## 1 Introduction
In line with the preceding discussion, it is clear that deterministic, purely stochastic, and fuzzy stochastic paradigms represent three principal possibilities for modeling in systems biology. The choice of modeling paradigm should be based on the model's scope and specific characteristics. In deterministic models, the outcome remains constant regardless of how many times the model is run, making them straightforward to analyze since they only need to be executed once. However, stochastic models yield different results with  
Figure 1: Illustration of how spatial scale and density analysis of biological systems influence the choice of modeling methods. each run, requiring thousands or even tens of thousands of replications to obtain reliable averages. This complexity makes stochastic models more challenging to analyze compared to deterministic ones. The fuzzy stochastic approach adds another layer of complexity by conducting stochastic simulations for each fuzzy number, making the analysis even more difficult. This study proposes a methodology to identify the optimal modeling paradigm by combining insights from the analysis of differences between simulations across three paradigms with the scale density analysis of biological systems. If the data sets from two or all three paradigms are sufficiently similar, the simplest paradigm should be preferred. Otherwise, the most appropriate approach is recommended for each biological system. Figure 2 schematically illustrates how the similarities and discrepancies between the results of deterministic, purely stochastic, and fuzzy stochastic simulations affect the selection of a modeling paradigm. The authors are unaware of any other work that addresses this methodological issue in the given context, although there are studies that compare various aspects of deterministic, stochastic, and fuzzy methods [8; 9]. In [10], we demonstrated how to select a relevant modeling framework for the p16-mediated pathway. The p16-mediated signaling pathway is a microscopic biological system, which is known to exhibit sparsity and inherent uncertainty. As a result, the p16-mediated pathway is most effectively studied using a fuzzy stochastic approach. In general, it can be stated that almost half of the scientific papers focused on modeling biological systems focus on metabolic networks, signal transduction pathways, and gene regulatory networks. About half of these studies employ a deterministic modeling approach. Each of these networks or pathways, being at the microscopic level, is characterized by high sparsity, making stochastic or fuzzy stochastic methods more suitable for their modeling. This is the primary issue highlighted as a problem in the present work. The applicability of this methodology is demonstrated for the synthesis of spinal motor neuron (SMN) protein from spinal motor neuron 2 gene (_SMN_2) [11]. We used descriptive statistics tests to measure the similarity among data sets: the Shapiro-Wilk test to assess normality, the Friedman test to compare all three data sets, and the Dunn-Bonferroni test to pairwise compare the data sets. For the synthesis of SMN, the Shapiro-Wilk test indicated  
Figure 2: An illustration of how the similarities and differences between results from deterministic, purely stochastic, and fuzzy stochastic simulations affect the selection of a modeling paradigm. a non-normal distribution of the data sets, while the Friedman and the Dunn-Bonferroni tests revealed significant differences between the data sets. Due to the fact that the SMN synthesis network operates at the cellular scale, the fuzzy stochastic approach is concluded to provide the most relevant results. The remainder of the paper is structured as follows: In the next section, we outline the research method, material, and background behind the present work. More specifically, we outline Petri nets, succinctly describe fuzzy logic, review statistical tests to measure similarities among data sets, and introduce associating biological context.