Law Of Mass Action Research Articles

Additive multiple contacts and saturation phenomena in epidemiological models are not detected by $R_0$

Many infections are transmitted by direct contacts. Usually one single direct contact is needed to transmit the required minimum infectious load. Most models describe contagions by single contacts using a term of the type mass action law. However, modelling infections that are transmitted after the susceptible individual had contact with several sources of infection requires more than mass action law terms. We call additive multiple contacts those that do not produce infection by themselves, but can produce infection if they happen simultaneously. We are interested in understanding the role played by R0 missing the mark in infections in which the minimum infectious load is reached not only by single contacts but also by additive multiple contacts. We propose different mathematical models describing not only infections by one single contact but also by additive multiple contacts. We show all models have the same value of R0, but correspond to different epidemiological mechanisms. Two models show contagions by additive multiple contacts and a third one shows reduction of infections by some saturation process which is not captured by R0. This shows that trying to control the epidemics by controlling R0 could be unsufficient or in some cases waste resources.

A Study on the Pyrolysis Behavior and Product Evolution of Typical Wood Biomass to Hydrogen-Rich Gas Catalyzed by the Ni-Fe/HZSM-5 Catalyst

The thermo-chemical conversion of biomass wastes is a practical approach for the value-added reclamation of bioenergy in large quantities, and pyrolysis plays a core role in this process. In this work, poplar (PR) and cedar (CR) were used as staple wood biomasses to investigate the apparent kinetics of TG/DTG at different heating rates. Secondly, miscellaneous wood chips (MWC), in which PR and CR were mixed in equal proportion, were subjected to comprehensive investigations on their pyrolysis behavior and product evolution in a fixed bed reactor with pyrolysis temperature, catalyst, and the flow rate H2O steam as influencing factors. The results demonstrated that both PR and CR underwent three consecutive pyrolysis stages, the TG/DTG curves shifted to higher temperatures, and the peak temperature intervals also enhanced as the heating rate increased. The kinetic compensation effect expression and apparent reaction kinetic model of CR and PR pyrolysis were obtained based on the law of mass action and the Arrhenius equation; the reaction kinetic parameter averages of Ea and A of its were almost the same, which were about 72.38 kJ/mol and 72.36 kJ/mol and 1147.11 min−1 and 1144.39 min−1, respectively. The high temperature was beneficial for the promotion of the pyrolysis of biomass, increased pyrolysis gas yield, and reduced tar yield. This process was strengthened in the presence of the catalyst, thus significantly increasing the yield of hydrogen-rich gas to 117.9 mL/g-biomass. It was observed that H2O steam was the most effective activator for providing a hydrogen source for the whole reaction process, promoted the reaction to proceed in the opposite direction of H2O steam participation, and was beneficial to the production of H2 and other hydrocarbons. In particular, when the flow rate of H2O steam was 1 mL/min, the gas yield and hydrogen conversion were 76.94% and 15.90%, and the H2/CO was 2.07. The yields of H2, CO, and CO2 in the gas formation were significantly increased to 107.35 mL/g-biomass, 53.70 mL/g-biomass, and 99.31 mL/g-biomass, respectively. Therefore, H2 was the most dominant species among gas products, followed by C-O bond-containing species, which provides a method for the production of hydrogen-rich gas and also provides ideas for compensating or partially replacing the fossil raw material for hydrogen production.

Evaluating the human neurotoxicity and toxicological interactions impact of co-occurring regulated and emerging mycotoxins

Mycotoxins can inflict harmful effects on diverse organs, and mounting evidence indicates their potential involvement in human neurodegenerative diseases. Given the common occurrence of these toxins in food, there is an increasing demand for a comprehensive assessment of their combined toxicity to enhance our understanding of their potential hazards. This research investigates mycotoxin exposure from widely consumed cereal-based products, including enniatin B (ENNB), sterigmatocystin (STG), aflatoxin B1 (AFB1), cyclopiazonic acid (CPZ), citrinin (CIT), and ochratoxin A (OTA). Employing the median-effect equation based on Chou and Talalay's mass-action law, we assessed their cytotoxicity in human SH-SY5Y neuronal cells. Notably, ENNB displayed the highest neurotoxicity (IC50 = 3.72 µM), followed by OTA (9.10 µM) and STG (9.99 µM). The combination of OTA + STG exhibited the highest toxicity (IC50 = 3.77 µM), while CPZ + CIT showed the least detrimental effect. Approximately 70 % of tested binary combinations displayed synergistic or additive effects, except for ENNB + STG, ENNB + AFB1, and CPZ + CIT, which showed antagonistic interactions. Intriguingly, the senary combination displayed moderate antagonism at the lowest exposure and moderate synergism at higher doses. OTA exhibited predominantly synergistic interactions, comprising approximately 90 %, a noteworthy finding considering its prevalence in food. Conversely, ENNB interactions tended to be antagonistic. The most remarkable synergy occurred in the STG and CIT combination, enabling a 50-fold reduction in CIT dosage for an equivalent toxic effect. These findings highlight the biological relevance of robust synergistic interactions, emphasizing the need to assess human exposure hazards accurately, particularly considering frequent mycotoxin co-occurrence in environmental and food settings.

