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Advanced undergraduate chemistry students can be introduced to or gain some experience with thermogravimetric analyzers while comparing the reactivities, and empirical behavior of three carbon allotropes. The experiment involves the thermal analysis of C60, graphite and diamond. Students learn some of the fascinating properties of C60 while also discovering that C60 significantly differs in behavior from the other two allotropes, which have similar behaviors.

The paper is focused on sensitivity analysis of large-scale models of biological systems that describe dynamics of the so called signaling pathways. These systems are continuous in time but their models are based on discrete-time measurements. Therefore, if sensitivity analysis is used as a tool supporting model development and evaluation of its quality, it should take this fact into account. Such models are usually very complex and include many parameters difficult to estimate in an experimental way. Changes of many of those parameters have little effect on model dynamics, and therefore they are called sloppy. In contrast, other parameters, when changed, lead to substantial changes in model responses and these are called stiff parameters. While this is a well-known fact, and there are methods to discern sloppy parameters from the stiff ones, they have not been utilized, so far, to create parameter rankings and quantify the influence of single parameter changes on system time responses. These single parameter changes are particularly important in analysis of signalling pathways, because they may pinpoint parameters, associated with the processes to be targeted at the molecular level in laboratory experiments. In the paper we present a new, original method of creating parameter rankings, based on an Hessian of a cost function which describes the fit of the model to a discrete experimental data. Its application is explained with simple dynamical systems, representing two typical dynamics exhibited by the signaling pathways.

The paper presents a review of models that can be used to describe dynamics of lung cancer growth and its response to treatment at both cell population and intracellular processes levels. To address the latter, models of signaling pathways associated with cellular responses to treatment are overviewed. First, treatment options for lung cancer are discussed, and main signaling pathways and regulatory networks are briefly reviewed. Then, approaches used to model specific therapies are discussed. Following that, models of intracellular processes that are crucial in responses to therapies are presented. The paper is concluded with a discussion of the applicability of the presented approaches in the context of lung cancer.

Background: Non-small cell lung cancer (NSCLC) is the most common type of lung cancer, and the median overall survival (OS) is approximately 2-3 years among patients with stage III disease. Furthermore, it is one of the deadliest types of cancer globally due to non-specific symptoms and the lack of a biomarker for early detection. The most important decision that clinicians need to make after a lung cancer diagnosis is the selection of a treatment schedule. This decision is based on, among others factors, the risk of developing metastasis., Methods: A cohort of 115 NSCLC patients treated using chemotherapy and radiotherapy (RT) with curative intent was retrospectively collated and included patients for whom positron emission tomography/computed tomography (PET/CT) images, acquired before RT, were available. The PET/CT images were used to compute radiomic features extracted from a region of interest (ROI), the primary tumor. Radiomic and clinical features were then classified to stratify the patients into short and long time to metastasis, and regression analysis was used to predict the risk of metastasis., Results: Classification based on binarized metastasis-free survival (MFS) was applied with moderate success. Indeed, an accuracy of 0.73 was obtained for the selection of features based on the Wilcoxon test and logistic regression model. However, the Cox regression model for metastasis risk prediction performed very well, with a concordance index (C-index) score equal to 0.84., Conclusions: It is possible to accurately predict the risk of metastasis in NSCLC patients based on radiomic features. The results demonstrate the potential use of features extracted from cancer imaging in predicting the risk of metastasis., Competing Interests: Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://tlcr.amegroups.com/article/view/10.21037/tlcr-23-60/coif). The authors have no conflicts of interest to declare., (2023 Translational Lung Cancer Research. All rights reserved.)

Regulatory networks structure and signaling pathways dynamics are uncovered in time- and resource consuming experimental work. However, it is increasingly supported by modeling, analytical and computational techniques as well as discrete mathematics and artificial intelligence applied to to extract knowledge from existing databases. This review is focused on mathematical modeling used to analyze dynamics and robustness of these networks. This paper presents a review of selected modeling methods that facilitate advances in molecular biology., (© 2023 The Authors.)

