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Mathematical Biosciences Feb 2015Biological systems present particular challengers to model for the purposes of formulating predictions of generating biological insight. These systems are typically... (Review)
Review
Biological systems present particular challengers to model for the purposes of formulating predictions of generating biological insight. These systems are typically multi-scale, complex, and empirical observations are often sparse and subject to variability and uncertainty. This manuscript will review some of these specific challenges and introduce current methods used by modelers to construct meaningful solutions, in the context of preserving biological relevance. Opportunities to expand these methods are also discussed.
Topics: Humans; Models, Biological; Models, Theoretical
PubMed: 25445734
DOI: 10.1016/j.mbs.2014.09.001 -
Sheng Wu Yi Xue Gong Cheng Xue Za Zhi =... Oct 2020Fracture is a common physical injury. Its healing process involves complex biological activities at tissue, cellular and molecular levels and is affected by mechanical...
Fracture is a common physical injury. Its healing process involves complex biological activities at tissue, cellular and molecular levels and is affected by mechanical and biological factors. Over recent years, numerical simulation methods have been widely used to explore the mechanisms of fracture healing, design fixators and develop novel treatment strategies, etc. This paper mainly recommend the numerical methods used for simulating fracture healing and their latest research progress, which helps people better understand the mechanism of fracture healing, and also provides direction and guidance for the numerical simulation research of fracture healing in the future. First, the fracture healing process and its relationship with mechanical stimulation and biological factors are described. Then, the numerical models used for simulating fracture healing (including mechano-regulatory model, biological regulatory model and mechano-biological regulatory model) and corresponding modeling techniques (mainly including agent-based techniques and fuzzy logic controlling method) were summarized in particular. Finally, the future research directions in numerical simulation of fracture healing were preliminarily prospected.
Topics: Computer Simulation; Fracture Healing; Fractures, Bone; Humans; Models, Biological; Stress, Mechanical
PubMed: 33140619
DOI: 10.7507/1001-5515.202004010 -
Journal of the Royal Society, Interface Jul 2019In this paper, we address the system identification problem in the context of biological modelling. We present and demonstrate a methodology for (i) assessing the...
In this paper, we address the system identification problem in the context of biological modelling. We present and demonstrate a methodology for (i) assessing the possibility of inferring the unknown quantities in a dynamic model and (ii) effectively estimating them from output data. We introduce the term Full Input-State-Parameter Observability (FISPO) analysis to refer to the simultaneous assessment of state, input and parameter observability (note that parameter observability is also known as identifiability). This type of analysis has often remained elusive in the presence of unmeasured inputs. The method proposed in this paper can be applied to a general class of nonlinear ordinary differential equations models. We apply this approach to three models from the recent literature. First, we determine whether it is theoretically possible to infer the states, parameters and inputs, taking only the model equations into account. When this analysis detects deficiencies, we reformulate the model to make it fully observable. Then we move to numerical scenarios and apply an optimization-based technique to estimate the states, parameters and inputs. The results demonstrate the feasibility of an integrated strategy for (i) analysing the theoretical possibility of determining the states, parameters and inputs to a system and (ii) solving the practical problem of actually estimating their values.
Topics: Models, Biological; Nonlinear Dynamics; Systems Biology
PubMed: 31266417
DOI: 10.1098/rsif.2019.0043 -
Progress in Biophysics and Molecular... Sep 2023The mystery of the morphogenesis of phyllotaxis has been of concern for several generations of botanists and mathematicians. Of particular interest is the fact that the... (Review)
Review
The mystery of the morphogenesis of phyllotaxis has been of concern for several generations of botanists and mathematicians. Of particular interest is the fact that the number of visible spirals is equal to the number from the Fibonacci series. The article proposes an analytical solution to two fundamental questions of phyllotaxis: what is the morphogenesis of patterns of spiral phyllotaxis? and why the number of visible spirals is equal to number from the Fibonacci series? The article contains videos illustrating the recursive dynamic model of spiral phyllotaxis morphogenesis.
Topics: Models, Biological; Morphogenesis
PubMed: 37209972
DOI: 10.1016/j.pbiomolbio.2023.04.004 -
Trends in Cell Biology Nov 2016Most current research in cell biology uses just a handful of model systems including yeast, Arabidopsis, Drosophila, Caenorhabditis elegans, zebrafish, mouse, and... (Review)
Review
Most current research in cell biology uses just a handful of model systems including yeast, Arabidopsis, Drosophila, Caenorhabditis elegans, zebrafish, mouse, and cultured mammalian cells. And for good reason - for many biological questions, the best system for the question is likely to be found among these models. However, in some cases, and particularly as the questions that engage scientists broaden, the best system for a question may be a little-studied organism. Modern research tools are facilitating a renaissance for unusual and interesting organisms as emerging model systems. As a result, we predict that an ever-expanding breadth of model systems may be a hallmark of future cell biology.
