In an effort to expand the domain of mathematical chemistry and inspire research beyond the realms of graph theory and quantum chemistry, we explore five mathematical chemistry spaces and their interconnectedness. These spaces comprise the chemical space, which encompasses substances and reactions; the space of reaction conditions, spanning the physical and chemical aspects involved in chemical reactions; the space of reaction grammars, which encapsulates the rules for creating and breaking chemical bonds; the space of substance properties, covering all documented measurements regarding substances; and the space of substance representations, composed of the various ontologies for characterising substances.

Understanding the ecological and evolutionary dynamics of populations is critical for both basic and applied purposes in a variety of biological contexts. Although several modeling frameworks have been developed to simulate eco-evolutionary dynamics, many fewer address how to model structured populations. In a prior paper, we put forth the first modeling approach to simulate eco-evolutionary dynamics in structured populations under the G function modeling framework. However, this approach does not allow for accurate simulation under fluctuating environmental conditions. To address this limitation, we draw on the study of periodic differential equations to propose a modified approach that uses a different definition of fitness more suitable for fluctuating environments. We illustrate this method with a simple toy model of life history trade-offs. The generality of this approach allows it to be used in a variety of biological contexts.

In recent discussions, the widespread conviction that scientific individuation practices are governed by theories and concepts of biological individuality has been challenged, particularly by advocates of practice-based approaches. This discussion raises questions about the relationship between individuation practices and concepts of individuality. In this paper, I discuss four studies of host-parasite systems and analyze the respective individuation practices to see whether they correspond to established concepts of biological individuality. My analysis suggests that scientists individuate biological systems on different levels of organization and that the researchers' respective emphasis on one of the levels depends on the explanandum and research context as well as epistemic aims and purposes. It thus makes sense to use different concepts of individuality to account for different individuation practices. However, not all individuation practices are represented equally well by concepts of biological individuality. To account for this observation, I propose that concepts of individuality should be understood as abstracted, idealized, or simplified models that represent only certain aspects of scientific practice. A modeling account suggests a pluralistic view of concepts of biological individuality that not only allows the coexistence of different kinds of individuality (e.g., evolutionary individuality, immunological individuality, ecological individuality) but also of normative and descriptive concepts.

A fundamental problem in biology is how cells obtain the reproducible, coherent phenotypes needed for natural selection to act or, put differently, how cells manage to limit their exploration of the vastness of phenotype space. A subset of this problem is how they regulate their cell cycle. Bacteria, like eukaryotic cells, are highly structured and contain scores of hyperstructures or assemblies of molecules and macromolecules. The existence and functioning of certain of these hyperstructures depend on phase transitions. Here, I propose a conceptual framework to facilitate the development of water-clock hypotheses in which cells use water to generate phenotypes by living 'on the edge of phase transitions'. I give an example of such a hypothesis in the case of the bacterial cell cycle and show how it offers a relatively novel 'view from here' that brings together a range of different findings about hyperstructures, phase transitions and water and that can be integrated with other hypotheses about differentiation, metabolism and the origins of life.

The conflict between individual and collective interests makes fostering cooperation in human societies a challenging task, requiring drastic measures such as the establishment of sanctioning institutions. These institutions are costly because they have to be maintained regardless of the presence or absence of offenders. Here, we revisit some improvements to the standard N-person prisoner's dilemma formulation with institutional punishment in a well-mixed population, namely the elimination of overpunishment, the requirement of a minimum number of contributors to establish the sanctioning institution, and the sharing of its maintenance costs once this minimum number is reached. In addition, we focus on large groups or communities for which sanctioning institutions are ubiquitous. Using the replicator equation framework for an infinite population, we find that by sufficiently fining players who fail to contribute either to the public good or to the sanctioning institution, a population of contributors immune to invasion by these free riders can be established, provided that the contributors are sufficiently numerous. In a finite population, we use finite-size scaling to show that, for some parameter settings, demographic noise helps to fixate the strategy that contributes to the public good but not to the sanctioning institution even for infinitely large populations when, somewhat counterintuitively, its proportion in the initial population vanishes with a small power of the population size.