Application of Machine Learning in the Quantitative Analysis of the Surface Characteristics of Highly Abundant Cytoplasmic Proteins: Toward AI-Based Biomimetics.

Proteins in the crowded environment of human cells have often been studied regarding nonspecific interactions, misfolding, and aggregation, which may cause cellular malfunction and disease. Specifically, proteins with high abundance are more susceptible to these issues due to the law of mass action. Therefore, the surfaces of highly abundant cytoplasmic (HAC) proteins directly exposed to the environment can exhibit specific physicochemical, structural, and geometrical characteristics that reduce nonspecific interactions and adapt to the environment. However, the quantitative relationships between the overall surface descriptors still need clarification. Here, we used machine learning to identify HAC proteins using hydrophobicity, charge, roughness, secondary structures, and B-factor from the protein surfaces and quantified the contribution of each descriptor. First, several supervised learning algorithms were compared to solve binary classification problems for the surfaces of HAC and extracellular proteins. Then, logistic regression was used for the feature importance analysis of descriptors considering model performance (80.2% accuracy and 87.6% AUC) and interpretability. The HAC proteins showed positive correlations with negatively and positively charged areas but negative correlations with hydrophobicity, the B-factor, the proportion of beta structures, roughness, and the proportion of disordered regions. Finally, the details of each descriptor could be explained concerning adaptative surface strategies of HAC proteins to regulate nonspecific interactions, protein folding, flexibility, stability, and adsorption. This study presented a novel approach using various surface descriptors to identify HAC proteins and provided quantitative design rules for the surfaces well-suited to human cellular crowded environments.

A chemical kinetics theory for interpreting the non-monotonic temperature dependence of enzymatic reactions

Abstract. One notable observation of enzymatic chemical reactions is that, for a given abundance of enzymes and substrates, temperature increases cause reaction rates to first increase consistent with the Arrhenius relationship, then plateau, and finally fall off quickly to zero at high temperatures. While many mathematical functions have been used to describe this pattern, we here propose a chemical kinetics theory which successfully replicates this observation and provides insights into the processes responsible for these dynamics. The chemical kinetics theory combines the law of mass action, von Smoluchowski's diffusion-limited chemical reaction theory, and Eyring's transition state theory. This new theory reveals that the thermally reversible enzyme denaturation ensured by the ceaseless thermal motion of molecules and ions in an enzyme solution explains the plateau and subsequent decrease in chemical reaction rates with increasing temperature. The temperature-dependent affinity parameter (K) that relates enzymes and substrates through their binding also affects the shape of the emergent temperature response. We demonstrate that with an increase in substrate availability, K shifts the optimal temperature, where reaction rates plateau, towards higher values. Further, we show that the chemical kinetics theory accurately represents 12 sets of published enzyme assay data and includes the popular mechanistic model by Ratkowsky et al. (2005) as a special case. Given its good performance and solid theoretical underpinning, we believe this new theory will facilitate the construction of more mechanistic-based environmental biogeochemical models.

Unstable cores are the source of instability in chemical reaction networks

In biochemical networks, complex dynamical features such as superlinear growth and oscillations are classically considered a consequence of autocatalysis. For the large class of parameter-rich kinetic models, which includes generalized mass action kinetics and Michaelis–Menten kinetics, we show that certain submatrices of the stoichiometric matrix, so-called unstable cores, are sufficient for a reaction network to admit instability and potentially give rise to such complex dynamical behaviour. The determinant of the submatrix distinguishes unstable-positive feedbacks, with a single real-positive eigenvalue, and unstable-negative feedbacks without real-positive eigenvalues. Autocatalytic cores turn out to be exactly the unstable-positive feedbacks that are Metzler matrices. Thus there are sources of dynamical instability in chemical networks that are unrelated to autocatalysis. We use such intuition to design non-autocatalytic biochemical networks with superlinear growth and oscillations.

Optimal enzyme profiles in unbranched metabolic pathways.

How to optimize the allocation of enzymes in metabolic pathways has been a topic of study for many decades. Although the general problem is complex and nonlinear, we have previously shown that it can be solved by convex optimization. In this paper, we focus on unbranched metabolic pathways with simplified enzymatic rate laws and derive analytic solutions to the optimization problem. We revisit existing solutions based on the limit of mass-action rate laws and present new solutions for other rate laws. Furthermore, we revisit a known relationship between flux control coefficients and enzyme abundances in optimal metabolic states. We generalize this relationship to models with density constraints on enzymes and metabolites, and present a new local relationship between optimal reaction elasticities and enzyme amounts. Finally, we apply our theory to derive simple kinetics-based formulae for protein allocation during bacterial growth.

