Mathematical Biology Research Articles

Robert Rosen’s Relational Biology Theory and His Emphasis on Non-Algorithmic Approaches to Living Systems

This paper examines the use of algorithms and non-algorithmic models in mathematics and science, especially in biology, during the past century by summarizing the gradual development of a conceptual rationale for non-algorithmic models in biology. First, beginning a century ago, mathematicians found it impossible to constrain mathematics in an algorithmic straitjacket via öö’s Incompleteness Theorems, so how would it be possible in biology? By the 1930s, biology was resolutely imitating classical physics, with biologists enforcing a reductionist agenda to expunge function, purpose, teleology, and vitalism from biology. Interestingly, physicists and mathematicians often understood better than biologists that mathematical representations of living systems required different approaches than those of dead matter. Nicolas Rashevsky, the Father of Mathematical Biology, and Robert Rosen, his student, pointed out that the complex systems of life cannot be reduced to machines or mechanisms as per the Newtonian paradigm. Robert Rosen concluded that living systems are not amenable to algorithmic models that are primarily syntactical. Life requires semantics for its description. Rashevsky and Rosen pioneered Relational Biology, initially using Graph Theory to model living systems. Later, Rosen created a metabolic–repair model (M, R)-system using Category Theory to encode the basic entailments of life itself. Although reductionism still dominates in current biology, several subsequent authors have built upon the Rashevsky–Rosen intellectual foundation and have explained, extended, and explored its ramifications. Algorithmic formulations have become increasingly inadequate for investigating and modeling living systems. Biology is shifting from a science of simple systems to complex ones. This transition will only be successful once mathematics fully depicts what it means to be alive. This paper is a call to mathematicians from biologists asking for help in doing this.

Peningkatan Kemampuan Pedagogi Mahasiswa Melalui Model Lesson Study pada Mata Kuliah Microteaching

The purpose of this research is to improve students pedagogical skills through a lesson study model in microteaching courses. The type of research conducted is descriptive research with a qualitative approach. The subjects of the study were 6 students from the Mathematics Education, Biology Education, English Education and Indonesian Education Study Programs at the Faculty of Teacher Training and Education, Iqra Buru University. Data collection uses observation sheets on the lesson plans made and the learning implementation process. The results of the research obtained are: 1) in preparing the learning implementation plan), from the 7 aspects that were assessed, namely: (1) the completeness of the identity of the RPP is obtained from 65% to 85%; (2) the formulation of learning objectives was obtained from 67.8% to 90%; (3) The description of the subject matter was obtained from 65% to 85%; (4) learning methods, strategies and media were obtained by 58%; to 92.6%; (5) the learning plan was obtained by 66.6%, to 84.3%; (6) The assessment was obtained by 70%, to 90%; and (7) learning resources were obtained by 75%, to 88.5. 2) Implementation (Do) with the application of lesson study there was a very good increase where from 3 aspects that were assessed to obtain ideals, namely (1) Introduction, 68.7% to 88% of categories; (2) Core, 61.6%, to 85%; and (3) 65% cover to 95. In conclusion, the application of the lesson study model in microteaching courses can improve students' pedagogical teaching skills.

A Study on Future Population Dynamics of Indigenous Earthworm Species in Golaghat District of Assam, India

This study presents a pioneering exploration into the population dynamics of indigenous earthworm species in the Golaghat district of Assam, India, through the lens of mathematical modeling. Recognizing the integral role of earthworms in enhancing soil productivity and ecosystem health, we embarked on a detailed longitudinal analysis spanning from 2018 to 2023 to assess their population trends across different seasons and subdivisions within the district. Utilizing the principles of Mathematical Biology, we employed the Malthus Growth model and the Logistic Growth model to estimate future population trajectories of earthworm species, integrating biological insights with mathematical rigor. Our methodology, combining extensive field data collection with sophisticated mathematical modeling, provides a replicable framework for similar ecological studies. This study contributes to the growing field of Mathematical Biology, offering a novel approach to understanding the complex interactions within ecosystems and the impact of environmental changes on key species. The outcomes offer valuable insights into sustainable agricultural practices and biodiversity conservation in tropical and subtropical regions, emphasizing the critical role of indigenous earthworm species in maintaining soil health and ecosystem services. Our findings reveal significant seasonal variations and highlight the resilience of these species in the face of ecological changes. The models suggest distinct population growth patterns, with the Logistic model providing a more realistic projection considering environmental constraints and resource availability. The bifurcation diagram is drawn for the Logistic map that presents the phenomena inside the chaotic region.