The tumor microenvironment constitutes a complex system shaped by the intricate interactions among tumor cells, immune cells, and cytokines. Within this environment, the interplay between immune cells and cytokines is crucial in influencing tumor growth and progression. Despite advancements in clinical tumor immunotherapy, there remains a gap in comprehensive simulations of tumor immune responses, particularly regarding cytokine-driven processes. This study aims to address this gap by investigating the regulatory interactions among tumor cells, immune cells, and cytokines to simulate the complexities of tumor immunotherapy. We develop a comprehensive modeling and computational framework incorporating PD-1 inhibitors and interleukin-10 (IL-10) antibodies. Through detailed mathematical analysis, we elucidate the impact of changes in the immune microenvironment on tumor cells number. Our findings highlight the significant therapeutic effect of anti-PD-1 and IL-10 inhibitors, with increased drug dosage correlating with a reduction in tumor burden. Furthermore, combination therapy demonstrates a marked extension of survival with reduced dosages compared to monotherapy. Based on model simulations, we proposed prognostic predictions by assessing the microenvironmental status before treatment. The findings indicate a promising method for enhancing treatment effectiveness and offering potential advantages to patients receiving tumor immunotherapy.

Herbal medicines are frequently blended in the form of multi-drug combinations primarily based on the precept of medicinal compatibility, to achieve the purpose of treating diseases. However, due to the lack of appropriate techniques and the multi-component and multi-target nature of Chinese medicine compounding, it is tough to explain how the drugs interact with each other. As a rising discipline, cyber pharmacology has formed a new approach characterized by using holistic and systematic "network targets" via the cross-fertilization of computer technology, bioinformatics, and different multidisciplinary disciplines. It can broadly screen the active ingredients of traditional Chinese medicine, enhance the effective utilization of drugs, and elucidate the mechanism of drug action. We will overview the principles of Chinese medicine compounding and dispensing, the research methods of network pharmacology, and the software of network pharmacology in the lookup of compounded Chinese medicines, aiming to supply thoughts for the better application of network pharmacology in the research of Chinese medicines.

The F-ATPase enzyme is the smallest-known molecular motor that rotates in 120° steps, driven by the hydrolysis of ATP. It is a multi-subunit enzyme that contains three catalytic sites. A central question is how the elementary chemical reactions that occur in the three sites are coupled to mechanical rotation. Various models and coupling schemes have been formulated in an attempt to answer this question. They can be classified as 2-site (bi-site) models, exemplified by Boyer's binding change mechanism first proposed 50 years ago, and 3-site (tri-site) models such as Nath's torsional mechanism, first postulated 25 years ago and embellished 1 year back. Experimental data collated using diverse approaches have conclusively shown that steady-state ATP hydrolysis by F-ATPase occurs in tri-site mode. Hence older models have been continually modified to make them conform to the new facts. Here, we have developed a pure mathematical approach based on combinatorics and conservation laws to test if proposed models are 2-site or 3-site. Based on this novel combinatorial approach, we have proved that older and modified models are effectively bi‒site models in that catalysis and rotation in F-ATPase occurs in these models with only two catalytic sites occupied by bound nucleotide. Hence these models contradict consensus experimental data. The recent 2023 model of ATP hydrolysis by F-ATPase has been proved to be a true tri-site model based on our novel mathematical approach. Such pure mathematical proofs constitute an important step forward for ATP mechanism. However, in what must be considered an aspect with great scientific potential, the power of such mathematical proofs has not been fully exploited to solve molecular biological problems, in our opinion. We believe that the creative application of pure mathematical proofs (for another example see Nath in Theory Biosci 141:249-260, 2022) can help resolve with finality various longstanding molecular-level issues that arise as a matter of course in the analysis of fundamental biological problems. Such issues have proved extraordinarily difficult to resolve by standard experimental, theoretical, or computational approaches.

The phenomenon of near death and dying experiences has been both of popular interest and of scientific speculation. However, the reality of mental perception at the point of death is currently a subjective experience and has not been formally evaluated. While postmortem gene expression, even in humans, has been evaluated, restoration of postmortem brain activity has heretofore only been attempted in animal models, at the molecular and cellular levels. Meanwhile, progress has been made to translate brain activity of living humans into speech and images. This paper proposes two inter-related thought experiments. First, assuming progress and refinement of the technology of translating human brain activity into interpretable speech and images, can an objective analysis of death experiences be obtained by utilizing these technologies on dying humans? Second, can human brain function be revived postmortem and, if so, can the relevant technologies be utilized for communication with (recently) deceased individuals? In this paper, these questions are considered and possible implications explored.

Until the mid-nineteenth century, "physiology" was a comprehensive theory of life, expounded and shaped by Johannes P. Müller (1801-1858). Biologists and medical doctors still refer to him today. In the summer term of 1851, Müller gave a lecture on the Comparative Anatomy of animals. This lecture was attended and recorded by Ernst Zeller (1830-1902), a future physician and zoologist, and has recently been published together with a German transcript. In this paper, we situate Johannes Müller within the intellectual history of his time. Through his "empirical idealism," we show how he opposed the speculative tendencies of the romantic understanding of nature, the emerging evolutionism, and the growing splits in the natural sciences. Müller focused on recognizing living nature as a whole and realizing ideal "phenomena" through his empirical research. He considered the notion of the soul of the world. Müller's lecture transcript serves as a poignant testament to German scientific culture in the mid-nineteenth century, a few years before the publication of Darwin's Origin of Species. It also provides valuable insights into the self-contained epistemological foundations of morphology.