Abstract B014: The number analysis of digital data in Nature’s ecosystem: The unified general dynamics theory of “Unity of One” and its fractional distribution, action and interaction principle, and algorithms for computerized translational informatics

Abstract Nature’s ecosystem is governed by the physical and chemical principle of the mass-action law (MAL). The conventional classical specific aimed observation/statistics-based scientific R&D is considered a “Bottom-Up” approach. Here, this author introduces a new mathematical approach that established the MAL-unified general dynamics theory-based “Top-Down” algorithms of scientific translational, computerized simulation for Econo-green R&D. The new math approach evoked the general system analysis with sequential, pattern, combinatorial analysis, and mathematical induction and deduction, which is distinct from the aim-specific derivation of Michaelis-Menten, Henderson-Hasselbalch, Hill, Scatchard, and Langmuir theoretical equations. In short, the unified MAL-based biodynamics, pharmacodynamics, and bio-informatics (BD/PD/BI) include three general equations/algorithms for Unity of One Theory (UOT): (i) For action, the median-effect equation (MEE), also called the doctrine of the median (DOM), where the median-effect dose (Dm) is the universal reference of action potency and the dynamic-order (m) common-link in which m=1, >1, <1 indicates hyperbolic, sigmoidal and flat sigmoidal, respectively for dose-effect curves (DEC); (ii) For interaction, the combination-index equation (CIE), in which CI=1, <1, and >1 quantitatively indicates additive-effect, synergism, and antagonism, respectively; (iii) For the consequence of interaction, the dose-reduction index equation (DRIE), in which DRI=1, >1 and <1, digitally defines no-dose-reduction, favorable, and not favorable dose-reduction, respectively. The linearization of DECs with the MEE plot (MEP) led to the minimum two dose-data points theory (MTDPT), which provides efficient, cost-effective, Econo-green scientific R&D in biomedical sciences such as in molecules, cells, tissues, organs, whole body, and clinical protocol design and data analysis/simulation in the general R&D, in which 2 becomes 4, 3 become 5, and 4 becomes 6 dose-data points. The automatically added default two data points in the algorithm are dose zero and Dm-dose in all dynamic studies, designs, and dynamic simulations. The most important feature of the MAL-dynamics and informatics theory is that all mathematical terms of MEE, CIE, and DRIE are dimensionless relativity ratios, thus ensuring universal applicability regardless of units, physical states, and mechanisms. As of September 11, 2023, the MAL-BD/PD/CI/BI theory, algorithm, and computer software have been cited in over 1,550 scientific journals and 1,188 patents, indicating broad applications in scientific R&D and patent discovery. These citations encompass biomedical, agricultural, environmental, marine, physical, and food sciences. The effectors can be nanoparticles, molecules, chemicals, biologicals, radiation, UV, microwave, thermal, and photo effects, or their mix. Relevant details are available at HTTPS://www.combosyn.com; DOI:10.1016/j.jbc.2023.103419, and dx.doi.org/10.1124/jpet.122.185320. Citation Format: Ting-Chao Chou. The number analysis of digital data in Nature’s ecosystem: The unified general dynamics theory of “Unity of One” and its fractional distribution, action and interaction principle, and algorithms for computerized translational informatics [abstract]. In: Proceedings of the AACR Special Conference in Cancer Research: Translating Cancer Evolution and Data Science: The Next Frontier; 2023 Dec 3-6; Boston, Massachusetts. Philadelphia (PA): AACR; Cancer Res 2024;84(3 Suppl_2):Abstract nr B014.

The interaction of radiotherapy and dual inhibition of BET and HAT/p300 in colorectal cancer.

