Molecular property prediction is a crucial task that guides the design of new compounds, including drugs and materials. While explainable artificial intelligence methods aim to scrutinize model predictions by identifying influential molecular substructures, many existing approaches rely on masking strategies that remove either atoms or atom-level features to assess importance via fidelity metrics. These methods, however, often fail to adhere to the underlying molecular distribution and thus yield unintuitive explanations. In this work, we propose counterfactual masking, a novel framework that replaces masked substructures with chemically reasonable fragments sampled from generative models trained to complete molecular graphs. Rather than evaluating masked predictions against implausible zeroed-out baselines, we assess them relative to counterfactual molecules drawn from the data distribution. Our method offers two key benefits: (1) molecular realism that underpins robust and distribution-consistent explanations, and (2) meaningful counterfactuals that directly indicate how structural modifications may affect predicted properties. We demonstrate that counterfactual masking is well-suited for benchmarking model explainers and yields more actionable insights across multiple datasets and property prediction tasks. Our approach bridges the gap between explainability and molecular design, offering a principled and generative path toward explainable machine learning in chemistry.

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.

Living cells utilize signaling pathways to sense, transduce, and process information. As the extracellular stimulation often has rich temporal characteristics which may govern dynamic cellular responses, it is important to quantify the rate of information flow through the signaling pathways. In this study, we used an epithelial cell line expressing a light-activatable FGF receptor and an ERK activity reporter to assess the ability of the MAPK/ERK pathway to transduce signal encoded in a sequence of pulses. By stimulating the cells with random light pulse trains, we demonstrated that the MAPK/ERK channel capacity is at least 6 bits per hour. The input reconstruction algorithm detects the light pulses with 1-min accuracy 5 min after their occurrence. The high information transmission rate may enable the pathway to coordinate multiple processes including cell movement and respond to rapidly varying stimuli such as chemoattracting gradients created by other cells.

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). CONTACT: [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

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).

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.