Cervical cancer is one of the most severe threats to women worldwide and holds fourth rank in lethality. It is estimated that 604, 127 cervical cancer cases have been reported in 2020 globally. With advancements in high throughput technologies and bioinformatics, several cervical candidate genes have been proposed for better therapeutic strategies. In this paper, we intend to prioritize the candidate genes that are involved in cervical cancer progression through a fractal time series-based cross-correlations approach. we apply the chaos game representation theory combining a two-dimensional multifractal detrended cross-correlations approach among the known and candidate genes involved in cervical cancer progression to prioritize the candidate genes. We obtained 16 candidate genes that showed cross-correlation with known cancer genes. Functional enrichment analysis of the candidate genes shows that they involve GO terms: biological processes, cell-cell junction assembly, cell-cell junction organization, regulation of cell shape, cortical actin cytoskeleton organization, and actomyosin structure organization. KEGG pathway analysis revealed genes' role in Rap1 signaling pathway, ErbB signaling pathway, MAPK signaling pathway, PI3K-Akt signaling pathway, mTOR signaling pathway, Acute myeloid leukemia, chronic myeloid leukemia, Breast cancer, Thyroid cancer, Bladder cancer, and Gastric cancer. Further, we performed survival analysis and prioritized six genes CDH2, PAIP1, BRAF, EPB41L3, OSMR, and RUNX1 as potential candidate genes for cervical cancer that has a crucial role in tumor progression. We found that our study through this integrative approach an efficient tool and paved a new way to prioritize the candidate genes and these genes could be evaluated experimentally for potential validation. We suggest this may be useful in analyzing the nucleotide sequences and protein sequences for clustering, classification, class affiliation, etc.

The definition, origin and recreation of life remain elusive. As others have suggested, only once we put life into reductionist physical terms will we be able to solve those questions. To that end, this work proposes the phenomenon of life to be the product of two dissipative mechanisms. From them, one characterises extant biological life and deduces a testable scenario for its origin. The proposed theory of life allows its replication, reinterprets ecological evolution and creates new constraints on the search for life.

The multilevel model of behavioral selection (MLBS) by Borgstede and Eggert (Behav Process 186:104370. 10.1016/j.beproc.2021.104370 , 2021) provides a formal framework that integrates reinforcement learning with natural selection using an extended Price equation. However, the MLBS is so far only formulated for homogeneous populations, thereby excluding all sources of variation between individuals. This limitation is of primary theoretical concern because any application of the MLBS to real data requires to account for variation between individuals. In this paper, I extend the MLBS to account for inter-individual variation by dividing the population into homogeneous sub-populations and including class-specific reproductive values as weighting factors for an individual's evolutionary fitness. The resulting formalism closes the gap between the theoretical underpinnings of behavioral selection and the application of the theory to empirical data, which naturally includes inter-individual variation. Furthermore, the extended MLBS is used to establish an explicit connection between the dynamics of learning and the maximization of individual fitness. These results expand the scope of the MLBS as a general theoretical framework for the quantitative analysis of learning and evolution.

We consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of neurons, which Green's function does not. Through a dynamic bifurcation analysis, we give explicit bifurcation conditions. Hopf bifurcations lead to temporally non-constant, but spatially constant solutions, but Turing-Hopf bifurcations generate spatially and temporally non-constant solutions, in particular, traveling waves. Bifurcation parameters are the coefficient of the exponential temporal kernel, the transmission speed of neural signals, the time delay rate of synapses, and the ratio of excitatory to inhibitory synaptic weights.

In this paper, we investigate the asymptotic behavior of a modified chemostat model. We first demonstrate the existence of equilibria. Then, we present a mathematical analysis for the model, the invariance, the positivity, the persistence of the solutions, and the asymptotic global stability of the interior equilibrium. Some numerical simulations are carried out to illustrate the main results.