146 Background: Colorectal cancer (CRC) is characterized by extensive DNA methylation at the promoters of tumor suppressor genes and enhanced activity of histone modifying proteins such as histone acetyltransferases (HATs) or histone readers such as bromodomain and extra-terminal domain (BET) proteins. BET inhibition has been associated with the reduced expression of DNA repair proteins and therefore can be used in combination with radiotherapy (RT) and chemotherapy. In the current study, we have evaluated the therapeutic potential of a clinical stage (phase 1) dual BET and CBP/p300 inhibitor, EP31670 (EP), in combination with RT. Methods: HCT116 CRC 2-D cultures were treated with EP 4 hours before RT. After pretreatment with EP (0, 0.1, 0.5, 1, 2, 5, and 10µM), cells were irradiated with various doses (0, 2, 4, 6, and 8Gy) of RT (300-kv x-rays). Crystal violet (CV) assay at 48 hours post RT was used to determine growth inhibition and viability between the various drug, RT, and combination groups. Synergy between treatments was evaluated by estimating the combination index (CI) values via mass-action law CompuSyn calculations using CV data. CI values of <1 from the growth inhibition assay suggested that EP synergized with RT for enhanced cytotoxicity in HCT116 CRC cells. Flow cytometry was used to assess DNA damage (γH2Ax), apoptosis and total death (Annexin V-PI assay), cell cycle analysis, and proliferation (EdU). Results: There was a significant dose-dependent increase in the residual DNA damage at 6 hours (8Gy + EP 0.5µM vs. 8Gy, p<0.0001) and 24 hours (8Gy + EP 0.5µM vs. 8Gy, p=0.002) for combination therapy over RT alone. Four-hour treatment with EP promoted G2 cell-cycle arrest (8Gy + EP 0.5µM vs. 8Gy, p<0.001) and significantly reduced the number of HCT cells in S-phase (8Gy + EP 0.5µM vs. 8Gy, p<0.001) and proliferation (EdU) of the HCT cells (8Gy + EP 0.5µM vs. 8Gy, p=0.0003) compared to RT alone. There was a significant increase in apoptotic cells the combination group (8Gy + EP 0.5µM vs. EP 0.5µM, p=0.008) when compared to the unirradiated cells. The combination group also showed significant increase in the total death compared to RT alone (8Gy + EP 0.5µM vs. 8Gy, p=0.03) at the G1-S checkpoint. Conclusions: EP31670 enhanced RT-induced growth arrest, reduced proliferation, and enhanced cell death in HCT116 CRC cells in synergy with the RT. Additional preclinical studies, in vivo studies, and eventual clinical studies can be conducted to further exploit this synergistic interaction.

Ion-ion association is lost by linearizing the Poisson-Boltzmann equation when deriving the Debye-Hückel equation.

In this work, we demonstrate how the ion association constant can be attributed to the difference between the full Poisson-Boltzmann equation and its linearized version in very dilute solutions. We follow a pragmatic approach first by deriving an analytical approximated solution to the Poisson-Boltzmann equation, then calculating its respective Helmholtz free energy and activity coefficient, and then finally comparing it to the contribution from the mass action law principle. The final result is the Ebeling association constant. We conclude that electrostatic ion-ion interaction models miss the ion association contribution naturally introduced in higher-order electrostatic theories. We also demonstrate how the negative deviations from the Debye-Hückel limiting law can be physically attributed to the ion association phenomenon.

Mathematical Modeling of Photo- and Thermomorphogenesis in Plants.

Increased day lengths and warm conditions inversely affect plant growth by directly modulating nuclear phyB, ELF3, and COP1 levels. Quantitative measures of the hypocotyl length have been key to gaining a deeper understanding of this complex regulatory network, while similar quantitative data are the foundation for many studies in plant biology. Here, we explore the application of mathematical modeling, specifically ordinary differential equations (ODEs), to understand plant responses to these environmental cues. We provide a comprehensive guide to constructing, simulating, and fitting these models to data, using the law of mass action to study the evolution of molecular species. The fundamental principles of these models are introduced, highlighting their utility in deciphering complex plant physiological interactions and testing hypotheses. This brief introduction will not allow experimentalists without a mathematical background to run their own simulations overnight, but it will help them grasp modeling principles and communicate with more theory-inclined colleagues.

Automation of the Formation of a Mathematical Formulation of Kinetics for Multistage Chemical Reactions and Numerical Solution to a Direct Problem