Dynamics behaviours of N-kink solitons in conformable Fisher–Kolmogorov–Petrovskii–Piskunov equation

PurposeThis manuscript is related to compute $N$-kink soliton solutions for conformable Fisher–Kolmogorov equation (CFKE) by using the generalized extended direct algebraic method (EDAM). The considered problem has important applications in mathematical biology and reaction diffusion processes. Also, the mentioned problem has significant applications in population dynamics. The fractional order conformable derivative has many features as compared to the other fractional order differential operators. For instance, the chain, product and quotient procedures do not satisfy by other fractional differential operators, but conformable operators obey the mentioned rules. Hence, we compute the soliton solutions for the mentioned problem and present its various dynamical behaviours graphically.Design/methodology/approachThe generalized EDAM is used in this article to examine the calculation of N-kink soliton solutions for the CFKE. In mathematical biology and reaction-diffusion processes, the topic under consideration holds great significance, especially when considering population dynamics.FindingsThe results highlight the benefits of utilising conformable derivatives in mathematical modelling and further our understanding of fractional differential equations and their applications.Research limitations/implicationsThe work focuses primarily on N-kink soliton solutions, which may limit the examination of alternative types of solutions (e.g., multi-soliton or periodic solutions) that might give new insights into the dynamics of the CFKE.Practical implicationsThe generated N N-kink soliton solutions can enhance mathematical models in biological contexts, notably in modelling population dynamics, disease propagation and ecological interactions, leading to better forecasts and interventions.Social implicationsPublic health initiatives can benefit from the understanding of disease transmission and intervention efficacy that comes from modelling population dynamics and reaction-diffusion processes.Originality/valueThe use of the generalized EDAM to obtain solutions for N-kink soliton problems is an innovative method for solving the conformable Fisher–Kolmogorov equation, demonstrating the power of this mathematical tool.

Biological Theories of Morphogenesis Based on Holistic Biophysical Thinking

AbstractThe roles played by physics in the study of the life sciences have taken many forms over the past 100 years. Here we analyze how physics can be brought to bear on the contemporary study of morphogenesis, where new tissue-scale forms arise out of simpler, more homogenous, initial structures. We characterize how morphogenesis has been studied through reductionist approaches and discuss their limitations. We suggest that an alternative way of approaching morphogenesis that begins with a consideration of the whole may also serve as a fruitful mode of scientific inquiry. Through historical analysis of concepts relevant for contemporary systems biology, we illustrate how physical thinking oriented toward the biological whole (“holistic biophysical thinking”) was exemplified in the biological theories presented earlier by D’Arcy Thompson (1860–1948) and Pere Alberch (1954–1998). We contrast the use of physics to develop the conceptual foundations of holistically oriented systems biology with the more prevalent contemporary use of physics that focuses on technological development and quantification, embedded within reductionist strategies. As an in-depth contemporary case study, we describe how in our research we have used holistic biophysical thinking to develop biological theories of vertebrate morphogenesis that account for and extend beyond genetic, molecular, and cellular processes. We propose a theory of skin development where both molecular and morphological patterns are orchestrated by emergent physical processes at the supracellular scale. We further posit that holistic biophysical thinking at the supracellular scale may advance theories of diseases such as cancer.