Mathematical modeling of signaling pathways and regulatory networks has been supporting experimental research for some time now. Sensitivity analysis, aimed at finding model parameters whose changes yield significantly altered cellular responses, is an important part of modeling work. However, sensitivity methods are often directly transplanted from analysis of technical systems, and thus, they may not serve the purposes of analysis of biological systems. This paper presents a novel sensitivity analysis method that is particularly suited to the task of searching for potential molecular drug targets in signaling pathways. Using two sample models of pathways, p53/Mdm2 regulatory module and IFN-β-induced JAK/STAT signaling pathway, we show that the method leads to biologically relevant conclusions, identifying processes suitable for targeted pharmacological inhibition, represented by the reduction of kinetic parameter values. That, in turn, facilitates subsequent search for active drug components.

Intracellular processes are cascades of biochemical reactions, triggered in response to various types of stimuli. Mathematical models describing their dynamics have become increasingly popular in recent years, as tools supporting experimental work in analysis of pathways and regulatory networks. Not only do they provide insights into general properties of these systems, but also help in specific tasks, such as search for drug molecular targets or treatment protocols. Different tools and methods are used to model complex biological systems. In this work, we focus on ordinary differential equations (ODEs) and Petri nets. We consider specific methods of analysis of such models, i.e., sensitivity analysis (SA) and significance analysis. So far, they have been applied separately, with different goals. In this paper, we show that they can complement each other, combining the sensitivity of ODE models and the significance analysis of Petri nets. The former is used to find parameters, whose change results in the greatest quantitative and qualitative changes in the model response, while the latter is a structural analysis and allows indicating the most important subprocesses in terms of information flow in Petri net. Ultimately, both methods facilitate finding the essential processes in a given signaling pathway or regulatory network and may be used to support medical therapy development. In the paper, the use of dual modeling is illustrated with an example of ATM/p53/NF-[Formula: see text]B pathway. Each method was applied to analyze this system, resulting in finding different subsets of important processes that might be prospective targets for changing this system behavior. While some of the processes were indicated in each of the approaches, others were found by one method only and would be missed if only that method was applied. This leads to the conclusion about the complementarity of the methods under investigation. The dual modeling approach of comprehensive structural and parametric analysis yields results that would not be possible if these two modeling approaches were applied separately. The combined approach, proposed in this paper, facilitates finding not only key processes, with which significant parameters are associated, but also significant modules, corresponding to subsystems of regulatory networks. The results provide broader insight into therapy targets in diseases in which the natural control of intracellular processes is disturbed, leading to the development of more effective therapies in medicine., (© 2022. The Author(s).)

This paper deals with development of signaling pathways models and using plasmid-based experiments to support parameter estimation. We show that if cells transfected with plasmids are used in experiments, the models should include additional components that describe explicitly effects induced by plasmids. Otherwise, when the model is used to analyze responses of wild type, i.e. non-transfected cells, it may not capture their dynamics properly or even lead to false conclusions. In order to illustrate this, an original mathematical model of miRNA-mediated control of gene expression in the NFκB pathway is presented. The paper shows what artifacts might appear due to experimental procedures and how to develop the models in order to avoid pursuing these artifacts instead of real kinetics.

Background: Epigenetic regulation contributes to many important processes in biological cells. Examples include developmental processes, differentiation and maturation of stem cells, evolution of malignancy and other. Cell cycle regulation has been subject of mathematical modeling by a number of authors that resulted in many interesting models and application of analytic techniques ranging from stochastic processes to partial differential equations and to integral, functional and operator equations. In this paper we address the question of how the regulation of protein contents influences the long-term dynamics of the population. To accomplish this, we follow the philosophy of a 1984 model by Kimmel et al., but adjust the details to fit the experimental data on protein PRC1 from a more recent paper., Results: We built a model of cell cycle dynamics of the PRC1 and fitted it to the data made available by Cohen and his co-authors. We have run the model for a large number of cell generations, recording the PRC1 contents in all cells of the resulting pedigree, at constant time intervals. During cell division the PRC1 is unequally divided between daughter cells. The picture emerging from simulations of Data set 1 is that of a very well-tuned regulatory circuit that provides a stable distribution of PRC1 contents and interdivision times. Data set 2 seems qualitatively different, with more variation in cell cycle duration., Conclusions: The main question we address is whether the regulatory feedbacks deduced from single cell cycle data provide epigenetic regulation of cell characteristics in long run. PRC1 is a good candidate because of its role in setting timing of division. Findings of the current paper include tight regulation of the cell cycle (particularly the timing of the cell cycle) even that PRC1 is only one of the players in cell dynamics. Understanding that association, even close, does not necessarily imply causation, we consider this an interesting and important result.