Introduction. The basis for research, analysis and mathematical optimization of any chemical process is an adequate mathematical model that takes into account the kinetics of the object. Kinetic analysis is a challenge in chemical technology, since it allows for optimizing synthesis processes and predicting their efficiency. Numerous chemical processes involve several stage reactions. For successful design and optimization, a mathematical model that describes each stage is needed. Creating such a model manually can be time-consuming and costly, since it requires processing a large amount of information. The modern level of automation makes it possible to accelerate the obtaining of a mathematical formulation of the kinetics of multistage reactions. In this case, working with data is greatly simplified, and the probability of making mistakes is reduced. The resulting mathematical model can be applied for further analysis and optimization of the process. The paper considers the industrial reaction of catalytic reforming of gasoline, which occupies an important place in the modern scheme of oil refining, since it is a source of high-octane components of commercial gasolines and individual aromatic hydrocarbons. This process is characterized by the participation of a large number (up to 300) of various hydrocarbons, a change in the number of moles, and non-isothermality in it. Mathematical modeling of such processes involves detailing the stages to the required level. The detailing of up to 173 stages is considered. In this setting, automation of the formation of a mathematical formulation of kinetics for catalytic reforming of gasoline has not been carried out before. Therefore, the presented work aimed at implementing effective numerical methods and algorithms for automating the building of a mathematical model taking into account kinetics, thermodynamics, and changes in the number of moles.Materials and Methods. The mathematical formulation of the kinetics of multistage reactions was developed on the basis of the mass action law. The kinetic parameters values were taken from literary sources. The direct kinetics problem was solved using algorithms: the Gear method, the Runge-Kutta method of the 4th order, and the scipy.odeint() method of the Python language. The automation concept was implemented using the IDEF0 methodology. The software was written in the Python programming language.Results. A new software was created to automate the process of forming a mathematical model, taking into account the kinetics, thermodynamics, and the volume of the reaction mixture. The program results were presented by the example of catalytic reforming of gasoline. The model implemented the possibility of taking into account the intermediate heating of the mixture in the reactor cascade. Numerical values of temperature changes corresponding to industrial data were obtained.Discussion and Conclusion. The results obtained through modeling chemical transformations in the cascade of gasoline catalytic reforming reactors confirmed the exothermic nature of the reaction. The developed software product provides displaying changes in the concentrations of reactants, as well as temperature variations in the reactor, and it can be used in scientific research organizations for the analysis of multistage catalytic processes. The results of the reaction kinetics modeling will be used in the subsequent optimization of the process conditions in production.

Generic algebraic conditions for the occurrence of switch-like behavior of a chemical kinetic system of the hypoxia pathway.

Weakly reversible chemical reaction networks with zero deficiency associated with mass-action kinetics admit, within each positive stoichiometric compatibility class, one positive steady state which is locally asymptotically stable and this irrespective of the values of the kinetics constants. Networks which do not enjoy these structural properties potentially exhibit more diverse dynamical behaviors. In this article, we consider a chemical reaction network associated with mass-action kinetics which is not weakly reversible and has a deficiency larger than one. The chemical reactions are at most bimolecular, but inflow and outflow reactions are present. Our results are as follows. We establish the existence of positive steady-state solutions and obtain their analytic expressions in the concentration space and in convex coordinates. We show that the system fulfills necessary conditions for a saddle-node and for a bifurcation into a saddle and a node. We apply a constructive approach to obtain a set of numerical values for the state variables and kinetic parameters, not reported previously, such that the reduced Jacobian is characterized by a zero eigenvalue with all other eigenvalues having negative real parts. The bifurcation diagram confirms the presence of the switch-like behavior.

Prediction and assessment of xenoestrogens mixture effects using the in vitro ERα-CALUX assay.

Introduction: Many natural or synthetic compounds used in foods, dietary supplements, and food contact materials (FCMs) are suspected endocrine disruptors (EDs). Currently, scientific evidence to predict the impacts on biological systems of ED mixtures is lacking. In this study, three classes of substances were considered: i) phytoestrogens, ii) plant protection products (PPP) and iii) substances related to FCMs. Fourteen compounds were selected based on their potential endocrine activity and their presence in food and FCMs. Methods: These compounds were evaluated using an in vitro gene expression assay, the ERα-CALUX, to characterize their responses on the estrogen receptor alpha. Cells were exposed to fixed ratio mixtures and non-equipotent mixtures of full and partial agonists. The concentration-response curves measured for the three classes of compounds were characterized by variable geometric parameters in terms of maximum response (efficacy), sensitivity (slope) and potency (median effective concentration EC50). To account for these variations, a generic response addition (GRA) model was derived from mass action kinetics. Results: Although GRA does not allow us to clearly separate the concentration addition (CA) and independent action (IA) models, it was possible to determine in a statistically robust way whether the combined action of the chemicals in the mixture acted by interaction (synergy and antagonism) or by additive behavior. This distinction is crucial for assessing the risks associated with exposure to xenoestrogens. A benchmark dose approach was used to compare the response of phytoestrogen blends in the presence and absence of the hormone estradiol (E2). At the same time, 12 mixtures of 2-5 constituents including phytoestrogens, phthalates and PPPs in proportions close to those found in food products were tested. In 95% of cases, the response pattern observed showed a joint and independent effect of the chemicals on ER. Discussion: Overall, these results validate a risk assessment approach based on an additive effects model modulated by intrinsic toxicity factors. Here, the CA and IA approaches cannot be distinguished solely based on the shape of the concentration response curves. However, the optimized GRA model is more robust than CA when the efficacy, potency, and sensitivity of individual chemical agonists show large variations.

Rumen fermentation of meal-fed sheep in response to diets formulated to vary in fiber and protein degradability.