Topics: Animals; Biological Evolution; Cell Biology; Humans; Models, Animal; Models, Biological; Models, Genetic
PubMed: 27639630
DOI: 10.1016/j.tcb.2016.08.005 -
Biological Cybernetics Aug 2021Model reduction is a central problem in mathematical biology. Reduced order models enable modeling of a biological system at different levels of complexity and the...
Model reduction is a central problem in mathematical biology. Reduced order models enable modeling of a biological system at different levels of complexity and the quantitative analysis of its properties, like sensitivity to parameter variations and resilience to exogenous perturbations. However, available model reduction methods often fail to capture a diverse range of nonlinear behaviors observed in biology, such as multistability and limit cycle oscillations. The paper addresses this need using differential analysis. This approach leads to a nonlinear enhancement of classical balanced truncation for biological systems whose behavior is not restricted to the stability of a single equilibrium. Numerical results suggest that the proposed framework may be relevant to the approximation of classical models of biological systems.
Topics: Biological Clocks; Models, Biological
PubMed: 34382116
DOI: 10.1007/s00422-021-00888-4 -
Mathematical Biosciences and... Feb 2022In the paper, under the stress of aggregation and reproduction mechanism of algae, we proposed a modified algae and fish model with aggregation and Allee effect, its...
In the paper, under the stress of aggregation and reproduction mechanism of algae, we proposed a modified algae and fish model with aggregation and Allee effect, its main purpose was to further ascertain the dynamic relationship between algae and fish. Several critical conditions were investigated to guarantee the existence and stabilization of all possible equilibrium points, and ensure that the model could undergo transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation and B-T bifurcation. Numerical simulation results of related bifurcation dynamics were provided to verify the feasibility of theoretical derivation, and visually demonstrate the changing trend of the dynamic relationship. Our results generalized and improved some known results, and showed that the aggregation and Allee effect played a vital role in the dynamic relationship between algae and fish.
Topics: Animals; Computer Simulation; Models, Biological
PubMed: 35341269
DOI: 10.3934/mbe.2022169 -
Biophysical Journal Oct 2021Biophysical modeling of development started with Alan Turing. His two-morphogen reaction-diffusion model was a radical but powerful simplification. Despite its apparent... (Review)
Review
Biophysical modeling of development started with Alan Turing. His two-morphogen reaction-diffusion model was a radical but powerful simplification. Despite its apparent limitations, the model captured real developmental processes that only recently have been validated at the molecular level in many systems. The precision and robustness of reaction-diffusion patterning, despite boundary condition-dependence, remain active areas of investigation in developmental biology.
Topics: Computational Biology; Diffusion; Models, Biological
PubMed: 34480925
DOI: 10.1016/j.bpj.2021.08.041 -
BMC Systems Biology Jun 2018Understanding the dynamical behaviour of biological systems is challenged by their large number of components and interactions. While efforts have been made in this...
BACKGROUND
Understanding the dynamical behaviour of biological systems is challenged by their large number of components and interactions. While efforts have been made in this direction to reduce model complexity, they often prove insufficient to grasp which and when model processes play a crucial role. Answering these questions is fundamental to unravel the functioning of living organisms.
RESULTS
We design a method for dealing with model complexity, based on the analysis of dynamical models by means of Principal Process Analysis. We apply the method to a well-known model of circadian rhythms in mammals. The knowledge of the system trajectories allows us to decompose the system dynamics into processes that are active or inactive with respect to a certain threshold value. Process activities are graphically represented by Boolean and Dynamical Process Maps. We detect model processes that are always inactive, or inactive on some time interval. Eliminating these processes reduces the complex dynamics of the original model to the much simpler dynamics of the core processes, in a succession of sub-models that are easier to analyse. We quantify by means of global relative errors the extent to which the simplified models reproduce the main features of the original system dynamics and apply global sensitivity analysis to test the influence of model parameters on the errors.
CONCLUSION
The results obtained prove the robustness of the method. The analysis of the sub-model dynamics allows us to identify the source of circadian oscillations. We find that the negative feedback loop involving proteins PER, CRY, CLOCK-BMAL1 is the main oscillator, in agreement with previous modelling and experimental studies. In conclusion, Principal Process Analysis is a simple-to-use method, which constitutes an additional and useful tool for analysing the complex dynamical behaviour of biological systems.
Topics: Animals; Circadian Rhythm; Feedback, Physiological; Models, Biological
PubMed: 29898718
DOI: 10.1186/s12918-018-0586-6 -
American Journal of Botany Dec 2018
Topics: Araceae; Ecology; Models, Biological
PubMed: 30452782
DOI: 10.1002/ajb2.1194