The study of biological systems is complex and of great importance. There exist numerous approaches to signal transduction processes, including symbolic modeling of cellular adaptation. The use of formal methods for computational biological systems eases the analysis of cellular models and the establishment of the causes and consequences of certain cellular situations associated with diseases. In this paper, we define an application of logic modeling with rewriting logic and soft set theory. Our approach to decision-making with soft sets offers a novel strategy that complements the standard strategies. We implement a metalevel strategy to control and guide the rewriting process of the Maude rewriting engine. In particular, we adopt the mathematical methods to capture imprecision, vagueness, and uncertainty in the available data. Using this new strategy, we propose an extension in the biological symbolic models of pathway logic. Our ultimate aim is to automatically determine the rules that are most appropriate and adjusted to reality in dynamic systems using decision-making with incomplete soft sets.

/pdf/soft-set-theory-for-decision-making-in-computational-biology-4wa5fta9z5.pdf

Soft Set Theory for Decision Making in Computational Biology Under Incomplete Information

In many complex systems that can be modeled using Petri nets time can be a very important factor which should be taken into account during creation and analysis of the model. Time data can describe starting moments of some actions or their duration before their immediate effects start to influence some other areas of the modeled system. Places in a Petri net often describe static components of the system, but they can also describe states. Such a state can have time restrictions, for example, telling how long it can influence other elements in the model. Time values describing some system may be inconsistent or incomplete, which can cause problems during the creation of the model. In this paper, a new extension of time Petri nets is proposed, which allows the creation of models with different types of time data, which previously were possible to be properly used in separate types of well-known time Petri nets. The proposed new time Petri net solves this problem by integrating different aspects of already existing time Petri nets into one unified net. 

pdf/extended-time-petri-nets-3rbz6mmj6u.pdf

Extended time Petri nets

This study presents early experimentation of a modular AI framework for multimodal drug discovery that integrates natural product based therapies with modern pharmaceuticals. The system combines structured biomedical data, knowledge graphs, and largea language models (LLMs) to generate explicit natural language hypotheses. The architecture has four phases: data aggregation, hypothesis generation, dynamic simulation, and in silico evaluation, and supports dual inference routes (compound → gene → disease/phenotype and disease/phenotype → gene → compound). As a case study, Phases 1 and 2 were applied to the Kampo formula Shakuyaku-kanzo-to, a typical example of a multicomponent and multi-target natural therapy. The framework originally arose from challenges in conventional filtering, where important but poorly annotated compounds were often overlooked. However, the focus has since shifted beyond filtering, toward uncovering hidden relationships across fragmented biomedical knowledge. This early implementation demonstrates the potential of natural language hypothesis generation to restructure fragmented knowledge into interpretable insights, providing a blueprint for future multimodal drug discovery. 

Dual Inference Routes for Natural Language Hypothesis Generation in Multimodal Drug Discovery: An Early Experimentation Study

Editorial: Petri nets for cellular process modelling

Retention-free Petri net has been used in modeling of signaling pathways, which is a timed Petri net such that total input and total output token flows are equivalent at any place. Previously we have investigated the dependency of transitions in retention-free Petri net. In this paper, we introduce a modeling method for signaling pathway by using Petri net, giving properties of retention-freeness by considering arc weight. Based on the obtained properties, we propose an algorithm to find shrinkable transitions and to shrink them into a single transition. This algorithm eventually provides a set of transitions whose firing frequencies are dependent. As an example, we apply the algorithm to IL-3 signaling pathway Petri net model to show the usefulness of our proposed algorithm.

/pdf/dependent-shrink-for-petri-net-models-of-signaling-pathways-2qcvu0sl9u.pdf

Dependent shrink for Petri net models of signaling pathways.

Despite the recent rapid progress in high throughput measurements of biological data, it is still difficult to gather all of the reaction speed data in biological pathways. This paper presents a Petri net-based algorithm that can derive estimated values for non-valid reaction speeds in a signaling pathway from biologically-valid data. In fact, these reaction speeds are reflected based on the delay times in the timed Petri net model of the signaling pathway. We introduce the concept of a “dependency relation” over a transition set of a Petri net and derive the properties of the dependency relation through a structural analysis. Based on the theoretical results, the proposed algorithm can efficiently shrink the transitions with two elementary structures into a single transition repeatedly to reduce the Petri net size in order to eventually discover all transition sets with a dependency relation. Finally, to show the usefulness of our algorithm, we apply our algorithm to the IL-3 Petri net model.

Dependent Shrink of Transitions for Calculating Firing Frequencies in Signaling Pathway Petri Net Model

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Dependent shrink for Petri net models of signaling pathways.

Dependent Shrink of Transitions for Calculating Firing Frequencies in Signaling Pathway Petri Net Model