The concentration of volatile fatty acid (VFA) provides an imprecise view of VFA dynamics due to the confounding effects of fluid pool size and dynamics. Determination of VFA flux using isotope is expensive and a complex methodology. Therefore, a rapid and affordable approach to explore VFA dynamics may allow comprehensive characterization of VFA availability. The objective of this study was to explore the use of VFA dynamics generated by meal feeding to derive time-series rates of VFA apparent appearance and disappearance driven by different protein and fiber sources. Six ruminally cannulated wethers were fed diets containing timothy hay or beet pulp (TH and BP) and soybean meal (SBM) or heated soybean meal (HSBM). Diets were, TH + HSBM; TH + SBM; BP + HSBM; and BP + SBM and the experimental design was a partially replicated 4 × 4 Latin Square. Concentrations of VFA and polyethylene glycol (PEG) in rumen fluid samples were estimated. Concentrations of PEG were used to estimate fluid passage and volume to calculate VFA mass, and fluid-mediated exit. Maximum apparent appearance rate (mmol/h), the rate of apparent appearance decline (mmol/mmol/h), mean apparent appearance flux (mmol/h), mean apparent disappearance (mmol/h), and apparent disappearance rate (mmol/mmol/h) were estimated by deriving a 1 pool model for each VFA on a mass basis where appearance was assumed to follow an exponential decay pattern and disappearance followed mass-action kinetics. Statistical analyses were conducted using a linear mixed effect regression with fixed effects for fiber source, protein source, and their interaction, as well as random effects for animal and period. Rumen fluid volume (L) was greater in HSBM diets (P = 0.033) and fluid passage (%/h) was greater in SBM diets (P = 0.048). Concentrations (higher acetate and butyrate, P = 0.002 and 0.004, respectively) and molar proportions (higher valerate, P = 0.035) of VFA were affected only by fiber source; however, protein source and fiber source interacted to significantly influence apparent appearance rates and absorption rates of many major VFA. On a flux basis, HSBM supported significantly elevated mean disappearance of propionate (P = 0.033). This data demonstrates that time-series evaluation of fermentation dynamics, including fluid dynamics and VFA concentrations can be used to estimate apparent appearance and disappearance of VFA. Although further work is needed to confirm the alignment of these estimates with measurements of VFA supplies to the animal, this modeling approach may provide a simpler way to better understand the kinetics of rumen.

Abstract LB_B20: The Unity Theory of One: The dynamic algorithm of mass action law for drug and biosimilar digital evaluation/simulation in molecules, cells, and organs, regardless of units, physical states, and mechanisms

Abstract Mathematical analysis of mass-action law (MAL) of the intermediate-forming system analysis led to the general median-effect equation (MEE) for action dynamics that determines potency (Dm, median-effect dose, and dynamic order [m, the shape of dose-effect-curve (DEC) where m=1, >1, <1 indicate hyperbolic, sigmoidal and flat sigmoidal, respectively]; the combination index equation (CIE) for interaction that quantifies synergism (CI<1), additive effect (CI=1) and antagonism (CI>1); and the dose-reduction index equation (DRIE) for interaction consequences, where DRI=1, >1 and <1 indicate no dose-reduction, favorable dose-reduction, and unfavorable dose-reduction. All terms of MEE, CIE, and DRIE are dimensionless relativity ratios, thus ensuring the general applicability of MAL. Therefore, the MAL biodynamics, pharmacodynamics, and bioinformatics (MAL-BD/PD/BI) is the top-down fundamental theory-based R&D, which approach is different from the classical observation/statistics-based bottom-up R&D. The MEE, CIE, and DRIE all center on “One” (the Unity Theory of One) (UTO), which are not feasible to derive from the classical specific-aimed derivations, such as Michaelis-Menten, Henderson-Hasselbalch, Hill, Scatchard, and Langmuir equations.  The most important extensions and utilities of AML-MEE/CIE  are the linearization of DECs with the median-effect plot (MEP) that led to the Minimum Two-dose Data Point Theory (MTDPT), which automatically adds two default data points to DECs (Do, dose-zero, and Dm, the universal reference point and the dynamic-orders common link). Thus, 2 becomes 4, 3 becomes 5, and 4 becomes 6 doses. This discovery allows digital quantitative, simple, efficient, cost-effective, Econo-Green biomedical R&D and drug evaluation of unified regulatory guidance. This MAL-theoretical approach is particularly beneficial in animal studies, clinical trial protocol design, and computerized analysis/simulation. The MAL-theoretical approach (MEE and CIE) was introduced by Chou and Talalay (1984), then by a Review article by Chou (2006) and a Perspective article (2006). Based on the bibliometrics by  Web of Science and Google Scholar, as of August 26, 2023, these three articles have been cited 8,020, 5,194, and 5,129 times in 1,523, 1,242, and 1,157 journals internationally. The MAL-BD/PD/CI/BI is an Econo-green complementary alternative to traditional bottom-up studies. The MAL dynamics and informatics have been cited by 1,184 patents and by thousands of research grants sponsored by international governmental institutions, including USA (NIH, NCI, NCATS,  NSF, and FDA), EU (Euro. Reginal Develop. Fund), China (Natl Key R&D), Japan (Soc. of Promotion of Sci),  Korea (Natl. Sci. Foundation), Germany (Deutsch Fortungsgemeinschaft), France (INSERM), England (MRC), etc. The MAL-BD/PD/CI BI dynamics and informatics provide a new avenue for efficient and cost-effective translational and precision medicine and beyond, including environmental, agricultural, marine, material, biophysical, radiation, and food sciences. Citation Format: Ting-Chao Chou. The Unity Theory of One: The dynamic algorithm of mass action law for drug and biosimilar digital evaluation/simulation in molecules, cells, and organs, regardless of units, physical states, and mechanisms [abstract]. In: Proceedings of the AACR-NCI-EORTC Virtual International Conference on Molecular Targets and Cancer Therapeutics; 2023 Oct 11-15; Boston, MA. Philadelphia (PA): AACR; Mol Cancer Ther 2023;22(12 Suppl):Abstract nr LB_B20.