Knowledge‐Based Deep Learning to Predict Vegetation Carbon, Nitrogen and Phosphorus Densities in China’s Shrublands

AbstractAccurate estimations of carbon (C), nitrogen (N), and phosphorus (P) densities in shrublands are pivotal for assessing terrestrial ecosystem carbon sequestration. Combining in‐situ investigations and machine learning facilitates large‐scale patterns mapping, however, which often overlooks underlying ecological regulations. Here we utilize data from 1,122 survey plots across China's shrublands and develop a novel knowledge‐based deep learning framework that integrates a structural equation model (SEM) to elucidate mechanisms and construct an artificial neural network (ANN) based on these causal relationships. Results show that biomass allocation to different organs follows allometric regulations and that N and P concentrations maintain a degree of stoichiometric homeostasis following biological stoichiometry theory. This insight guides the construction of our ANN, which outperforms both SEM and other prevalent machine learning methods. By leveraging ecological theories to inform model construction, our framework not only enhances prediction accuracy and explainability but also provides a methodological blueprint for ecological research.

Misinformation and perception of COVID-19 and risk assessment among people in Pakistan: A pilot study.

During the coronavirus pandemic, misinformation was circulated through technology and social media on a large scale. Since people rely on media to keep connected and informed, misinformation can prevent them from staying safe. To examine the quality of information reaching Pakistanis, the effect of information/misinformation on people's perception, and its relationship with risky health behaviours in different demographical groups. A community sample of N= 103 Pakistanis was assessed using a mixed-method cross-sectional survey research design to investigate their sources of knowledge/information, perceptions of coronavirus-related facts, and risky health behaviours. Content analysis of the material that participants read/watched indicated the possible effect of media on people's perception of COVID-19. Specific demography (e.g., increasing age) and people's tendency to believe misinformation/information may indicate risky health behaviours pertaining to coronavirus infection. Findings showed how the models considered (social cognitive theory, biological warfare conspiracy theory, theory of planned behaviour, protection motivation theory, the health belief model, and biopsychosocial model) may be relevant to examination of the effects of misinformation on different demographic groups. The findings and models need to be verified on larger, more representative samples of Pakistanis using a large-scale survey based on the insights obtained from this pilot study.

Synergistic co-evolution of rhizosphere bacteria in response to acidification amelioration strategies: impacts on the alleviation of tobacco wilt and underlying mechanisms.

Soil acidification represents a severe threat to tobacco cultivation regions in South China, exacerbating bacterial wilt caused by Ralstonia solanacearum. The comprehension of the underlying mechanisms that facilitate the restoration of rhizosphere microbial communities in "healthy soils" is imperative for ecologically managing tobacco bacterial wilt. This study focuses on acidified tobacco soils that have been subjected to continuous cultivation for 20 years. The experimental treatments included lime (L), biochar (B), and a combination of lime and biochar (L+B), in addition to a control group (CK). Utilizing rhizosphere biology and niche theory, we assessed disease suppression effects, changes in soil properties, and the co-evolution of the rhizosphere bacterial community. Each treatment significantly reduced tobacco bacterial wilt by 16.67% to 20.14% compared to the control group (CK) (p < 0.05) and increased yield by 7.86% to 27.46% (p < 0.05). The biochar treatment (B) proved to be the most effective, followed by the lime-biochar combination (L+B). The key factors controlling wilt were identified through random forest regression analysis as an increase in soil pH and exchangeable bases, along with a decrease in exchangeable acidity. However, lime treatment alone led to an increase in soil bulk density and a decrease in available nutrients, whereas both biochar and lime-biochar treatments significantly improved these parameters (p < 0.05). No significant correlation was found between the abundance of Ralstonia and wilt incidence. Nonetheless, all treatments significantly expanded the ecological niche breadth and average variation degree (AVD), enhanced positive interactions and cohesion within the community, and intensified negative interactions involving Ralstonia. This study suggests that optimizing community niches and enhancing pathogen antagonism are key mechanisms for mitigating tobacco wilt in acidified soils. It recommends using lime-biochar mixtures as soil amendments due to their potential ecological and economic benefits. This study offers valuable insights for disease control strategies and presents a novel perspective for research on Solanaceous crops.

