Mathematical Modeling and Data Science for Biology and Medicine, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E3: Mathematical Biology".

Deadline for manuscript submissions: 15 September 2026 | Viewed by 1267

Special Issue Editor


E-Mail Website
Guest Editor
Center for Mathematical Modeling and Data Science, Osaka University, Osaka 560-8531, Japan
Interests: nonlinear partial differential equations; mathematical physics; mathematical biology
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The importance of mathematical modeling and data science is growing for understanding biological events and medical applications. This Special Issue, as a follow up to the previous edition, will attempt to study these still-mysterious matters observed in living things from mathematics and data science, covering topics including mathematical modelling of complex biological systems, optimal control strategies for biological systems, numerical methods for solving differential equations in biology and healthcare models, stochastic and hybrid models in biology and medicine, data-driven modeling of biology and medicine, statistics and data science for biological and biomedical data analysis, etc.

Here is a list of examples of biological questions for which a new mathematical approach is expected. New ideas, concepts, models, analysis, predictions, biological, and medical applications are welcome:

  1. Dynamic mechanism of complex biological systems
  2. Biological reactions caused by several interactions of stimulations, such as high and low temperatures, pH, osmotic pressures, cytokines, hormones, viruses, etc.;
  3. Analysis of the effect of multisensing in multi-scale biological events;
  4. Communications between heterogeneous cells, reactions to organs, and their interactions;
  5. Biological homeostasis through a reaction network and its breakdown;
  6. The role of the microenvironment in the malignancy of cancer cells;
  7. Mathematical modeling of signal transmission and cross-talks of signals inside and outside cells;
  8. Data science methods used to detect biological mechanisms which were not known before, and applications;
  9. New diagnoses and therapies using mathematical methods;
  10. New mathematical concepts motivated by biological and medical events, their analysis, and applications;
  11. How to deal with social data of healthcare and the deceased to construct mathematical models to predict events.
  12. Multi-scale modeling and agent-based simulation of cell–cell interactions.
  13. Mathematical methods for the detection and prediction of gene expression and metabolism.

Prof. Dr. Takashi Suzuki
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematical oncology
  • mathematical immunology
  • mathematical epidemiology
  • population dynamics
  • mathematical methods in diagnosis and therapy
  • systems biology
  • infectious disease modeling
  • epidemiological dynamics
  • human behaviors
  • evolution dynamics
  • signaling pathways
  • cell dynamics
  • biomedical data analysis
  • biological signal analysis
  • regression models
  • data-driven modeling machine learning approaches
  • data science
  • multi-scale modeling

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (2 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

21 pages, 15000 KB  
Article
Hierarchically Coupled Biochemical Switches for Stem Cell Differentiation
by Nikolaos K. Voulgarakis
Mathematics 2026, 14(4), 678; https://doi.org/10.3390/math14040678 - 14 Feb 2026
Viewed by 354
Abstract
In multicellular organisms, the development of diverse cell types relies on stem cell differentiation through a hierarchy of fate decisions. Pluripotent stem cells first give rise to multipotent progenitors, which then undergo successive fate decisions to generate specialized cells within their respective lineages. [...] Read more.
In multicellular organisms, the development of diverse cell types relies on stem cell differentiation through a hierarchy of fate decisions. Pluripotent stem cells first give rise to multipotent progenitors, which then undergo successive fate decisions to generate specialized cells within their respective lineages. Waddington used the metaphor of a marble rolling down a hill through hierarchically branching valleys that represent the various states of cell differentiation, with the final valleys at the bottom symbolizing the specialized cells. Mathematically, specialized cells are seen as stable attractors in a complex dynamical system that displays multistability. However, this framework does not necessarily describe the hierarchical branching of stem cell differentiation. In a recent study, we addressed this issue by assuming that each gene regulatory network (GRN) consists of hierarchically coupled gene subnetworks (modules) that are self-regulated due to epigenetic factors. Each module was modeled using the normal form of relevant bifurcations. Overall, this approach captures both multistability and hierarchical branching in differentiation. Here, the normal forms of bifurcations are replaced by realistic biochemical switches. Theoretical analysis and numerical simulations demonstrated that hierarchically coupled biochemical switches can depict the three fundamental aspects of Waddington’s epigenetic landscape: (a) differentiation trajectories exhibit hierarchical branching, (b) attractors are robust to perturbations (homeorhesis), and (c) the proportions of specialized cells are preserved. It was further shown that appropriate external interventions can induce either probabilistic cellular reprogramming or highly predictable reprogramming outcomes. The incorporation of biochemical switches, rather than purely abstract normal forms, can contribute to more biologically grounded mathematical models of stem cell differentiation. This work also highlights the importance of normal forms for qualitatively understanding cell state dynamics and for building realistic modular GRNs. Full article
Show Figures

Figure 1

14 pages, 938 KB  
Article
Autonomous Normal–Cancer Discrimination by a LATS/pLATS-Explicit Hippo–YAP/TAZ Reaction System
by Toshihito Umegaki and Takashi Suzuki
Mathematics 2026, 14(1), 99; https://doi.org/10.3390/math14010099 - 26 Dec 2025
Viewed by 500
Abstract
In this study, we propose a minimal reaction system for the Hippo–YAP/TAZ pathway that explicitly includes inactive LATS, active pLATS, cytoplasmic and nuclear YAP/TAZ, and phosphorylated YAP/TAZ. Local cell density is incorporated into the LATS activation term, and nuclear YAP/TAZ controls a threshold-type [...] Read more.
In this study, we propose a minimal reaction system for the Hippo–YAP/TAZ pathway that explicitly includes inactive LATS, active pLATS, cytoplasmic and nuclear YAP/TAZ, and phosphorylated YAP/TAZ. Local cell density is incorporated into the LATS activation term, and nuclear YAP/TAZ controls a threshold-type switch between proliferative and quiescent cell states. This five-variable system of ordinary differential equations is coupled to a three-dimensional molecular dynamics model that provides time-dependent cell positions and densities. We define normal-like and cancer-like conditions by varying only the LATS phosphorylation rate while keeping the initial distribution of YAP/TAZ identical. Under normal-like parameters, increasing cell density leads to rapid accumulation of pLATS and suppression of nuclear YAP/TAZ below the proliferative threshold, resulting in a contact-inhibited epithelium dominated by quiescent cells. In contrast, under cancer-like parameters with delayed LATS activation, nuclear YAP/TAZ in a subset of cells remains above the threshold, and proliferative clusters persist even in high-density regions. These simulations show that, even without any bias in initial concentrations, modest changes in the kinetics of LATS phosphorylation alone can induce a clear bifurcation between normal-like and cancer-like growth at the tissue scale. The results provide a mechanistic bridge linking molecular-level dysregulation of the Hippo pathway to macroscopic tumor expansion. Full article
Show Figures

Figure 1

Back to TopTop