Abstract A017: Computer simulation and quantification of the mass-action law-base pharmacodynamics parameters for anti-cancer and anti-viral therapeutics for single drugs and their combinations

Abstract The biophysical and biochemical fundamental principle of the mass-action law (MAL) was used as the solo model for broad-spectrum system analysis. These included linear and circular sequential analysis, pattern analysis, combinatorial analysis, and mathematical induction-deduction, for deriving unified general pharmacodynamics/biodynamics/combination index/and bioinformatics (PD/BD/CI/BI).  The two unified general dose-effect dynamics theories are: “action” (Median-effect Eq., MEE) and “interaction” (Combination index Eq. CIE). All terms of MEE and CIE are dimensionless relativity ratios; thus, the applicability of the dynamics is regardless of unit (e.g., uM, IU, rad), mechanisms (e.g., sequential, ordered, random; competitive, non-competitive, uncompetitive), and physical states (e.g., chemicals, biologicals, radiation,  photonic, and thermal effects), and their interactions. The unified “action” dynamics (MEE) is applicable for R&D for MAL identity’s basic-PD parameters: Dm, the median-effect dose, signifying potency; and m, the dynamic-order, signifying shapes of dose-effect curves (DEC), for single drugs or in combinations. The Dm and m values can be determined by computer simulation based on MEE and CIE algorithms computer software, which allows digital determination of synergism (CI<1), additive effect (CI=1), and antagonism (CI>1) by automated simulations, instantly, after Dose and Effect paired data entries. The MEE algorithm and plot (MEP) linearized DEC into straight lines. This linearization principle led to the minimum two data points theory (MTDPT), which adds “dose-zero” and “Dm)” two dose-data points to the PD algorithm by default, for dynamics simulations. The MTDPT is the theoretical basis for Econo-green, efficient, cost-effective biomedical research in vitro, animals, humans, environmental, agricultural, marine, and food sciences. This allows using small-size experimental studies, reducing cost, and increasing efficiency by computer simulation. This paper illustrates the examples (experimental or clinical trial protocol) of PD design, step-by-step, for dose-dependent PD computer analysis, for anti-cancer and anti-viral agents, e.g., fludelone +/- panaxytriol in vitro; microtubule-stabilization agent  +/- T607 antineoplastic in colon carcinoma HCT116 tumor-bearing nude mice; as well as anti-HIV clinical trials [nucleoside reverse transcriptase inhibitor +/- Interferon], are used for detailed illustrations for study design, computerized data analysis, and automated print-out. Thus, the unified general MAL- PD/BD/CI/BI can be used in vitro, in animals, and in clinical trials, for digital informatics or ranking.  It is worth noting that the Google Scholar and Web of Science bibliometrics (as of May 29, 2023), on the MAL-PD/CI original article (Chou TC & Talalay P, 1984), Review (Chou TC, 2006), and Perspectives (Chou TC, 2010) have received a total of 18,046 citations in over 1,500 journals. For relevant 2023 references, please visit https://doi.org/10.1016/j.jbc.2023.103419 and dx.doi.org/10.1124/jpet.122.185320. Citation Format: Ting-Chao David Chou. Computer simulation and quantification of the mass-action law-base pharmacodynamics parameters for anti-cancer and anti-viral therapeutics for single drugs and their combinations [abstract]. In: Proceedings of the AACR-NCI-EORTC Virtual International Conference on Molecular Targets and Cancer Therapeutics; 2023 Oct 11-15; Boston, MA. Philadelphia (PA): AACR; Mol Cancer Ther 2023;22(12 Suppl):Abstract nr A017.