We review a large volume of literature concerning mathematical models of cancer therapy, oriented towards optimization of treatment protocols. The review, although partly idiosyncratic, covers such major areas of therapy optimization as phase-specific chemotherapy, antiangiogenic therapy and therapy under drug resistance. We start from early cell cycle progression models, very simple but admitting explicit mathematical solutions, based on methods of control theory. We continue with more complex models involving evolution of drug resistance and pharmacokinetic and pharmacodynamic effects. Then, we consider two more recent areas: angiogenesis of tumors and molecular signaling within and among cells. We discuss biological background and mathematical techniques of this field, which has a large although only partly realized potential for contributing to cancer treatment.

Motivation: Interferon-beta induced JAK-STAT signaling pathways contribute to mucosal immune recognition and an anti-viral state. Though the main molecular mechanisms constituting these pathways are known, neither the detailed structure of the regulatory network, nor its dynamics has yet been investigated. The objective of this work is to build a mathematical model for the pathway that would serve two purposes: (1) to reproduce experimental results in simulation of both early and late response to Interferon-beta stimulation and (2) to explain experimental phenomena generating new hypotheses about regulatory mechanisms that cannot yet be tested experimentally., Results: Experimentally determined time dependent changes in the major components of this pathway were used to build a mathematical model describing pathway dynamics in the form of ordinary differential equations. The experimental results suggested existence of unknown negative control mechanisms that were tested numerically using the model. Together, experimental and numerical data show that the epithelial JAK-STAT pathway might be subjected to previously unknown dynamic negative control mechanisms: (1) activation of dormant phosphatases and (2) inhibition of nuclear import of IRF1.

This paper presents analysis and biomedical implications of a certain class of bilinear systems that can be applied in modeling of cancer chemotherapy. It combines models that so far have been studied separately, taking into account both the phenomenon of gene amplification and drug specificity in chemotherapy in their different aspects. The methodology of analysis of such models, based on system decomposition, is discussed. The mathematical description is given by an infinite dimensional state equation with a system matrix, the form of which allows decomposing the model into two interacting subsystems. While the first one, of a finite dimension, can have any form, the second one is infinite-dimensional and tridiagonal. Then the optimal control problem is defined in l1 space. To derive necessary conditions for optimal control, the model description is transformed into an integrodifferential one.

Langmuir-Blodgett (LB) films of copper (II) 1,4,8,11,15,18,22,25-octabutoxyphthalocyanine, nCuPc(OBu)(8), (non-peripheral substitution) and copper (II) 2,3,9,10,16,17,23,24-octabutoxyphthalocyanine, pCuPc(OBu)(8), (peripheral substitution), were fabricated and characterized by optical spectroscopy and scanning probe microscopy. The LB films were transferred onto hydrophilic substrates by vertical dipping. Although they posses relatively short polar substituents both compounds form smooth, uniform, dense, and highly stable LB monolayers composed of linear arrays of cofacial oligomers. The long range discotic assemblies of LB and spun cast films of pCuPc(OBu)(8) and nCuPc(OBu)(8) posses physical and chemical properties favorable for molecular electronic device application.

Radiolytic reduction at 77 K of oxo/hydroxo-bridged dinuclear iron(III) complexes in frozen solutions forms kinetically stabilized, mixed-valent species in high yields that model the mixed-valent sites of non-heme, diiron proteins. The mixed-valent species trapped at 77 K retain ligation geometry similar to the initial diferric clusters. The shapes of the mixed-valent EPR signals depend strongly on the bridging ligands. Spectra of the Fe(II)OFe(III) species reveal an S = 1/2 ground state with small g-anisotropy as characterized by the uniaxial component (gz-gav/2 < 0.03) observable at temperatures as high as approximately 100 K. In contrast, hydroxo-bridged mixed-valent species are characterized by large g-anisotropy (gz-gav/2 > 0.03) and are observable only below 30 K. Annealing at higher temperatures causes structural relaxation and changes in the EPR characteristics. EPR spectral properties allow the oxo- and hydroxo-bridged, mixed-valent diiron centers to be distinguished from each other and can help characterize the structure of mixed-valent centers in proteins.