Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study

The Digital Twin: A Potential Solution for the Personalized Diagnosis and Treatment of Musculoskeletal System Diseases

Due to the high prevalence and rates of disability associated with musculoskeletal system diseases, more thorough research into diagnosis, pathogenesis, and treatments is required. One of the key contributors to the emergence of diseases of the musculoskeletal system is thought to be changes in the biomechanics of the human musculoskeletal system. However, there are some defects concerning personal analysis or dynamic responses in current biomechanical research methodologies. Digital twin (DT) was initially an engineering concept that reflected the mirror image of a physical entity. With the application of medical image analysis and artificial intelligence (AI), it entered our lives and showed its potential to be further applied in the medical field. Consequently, we believe that DT can take a step towards personalized healthcare by guiding the design of industrial personalized healthcare systems. In this perspective article, we discuss the limitations of traditional biomechanical methods and the initial exploration of DT in musculoskeletal system diseases. We provide a new opinion that DT could be an effective solution for musculoskeletal system diseases in the future, which will help us analyze the real-time biomechanical properties of the musculoskeletal system and achieve personalized medicine.

Optimal experimental design for mathematical models of haematopoiesis

The haematopoietic system has a highly regulated and complex structure in which cells are organized to successfully create and maintain new blood cells. It is known that feedback regulation is crucial to tightly control this system, but the specific mechanisms by which control is exerted are not completely understood. In this work, we aim to uncover the underlying mechanisms in haematopoiesis by conducting perturbation experiments, where animal subjects are exposed to an external agent in order to observe the system response and evolution. We have developed a novel Bayesian hierarchical framework for optimal design of perturbation experiments and proper analysis of the data collected. We use a deterministic model that accounts for feedback and feedforward regulation on cell division rates and self-renewal probabilities. A significant obstacle is that the experimental data are not longitudinal, rather each data point corresponds to a different animal. We overcome this difficulty by modelling the unobserved cellular levels as latent variables. We then use principles of Bayesian experimental design to optimally distribute time points at which the haematopoietic cells are quantified. We evaluate our approach using synthetic and real experimental data and show that an optimal design can lead to better estimates of model parameters.

Using Systems Biology and Mathematical Modeling Approaches in the Discovery of Therapeutic Targets for Spinal Muscular Atrophy

Systems biology uses a combination of experimental and mathematical approaches to investigate the complex and dynamic interactions with a given system or biological process. Systems biology integrates genetics, signal transduction, biochemistry and cell biology with mathematical modeling. It can be used to identify novel pathways implicated in diseases as well as to understand the mechanisms by which a specific gene is regulated. This review describes the development of mathematical models for the regulation of an endogenous modifier gene, SMN2, in spinal muscular atrophy-an early-onset motor neuron disease that is a leading genetic cause of infant mortality worldwide-by cAMP signaling. These mathematical models not only can aid in understanding how SMN2 expression is regulated but they can also be used to examine the best ways to manipulate cAMP signaling to maximally increase SMN2 expression. These models will lead to the development of therapeutic strategies for treating SMA. This systems biology approach can also be applied to other neurological diseases, particularly those in which a disease-causing gene or a modifier gene has been identified.

Modelling the molecular mechanisms of aging

The aging process is driven at the cellular level by random molecular damage that slowly accumulates with age. Although cells possess mechanisms to repair or remove damage, they are not 100% efficient and their efficiency declines with age. There are many molecular mechanisms involved and exogenous factors such as stress also contribute to the aging process. The complexity of the aging process has stimulated the use of computational modelling in order to increase our understanding of the system, test hypotheses and make testable predictions. As many different mechanisms are involved, a wide range of models have been developed. This paper gives an overview of the types of models that have been developed, the range of tools used, modelling standards and discusses many specific examples of models that have been grouped according to the main mechanisms that they address. We conclude by discussing the opportunities and challenges for future modelling in this field.

Algebraic Systems Biology: A Case Study for the Wnt Pathway

Steady-state analysis of dynamical systems for biological networks gives rise to algebraic varieties in high-dimensional spaces whose study is of interest in their own right. We demonstrate this for the shuttle model of the Wnt signaling pathway. Here, the variety is described by a polynomial system in 19 unknowns and 36 parameters. It has degree 9 over the parameter space. This case study explores multistationarity, model comparison, dynamics within regions of the state space, identifiability, and parameter estimation, from a geometric point of view. We employ current methods from computational algebraic geometry, polyhedral geometry, and combinatorics.