A query-response causal analysis of reaction events in biochemical reaction networks

The stochastic kinetics of biochemical reaction networks is described by a chemical master equation (CME) and the underlying laws of mass action. Assuming network-free simulations of the rule-based models of biochemical reaction networks (BRNs), this paper departs from the usual analysis of network dynamics as the time-dependent distributions of chemical species counts, and instead considers statistically evaluating the sequences of reaction events generated from the stochastic simulations. The reaction event-time series can be used for reaction clustering, identifying rare events, and recognizing the periods of increased or steady-state activity. However, the main aim of this paper is to device an effective method for identifying causally and anti-causally related sub-sequences of reaction events using their empirical probabilities. This allows discovering some of the causal dynamics of BRNs as well as uncovering their short-term deterministic behaviors. In particular, it is proposed that the reaction sub-sequences that are conditionally nearly certain or nearly uncertain can be considered as being causally related. Moreover, since the time-ordering of reaction events is locally irrelevant, the reaction sub-sequences can be transformed into the reaction sets or multi-sets. The distance metrics can be then used to define the equivalences among the reaction events. The proposed method for identifying the causally related reaction sub-sequences has been implemented as a computationally efficient query-response mechanism. The method was evaluated for five models of genetic networks in seven defined numerical experiments. The models were simulated in BioNetGen using the open-source network-free simulator NFsim. This simulator had to be modified first to allow recording the traces of reaction events, and it is available in the Github repository, ploskot/nfsim_1.20. The generated event time-series were analyzed with Python and Matlab scripts. The whole process of data generation, analysis and visualization has been nearly fully automated using shell scripts. This demonstrates the opportunities for substantially increasing the research productivity by creating automated data generation and processing pipelines.

Physical origin of adsorption heat and its significance in the isotherm equation

Adsorption heat is a cornerstone concept underpinning almost all the existing theoretical isotherms for porous media. Yet, it remains elusive what this concept stands for and what are the physical sources for it. Here, a rigorous thermodynamic formulation is derived for the adsorption process with the aid of the law of mass action, leading to an expression of adsorption heat as the external chemical potential difference between two adjacent adsorbate layers. The interaction between adsorbent and adsorbates like van der Waals is theoretically identified as the intermolecular source for the change of adsorption heat. Thereby, adsorption heat is formulated as a spatially varied function of the distance to adsorbent surfaces. This adsorption heat function facilitates the establishment of a two-parameter sorption isotherm equation. The equation can be theoretically converted to two widely used adsorption isotherm equations, namely Brunauer–Emmet–Teller (BET) and Guggenheim-Anderson-de Boer (GAB) equations, and shows excellent performance in capturing experimental isotherm data of a wide array of materials. The comparative analysis demonstrates that the derived two-parameter isotherm equation outperforms the two-parameter BET equation and the three-parameter GAB equation in most cases. Such performance verifies the generality of the derived isotherm equation, thus further confirming the validity of the derived formulation of adsorption heat.

Numerical simulation of ore formation within skarn-type Pb-Zn deposits: Implications for mineral exploration and the duration of ore-forming processes

Skarn-type deposits are typical hydrothermal mineral deposits distributed throughout the world with multiple metal resources and huge economic value. However, their extremely complex forming processes hinder us from further understanding their forming mechanism and exploring their economic potential. This study builds an integrated and simplified model of skarn-type Pb-Zn deposits and applies numerical simulation approach to quantitatively describe the formation of mineralization, analyzing the continuous dynamic changes of the concentrations of generated garnet, diopside and galena/sphalerite within the system. This numerical model includes chemical reactions, heat conduction, fluid-flow, materials migration and diffusion and their complex coupled relationships. The results show that the alterations at the contact of wall rocks and intrusions have clear zoning of garnet and diopside, and the amount of diopside exceeds that of garnet at the distal end of the generated alteration zone; the generation processes of garnet, diopside and galena/sphalerite follows a strict chronological order, controlling the variation of rock porosity; the cooling process of P3 (Fig. 4b) from 700 °C to 170 °C costs 55,000 years, within which the formation of galena/sphalerite merely lasts 30,000 years, meaning that the effective lifespan of Pb/Zn mineralization takes up only 54.54 % of the whole 55,000 years. All these results provide useful information for metallogenic research of skarn-type Pb-Zn deposits as well as magmatic-hydrothermal system. However, the method applied in this research still has limitations, such as the restriction from the single-period magmatic activity, the law of mass action, and the simplified chemical equations. Future development into both mathematical geosciences and geological analytical tests will definitely provide more appropriate calculation models and testing data with higher precision, improving the accuracy and practical significance of numerical simulation of ore formation, and providing more detailed quantitative answers for remaining hot issues related to economic geology research.