the polybasic cleavage site at the S1/S2 boundary). These mutants may hinder efficiency of existing vaccines and expand in response to the increasing after-infection or vaccine-induced seroprevalence.
Mutual information is a general statistical dependency measure which has found applications in representation learning, causality, domain generalization and computational biology. However, mutual information estimators are typically evaluated on simple families of probability distributions, namely multivariate normal distribution and selected distributions with one-dimensional random variables. In this paper, we show how to construct a diverse family of distributions with known ground-truth mutual information and propose a language-independent benchmarking platform for mutual information estimators. We discuss the general applicability and limitations of classical and neural estimators in settings involving high dimensions, sparse interactions, long-tailed distributions, and high mutual information. Finally, we provide guidelines for practitioners on how to select appropriate estimator adapted to the difficulty of problem considered and issues one needs to consider when applying an estimator to a new data set.
Abstract 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.
We show that the conformal standard model supplemented with asymptotically safe gravity can be valid up to arbitrarily high energies and give a complete description of particle physics phenomena. We restrict the mass of the second scalar particle to $\ensuremath{\sim}300\text{ }\text{ }\mathrm{GeV}$ and the masses of heavy neutrinos to $\ensuremath{\sim}340\text{ }\text{ }\mathrm{GeV}$. These predictions can be explicitly tested in the nearby future.
