Mathematical Modeling of Biological Systems

Mathematical modeling is a powerful approach supporting the investigation of open problems in natural sciences, in particular physics, biology and medicine. Applied mathematics allows to translate the available information about real-world phenomena into mathematical objects and concepts. Mathematical models are useful descriptive tools that allow to gather the salient aspects of complex biological systems along with their fundamental governing laws, by elucidating the system behavior in time and space, also evidencing symmetry, or symmetry breaking, in geometry and morphology. Additionally, mathematical models are useful predictive tools able to reliably forecast the future system evolution or its response to specific inputs. More importantly, concerning biomedical systems, such models can even become prescriptive tools, allowing effective, sometimes optimal, intervention strategies for the treatment and control of pathological states to be planned. The application of mathematical physics, nonlinear analysis, systems and control theory to the study of biological and medical systems results in the formulation of new challenging problems for the scientific community. This Special Issue includes innovative contributions of experienced researchers in the field of mathematical modelling applied to biology and medicine

Systems biology in animal sciences

Systems biology is a rapidly expanding field of research and is applied in a number of biological disciplines. In animal sciences, omics approaches are increasingly used, yielding vast amounts of data, but systems biology approaches to extract understanding from these data of biological processes and animal traits are not yet frequently used. This paper aims to explain what systems biology is and which areas of animal sciences could benefit from systems biology approaches. Systems biology aims to understand whole biological systems working as a unit, rather than investigating their individual components. Therefore, systems biology can be considered a holistic approach, as opposed to reductionism. The recently developed ‘omics’ technologies enable biological sciences to characterize the molecular components of life with ever increasing speed, yielding vast amounts of data. However, biological functions do not follow from the simple addition of the properties of system components, but rather arise from the dynamic interactions of these components. Systems biology combines statistics, bioinformatics and mathematical modeling to integrate and analyze large amounts of data in order to extract a better understanding of the biology from these huge data sets and to predict the behavior of biological systems. A ‘system’ approach and mathematical modeling in biological sciences are not new in itself, as they were used in biochemistry, physiology and genetics long before the name systems biology was coined. However, the present combination of mass biological data and of computational and modeling tools is unprecedented and truly represents a major paradigm shift in biology. Significant advances have been made using systems biology approaches, especially in the field of bacterial and eukaryotic cells and in human medicine. Similarly, progress is being made with ‘system approaches’ in animal sciences, providing exciting opportunities to predict and modulate animal traits

The Hopfield model and its role in the development of synthetic biology

Neural network models make extensive use of concepts coming from physics and engineering. How do scientists justify the use of these concepts in the representation of biological systems? How is evidence for or against the use of these concepts produced in the application and manipulation of the models? It will be shown in this article that neural network models are evaluated differently depending on the scientific context and its modeling practice. In the case of the Hopfield model, the different modeling practices related to theoretical physics and neurobiology played a central role for how the model was received and used in the different scientific communities. In theoretical physics, where the Hopfield model has its roots, mathematical modeling is much more common and established than in neurobiology which is strongly experiment driven. These differences in modeling practice contributed to the development of the new field of synthetic biology which introduced a third type of model which combines mathematical modeling and experimenting on biological systems and by doing so mediates between the different modeling practices

Mathematical modeling of nitrogen regulated biological systems

Mención Internacional en el título de doctorThis doctoral thesis was supported through the FPI contract BES-2017-079755 associated to the grant FIS2016-78313-P from Ministerio de Ciencia e Innovación (MCIN)/Agencia Estatal de Investigación (AEI)/ 10.13039/501100011033/ and FEDER Una manera de hacer Europa. Additionally the author also acknowledge finantial support from MCIN/AEI/10.13039/501100011033 through grant BADS, no. PID2019-109320GB-100Programa de Doctorado en Ingeniería Matemática por la Universidad Carlos III de MadridPresidente: Luis Guillermo Morelli.- Secretaria: María Pilar Guerrero Contreras.- Vocal: Vicente Mariscal Romer

Charting a new frontier of science by integrating mathematical modeling to understand and predict complex biological systems