Genome-wide identification of the histone modification gene family in Aquilaria sinensis and functional analysis of several HMs in response to MeJA and NaCl stress

Histone modifications (HMs) play various roles in growth, development, and resistance to abiotic stress. However, HMs have been systematically identified in a few plants, and identification of HMs in medicinal plants is very rare. Aquilaria sinensis is a typical stress-induced medicinal plant, in which HMs remain unexplored. We conducted a comprehensive study to identify HMs and obtained 123 HMs. To conduct evolutionary analysis, we constructed phylogenetic trees and analyzed gene structures. To conduct functional analysis, we performed promoter, GO, and KEGG analyses and ortholog analyses against AtHMs. Based on the expression profiles of different tissues and different layers of Agar-Wit, some HMs of A. sinensis (AsHMs) were predicted to be involved in the formation of agarwood, and their response to MeJA and NaCl stress was tested by qRT-PCR analysis. By analyzing the enrichment of H3K4me3, H3K27me3, and H4K5ac in the promoter regions of two key sesquiterpene synthase genes, AsTPS13/18, we hypothesized that AsHMs play important roles in the synthesis of agarwood sesquiterpenes. We confirmed this hypothesis by conducting RNAi transgenic interference experiments. This study provided valuable information and important biological theories for studying epigenetic regulation in the formation of agarwood. It also provided a framework for conducting further studies on the biological functions of HMs.

Traveling waves reflecting various processes represented by reaction–diffusion equations

The aim of this paper is to discover analytically the interactional responses of populations in a dynamic region where the reaction–diffusion process with forcing effects takes place through traveling wave solutions. An expansion method is considered here to properly capture the responses for the first time. In order to profoundly analyze the physical and mathematical discussions, some illustrative behavioral results are exhibited for various values of physical parameters. Especially for the different values of diffusion coefficients in the model under consideration, their effects on the behavior of the solitary wave are discussed and observationally supported by considering various illustrations. It is also seen that the solutions representing the diffusion seen to be in the form of the behavior of hexagonal Turing patterns in different time periods. The application of this study in mathematical biology is to analyze the relationship between the population density of certain species in any local region and the specific population density with invasion characteristics. In addition, the formation of the extinction vortex of the invading population, depending on the characteristics of the solutions presented, is also descriptively discussed.

Editorial: Modelling and numerical simulations with differential equations in mathematical biology, medicine and the environment, volume II

Editorial: Modelling and numerical simulations with differential equations in mathematical biology, medicine and the environment, volume II

A brief tutorial on information theory

At the 2023 Les Houches Summer School on Theoretical Biological Physics, several students asked for some background on information theory, and so we added a tutorial to the scheduled lectures. This is largely a transcript of that tutorial, lightly edited. It covers basic definitions and context rather than detailed calculations. We hope to have maintained the informality of the presentation, including exchanges with the students, while still being useful.

On the well‐posedness of some model arising in the mathematical biology

On the well‐posedness of some model arising in the mathematical biology

Modelling Yeast Prion Dynamics: A Fractional Order Approach with Predictor–Corrector Algorithm

This work aims to comprehend the dynamics of neurodegenerative disease using a mathematical model of fractional-order yeast prions. In the context of the Caputo fractional derivative, we here study and examine the solution of this model using the Predictor–Corrector approach. An analysis has been conducted on the existence and uniqueness of the selected model. Also, we examined the model’s stability and the existence of equilibrium points. With the purpose of analyzing the dynamics of the Sup35 monomer and Sup35 prion population, we displayed the graphs to show the obtained solutions over time. Graphical simulations show that the behaviour of the populations can change based on fractional orders and threshold parameter values. This work may present a good example of how biological theories and data can be better understood via mathematical modelling.