The present study provides new insight into the key aspects of the early formative period of the ecosystem concept in aquatic ecology. Raymond Lindeman's trophodynamics is known to be a starting point for the development of the modern concept of ecosystem. The trophodynamic approach in ecology was proposed by Lindeman in his widely cited paper of 1942. Lindeman's views are analyzed in comparison with the contemporary production studies in aquatic ecology. It is shown that a similar theoretical system has been proposed in the USSR at the end of the 1930s by Georgiy G. Vinberg. He introduced the concept of biotic balance based on the wide appraisal of the dark and light bottles method. The study shows that both Lindeman's trophodynamics and Vinberg's concept of biotic balance relied on an energy-based approach in considering the wholeness of a water body. The two scientists, however, differed in several important aspects concerning the interpretation of the role of living organisms. The holistic interpretation of ecosystem by Lindeman and Vinberg can be seen as part of the dilemma between physicalism and organicism. At the same time, the main emphasis in the concepts of both Vinberg and Lindemann was on the primary production component, a feature that was common to the first holistic systems in production hydrobiology (e.g., E. Naumann's regional limnology). It is clear that modern problems of aquatic ecology should be addressed from the perspective of the organismocentric understanding of the ecosystem, but undoubtedly at the new level of development of this view.

This study proposes a landscape-based scenario for the origin of viruses and cells, focusing on the adaptability of preexisting replicons from the RNP (ribonucleoprotein) world. The scenario postulates that life emerged in a subterranean "warm little pond" where organic matter accumulated, resulting in a prebiotic soup rich in nucleotides, amino acids, and lipids, which served as nutrients for the first self-replicating entities. Over time, the RNA world, followed by the RNP world, came into existence. Replicators/replicons, along with the nutritious soup from the pond, were washed out into the river and diluted. Lipid bubbles, enclosing organic matter, provided the last suitable environment for replicons to replicate. Two survival strategies emerged under these conditions: cell-like structures that obtained nutrients by merging with new bubbles, and virus-like entities that developed various techniques to transmit themselves to fresh bubbles. The presented hypothesis provides the possibility for the common origin of cells and viruses on rocky worlds hosting liquid water, like Earth.

In 1913, the geneticist William Bateson called for a halt in studies of genetic phenomena until evolutionary fundamentals had been sufficiently addressed at the molecular level. Nevertheless, in the 1960s, the theoretical population geneticists celebrated a "modern synthesis" of the teachings of Mendel and Darwin, with an exclusive role for natural selection in speciation. This was supported, albeit with minor reservations, by historians Mark Adams and William Provine, who taught it to generations of students. In subsequent decades, doubts were raised by molecular biologists and, despite the deep influence of various mentors, Adams and Provine noted serious anomalies and began to question traditional "just-so-stories." They were joined in challenging the genetic orthodoxy by a scientist-historian, Donald Forsdyke, who suggested that a "collective variation" postulated by Darwin's young research associate, George Romanes, and a mysterious "residue" postulated by Bateson, might relate to differences in short runs of DNA bases (oligonucleotides). The dispute between a small network of historians and a large network of geneticists can be understood in the context of national politics. Contrasts are drawn between democracies, where capturing the narrative makes reversal difficult, and dictatorships, where overthrow of a supportive dictator can result in rapid reversal.

Mathematical models of cancer and bacterial evolution have generally stemmed from a gene-centric framework, assuming clonal evolution via acquisition of resistance-conferring mutations and selection of their corresponding subpopulations. More recently, the role of phenotypic plasticity has been recognized and models accounting for phenotypic switching between discrete cell states (e.g., epithelial and mesenchymal) have been developed. However, seldom do models incorporate both plasticity and mutationally driven resistance, particularly when the state space is continuous and resistance evolves in a continuous fashion. In this paper, we develop a framework to model plastic and mutational mechanisms of acquiring resistance in a continuous gradual fashion. We use this framework to examine ways in which cancer and bacterial populations can respond to stress and consider implications for therapeutic strategies. Although we primarily discuss our framework in the context of cancer and bacteria, it applies broadly to any system capable of evolving via plasticity and genetic evolution.

A two-patch logistic metapopulation model is investigated both analytically and numerically focusing on the impact of dispersal on population dynamics. First, the dependence of the global dynamics on the stability type of the full extinction equilibrium point is tackled. Then, the behaviour of the total population with respect to the dispersal is studied analytically. Our findings demonstrate that diffusion plays a crucial role in the preservation of both subpopulations and the full metapopulation under the presence of stochastic perturbations. At low diffusion, the origin is a repulsor, causing the orbits to flow nearly parallel to the axes, risking stochastic extinctions. Higher diffusion turns the repeller into a saddle point. Orbits then quickly converge to the saddle's unstable manifold, reducing extinction chances. This change in the vector field enhances metapopulation robustness. On the other hand, the well-known fact that asymmetric conditions on the patches is beneficial for the total population is further investigated. This phenomenon has been studied in previous works for large enough or small enough values of the dispersal. In this work, we complete the theory for all values of the dispersal. In particular, we derive analytically a formula for the optimal value of the dispersal that maximizes the total population.