Biological systems are staggeringly complex. To untangle this complexity and make predictions about biological systems is a continuous goal of biological research. One approach to achieve these goals is to emphasize the use of quantitative measures of biological processes. Advances in quantitative biology data collection and analysis across scales (molecular, cellular, organismal, ecological) has transformed how we understand, categorize, and predict complex biological systems. Simultaneously, thanks to increased computational power, mathematicians, engineers and physical scientists -- collectively termed theoreticians -- have developed sophisticated models of biological systems at different scales. But there is still a disconnect between the two fields. This surge of quantitative data creates an opportunity to apply, develop, and evaluate mathematical models of biological systems and explore novel methods of analysis. The novel modeling schemes can also offer deeper understanding of principles in biology. In the context of this paper, we use “models” to refer to mathematical representations of biological systems. This data revolution puts scientists in a unique position to leverage information-rich datasets to improve descriptive modeling. Moreover, advances in technology allow inclusion of heterogeneity and variability within these datasets and mathematical models. This inclusion may lead to identifying previously undetermined variables driving or maintaining heterogeneity and diversity. Improved inclusion of variation may even improve biologically meaningful predictions about how systems will respond to perturbations. Although some of these practices are mainstream in specific sub-fields of biology, such practices are not widespread across all fields of biological sciences. With resources dedicated to better integrating biology and mathematical modeling, we envision a transformational improvement in the ability to describe and predict complex biological systems

PlantSimLab - a modeling and simulation web tool for plant biologists.

BACKGROUND: At the molecular level, nonlinear networks of heterogeneous molecules control many biological processes, so that systems biology provides a valuable approach in this field, building on the integration of experimental biology with mathematical modeling. One of the biggest challenges to making this integration a reality is that many life scientists do not possess the mathematical expertise needed to build and manipulate mathematical models well enough to use them as tools for hypothesis generation. Available modeling software packages often assume some modeling expertise. There is a need for software tools that are easy to use and intuitive for experimentalists. RESULTS: This paper introduces PlantSimLab, a web-based application developed to allow plant biologists to construct dynamic mathematical models of molecular networks, interrogate them in a manner similar to what is done in the laboratory, and use them as a tool for biological hypothesis generation. It is designed to be used by experimentalists, without direct assistance from mathematical modelers. CONCLUSIONS: Mathematical modeling techniques are a useful tool for analyzing complex biological systems, and there is a need for accessible, efficient analysis tools within the biological community. PlantSimLab enables users to build, validate, and use intuitive qualitative dynamic computer models, with a graphical user interface that does not require mathematical modeling expertise. It makes analysis of complex models accessible to a larger community, as it is platform-independent and does not require extensive mathematical expertise

Biological Systems from an Engineer’s Point of View

Mathematical modeling of the processes that pattern embryonic development (often called biological pattern formation) has a long and rich history [1,2]. These models proposed sets of hypothetical interactions, which, upon analysis, were shown to be capable of generating patterns reminiscent of those seen in the biological world, such as stripes, spots, or graded properties. Pattern formation models typically demonstrated the sufficiency of given classes of mechanisms to create patterns that mimicked a particular biological pattern or interaction. In the best cases, the models were able to make testable predictions [3], permitting them to be experimentally challenged, to be revised, and to stimulate yet more experimental tests (see review in [4]). In many other cases, however, the impact of the modeling efforts was mitigated by limitations in computer power and biochemical data. In addition, perhaps the most limiting factor was the mindset of many modelers, using Occam’s razor arguments to make the proposed models as simple as possible, which often generated intriguing patterns, but those patterns lacked the robustness exhibited by the biological system. In hindsight, one could argue that a greater attention to engineering principles would have focused attention on these shortcomings, including potential failure modes, and would have led to more complex, but more robust, models. Thus, despite a few successful cases in which modeling and experimentation worked in concert, modeling fell out of vogue as a means to motivate decisive test experiments. The recent explosion of molecular genetic, genomic, and proteomic data—as well as of quantitative imaging studies of biological tissues—has changed matters dramatically, replacing a previous dearth of molecular details with a wealth of data that are difficult to fully comprehend. This flood of new data has been accompanied by a new influx of physical scientists into biology, including engineers, physicists, and applied mathematicians [5–7]. These individuals bring with them the mindset, methodologies, and mathematical toolboxes common to their own fields, which are proving to be appropriate for analysis of biological systems. However, due to inherent complexity, biological systems seem to be like nothing previously encountered in the physical sciences. Thus, biological systems offer cutting edge problems for most scientific and engineering-related disciplines. It is therefore no wonder that there might seem to be a “bandwagon” of new biology-related research programs in departments that have traditionally focused on nonliving systems. Modeling biological interactions as dynamical systems (i.e., systems of variables changing in time) allows investigation of systems-level topics such as the robustness of patterning mechanisms, the role of feedback, and the self-regulation of size. The use of tools from engineering and applied mathematics, such as sensitivity analysis and control theory, is becoming more commonplace in biology. In addition to giving biologists some new terminology for describing their systems, such analyses are extremely useful in pointing to missing data and in testing the validity of a proposed mechanism. A paper in this issue of PLoS Biology clearly and honestly applies analytical tools to the authors’ research and obtains insights that would have been difficult if not impossible by other means [8]