STUDYING INDICATORS OF CIRCADIAN RHYTHMS OF MACROELEMENTS CONCENTRATION IN HUMAN SALIVA UNDER NORMAL CONDITIONS

Seasonal and circadian research in the field of chronobiology and chronomedicine is currently of particular interest to scientists. Chronobiology has discovered previously unknown approaches to the diagnosis, treatment and prevention of diseases. For biological objects, as an open thermodynamic system, in their development have absorbed all the laws of the rhythmically oscillating external world and interact with it with the help of these vibrations. Therefore, at the present stage of the development of chronobiology, any research that fills, like bricks, still empty niches of new knowledge reflects the advanced frontiers of natural science and is included in the creation of a future general theory of biology. This is confirmed by a number of discoveries of scientists in the field of physics, physiology and medicine. Thus, a group of scientists became laureates of the Nobel Prize in physics in 2017 for the discovery of gravitational waves, and in the field of physiology and medicine, a number of scientists (Hall, Rosbash, Young) became Nobel laureates for a series of works on the topic: "Studying the mechanisms of the circadian dynamics of the body." Today, chronobiology can characterize periodic fluctuations of, perhaps, all organs, all body systems. A large amount of data has been accumulated on the daily and seasonal rhythms of the digestive and urinary tract organs, respiratory and cardiovascular systems, brain, etc. A violation of biorhythms can lead to the development of defects in oral and maxillofacial tissues, the development of inflammation and tumors, which affects cell proliferation, apoptosis, oxidative stress, etc. The main purpose of this work was to study the characteristics of circadian rhythms of macroelement concentrations in human saliva under normal conditions. A feature of the research work is the determination of the concentration of macroelements in saliva in the summer. The saliva of 12 healthy volunteers was taken as the study material. Age 22-30 years. The method of spectrophotometry was used in this research work. The research work was carried out in the summer at the Department of Biophysics, Biomedicine and Neuroscience of the al-Farabi Kazakh National University and at the City Clinical Hospital №1 in Almaty. During the study, a saliva sample was collected on 1.5 ml of Eppendorf. All samples were stored in the freezer. Before the experiment, the material was soaked at room temperature for 30-40 minutes. Using the spectrophotometric method, we determined the concentration of macroelements in saliva using a set of special reagents. We have identified the features of the daily dynamics of the concentration of macroelements in the saliva of healthy people in summer: K, Na, Ca, Mg and P. The concentration of macroelements varied widely throughout the day. As a result of the study, the concentration index of K during the day normally ranges from 528±36 µg/ml to 634±42 µg/ml; Na - from 153.4±19.8 µg/ml to 144.9±25.1 µg/ml; Ca-from 35.4±4.0 µg/ml to 45.5±5.1 µg/ml; Mg-from 2.12±0.15 µg/ml to 4.02±0.25 µg/ml and P-from 134.5±7.7 µg/ml to 151.6±10.1 µg/ml. Summing up, we have identified the features of the daily dynamics of the concentration of macroelements in the saliva of healthy people in summer. In summer, the daily dynamics of the concentration of macroelements in saliva ranged from 2.12±0.15 µg/ml (Mg) to 634±12 µg/ml (K).

Digitizing DNA Sequences Using Multiset-Based Nucleotide Frequencies for Machine Learning-Based Mutation Detection

Investigating algebraic structures in a non-conventional framework supplements mathematics for hard-nosed practical applications to the fields of theoretical biology and computer science. One such algebraic structure is multigroup whose underlying set is a multiset. The genome is the entire set of DNA instructions found within a cell which contains all the information needed for an individual to develop and function. DNA and RNA are the hereditary materials that play a vital role in the metabolism process of living things, especially protein synthesis. In genomic database DNA sequences are stored in the form of string or text data types. The only data that works with machine learning algorithms is numerical. Thus, it is necessary to transform DNA sequence strings to numerical values. This article is organized in the following manner. Firstly, we prove that standard genetic code is a multigroup and genome architecture of the whole population can be interpreted as the sum of multisets. Next, it is described how a numerical representation of DNA bases relates to its algebraic representation. We further employed Gated Recurrent Unit, Long Short-Term Memory, and Bidirectional Long Short-Term Memory to identify changes between the DNA sequences. Experimental results show that GRU with multiset-based numerical values for DNA bases offers 98% accuracy on testing data. This novel technique will aid in the detection of mutations in complex diseases.

Antibody-drug conjugates in gastric cancer: from molecular landscape to clinical strategies.

Antibody-drug conjugates (ADCs) represent a crucial component of targeted therapies in gastric cancer, potentially altering traditional treatment paradigms. Many ADCs have entered rigorous clinical trials based on biological theories and preclinical experiments. Modality trials have also been conducted in combination with monoclonal antibody therapies, chemotherapies, immunotherapies, and other treatments to enhance the efficacy of drug coordination effects. However, ADCs exhibit limitations in treating gastric cancer, including resistance triggered by their structure or other factors. Ongoing intensive researches and preclinical experiments are yielding improvements, while enhancements in drug development processes and concomitant diagnostics during the therapeutic period actively boost ADC efficacy. The optimal treatment strategy for gastric cancer patients is continually evolving. This review summarizes the clinical progress of ADCs in treating gastric cancer, analyzes the mechanisms of ADC combination therapies, discusses resistance patterns, and offers a promising outlook for future applications in ADC drug development and companion diagnostics.

Dynamics Behaviours of Kink Solitons in Conformable Kolmogorov–Petrovskii–Piskunov Equation

The current study introduces the generalised New Extended Direct Algebraic Method (gNEDAM) for producing and examining propagation of kink soliton solutions within the framework of the Conformable Kolmogorov–Petrovskii–Piskunov Equation (CKPPE), which entails conformable fractional derivatives into account. The primary justification around employing conformable derivatives in this study is their special ability to comply with the chain rule, allowing for in the solution of aimed nonlinear model. The CKPPE is a crucial model for a number of disciplines, such as mathematical biology, reaction-diffusion mechanisms, and population increase. CKPPE is transformed into a Nonlinear Ordinary Differential Equation by the proposed gNEDAM, and many kink soliton solutions are found by applying the series form solution. These kink soliton solutions shed light on propagation mechanisms within the framework of the CKPPE model. Furthermore, our research offers multiple graphical depictions that facilitate the examination and analysis of the propagation patterns of the identified kink soliton solutions. Through the integration of mathematical biology and reaction-diffusion principles, our research broadens our comprehension of intricate occurrences in various academic domains.

Should We Believe in Cells, or Just Remain Agnostic about Them? A Critical Analysis Through Bas van Fraassen’s Lenses.

For constructive empiricism, being observable or unobservable is defining for deciding about the empirical adequacy and epistemic value of theory components. The classification of microscopic images has been particularly debated. van Fraassen initially classified microscope images as unobservable and then as mere images, like rainbows. Afterwards, he claimed it is not irrational to maintain neutrality about their classification and left them in some kind of limbo between being images of something real or being mere images. Here, I provide an argument to classify microscopic images of cells as copy-qualified images. The argument is described in general terms to sustain that any unobservable entity that is derived from observable self-dividing entities and looks similar to the observable entity when detected under the microscope, corresponds to a copy-qualified image of something real. Because of the existence in nature of large observable cells that fulfil these properties, I conclude that microscopic images of cells are images of something real. This determines their empirical adequacy and epistemic value, making them hard-core and stable components of biological theories. The argument described provides a strategy to develop a more grained classification of what is observable and unobservable with the consequent implications for theory development.

Sosialisasi Bahaya Narkotika sebagai Bentuk Kenakalan Remaja di kalangan Siswa SMKN 1 Kecamatan Kragilan Kabupaten Serang

Narcotics are a substance that is very dangerous if its use is misused and permission is not obtained from the authorities, narcotics will damage the nation's next generation who will run the government in the future. The rise in the use of narcotics is in line with the influx of globalization and modernization which makes it easier for people to obtain them as well as a network of dealers who are aggressively looking for marketing targets among young people who are susceptible to sweet advances and do not yet have clear life principles. Indonesia is one of the countries that is fighting drug dealers, users and networks, this is because every 17 seconds someone is arrested for violating drug-related laws. Indonesia has 2 laws that regulate the misuse of narcotics, namely Law No. 35 of 2009 and Law No. 5 of 1997. All of them are clear about the sanctions and dangers of using narcotics, the punishment can even be death. This service journal refers to biological theory which explains the biological theory of the brain, metabolic imbalance theory, and genetic theory. Many experts, especially biological experts, say that narcotics will damage brain growth and development. This service journal uses literature and seminar methods which are expected to provide an explanation of a situation where an individual or person will have a bleak future if they fall into the use of narcotics because it will damage brain tissue and damage the body. As early as possible, we will unite together to fight against narcotics, not only for law officers who work, but all elements of society are involved in fighting the use of narcotics which has penetrated young people, especially among teenagers who are still at school, who are vulnerable to the temptation of using narcotics.