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PubMed2006

Lung cancer risk in mice: analysis of fractionation effects and neutron RBE with a biologically motivated model.

Data from Argonne National Laboratory on lung cancer in 15,975 mice with acute and fractionated exposures to gamma rays and neutrons are analyzed with a biologically motivated model with two rate-limiting steps and clonal expansion. Fractionation effects and effects of radiation quality can be explained well by the estimated kinetic parameters. Both an initiating and a promoting action of neutrons and gamma rays are suggested. While for gamma rays the initiating event is described well with a linear dose-rate dependence, for neutrons a nonlinear term is needed, with less effectiveness at higher dose rates. For the initiating event, the neutron RBE compared to gamma rays is about 10 when the dose rate during each fraction is low. For higher dose rates this RBE decreases strongly. The estimated lifetime relative risk for radiation-induced lung cancers from 1 Gy of acute gamma-ray exposure at an age of 110 days is 1.27 for male mice and 1.53 for female mice. For doses less than 1 Gy, the effectiveness of fractionated exposure to gamma rays compared to acute exposure is between 0.4 and 0.7 in both sexes. For lifetime relative risk, the RBE from acute neutrons at low doses is estimated at about 10 relative to acute gamma-ray exposure. It decreases strongly with dose. For fractionated neutrons, it is lower, down to about 4 for male mice.

Animals↗
PubMed2006

An opposite role for tau in circadian rhythms revealed by mathematical modeling.

Biological clocks with a period of approximately 24 h (circadian) exist in most organisms and time a variety of functions, including sleep-wake cycles, hormone release, bioluminescence, and core body temperature fluctuations. Much of our understanding of the clock mechanism comes from the identification of specific mutations that affect circadian behavior. A widely studied mutation in casein kinase I (CKI), the CKIepsilon(tau) mutant, has been shown to cause a loss of kinase function in vitro, but it has been difficult to reconcile this loss of function with the current model of circadian clock function. Here we show that mathematical modeling predicts the opposite, that the kinase mutant CKIepsilon(tau) increases kinase activity, and we verify this prediction experimentally. CKIepsilon(tau) is a highly specific gain-of-function mutation that increases the in vivo phosphorylation and degradation of the circadian regulators PER1 and PER2. These findings experimentally validate a mathematical modeling approach to a complex biological function, clarify the role of CKI in the clock, and demonstrate that a specific mutation can be both a gain and a loss of function depending on the substrate.

Animals↗
PubMed2002

Population dynamics of clock-controlled biological species: models and why circadian rhythms are circadian.

Conventional models of population dynamics of biological species do not take into account the fact that activity of most living organisms is under control of biological clocks, which are oscillators with periods near 1 day, 1 year, and so on. Here proposed are new categories of population dynamics models which are combinations of Lotka-Volterra type of equations (as a simplest example; in fact, an arbitrary type may be used) and equations of the biological oscillators. Such models may be particularly useful in addressing to those problems which are inaccessible with conventional models. A simple example of such models with distributed clock periods is proposed and studied numerically and analytically to consider why periods of biological rhythms are not precisely one day or one year, etc., as is often questioned. For this purpose, a notion of survival index is introduced to measure the degree of success in survival. It turns out that clock periods equal or close to that of the milieu are not necessarily advantageous for survival and can even lead to extinction; survival is then most successful at the edge of entrainment. This may provide a clue to answer the question. It is also found that survival is difficult for those species which cannot be entrained by the environmental cycle.

Animals↗
PubMed1990

A two-phase linear regression model for biologic half-life data.

In estimating the biologic half-life of an infused drug or biologic agent, one very frequently used model is the biexponential, which reflects a two-compartment physiologic model. The difficulty in using this model is that it is nonlinear in the parameters and requires relatively sophisticated analysis. Furthermore, an interval estimate is not usually reported. We propose the use of a two-phase linear regression approach, which is tantamount to breaking down the model into two straight lines based on the selection of the logarithm of concentration as the ordinate and time as the abscissa. We show how to determine the joint or changeover point for the two lines using a simple iterative procedure, how to select between a one-phase and a two-phase model, and how to provide a simple confidence interval estimate for half-life when it exists. An example using data from a study of Factor VIII pharmacokinetics is given.

Factor VIII↗
PubMed1977

Oscillatory chemical reactions: the Tomita-Kitahara model.

Biological clocks share with excitable membrane (nerve, muscle) the requirement that the chemical systems that underlie them have unstable steady states, and hence are capable of limit-cycle oscillations. A particularly simple model of a chemical oscillator is discussed, especially with reference to the reverse reaction, which tends to damp the oscillations. For thermodynamic reasons (entropy production) reversibility can not, however, be neglected. The steady state, even when stable, does not minimize the dissipation function. Computer studies show the response to sinusoidal variation of the rate constant governing the autocatalytic step.

Animals↗
PubMed1989

The interactions of bilirubin with model and biological membranes.

The partitioning of bilirubin between albumin and model and biological membranes and the differential partitioning of bilirubin between membranes with different lipid and protein compositions were measured. Partition coefficients were independent of the concentration of bilirubin in membranes up to at least 7 mol of bilirubin/mol of phospholipid. The avidity of albumin for bilirubin was greater than that of membranes, but the avidity of the latter for bilirubin depended on the composition of the membrane. Bilirubin partitioned preferentially into model membranes comprised of microsomal lipids greater than dioleoylphosphatidylcholine = plasma membrane lipids much greater than egg phosphatidylcholine = dimyristoylphosphatidylcholine. Partitioning into membranes was increased if these contained proteins, but the effect of proteins could not be attributed to specific binding to sites on proteins, as reflected by the temperature independence of partition coefficients. Differential partitioning of bilirubin into different membranes of pure lipids also was independent of temperature. Differences in the bulk phase fluidity of membranes does not appear to account for the preferential partitioning of bilirubin into some membranes. It appears that bilirubin partitions into elements of free volume of differing sizes in membranes with variable lipid compositions and that the size of these elements can be increased by adding proteins to membranes.

Animals↗
PubMed1999

Right-left discrimination in a biologically oriented model of the cockroach escape system.

We present a biologically oriented model that accounts for left-right discrimination in the cockroach's escape behavior. The model includes the main groups of neurons found to be involved in the escape response. Each one of the included neurons is described by the actual processes taking place in an individual neuron (formation of an action potential, transmitter release, conductance changes, etc.). Furthermore, realistic chemical synapses (excitatory or inhibitory and able to undergo different types of modulation) connect the various neurons. With this model, we ere able to achieve, for a wide range of inputs representing different wind directions, behavior which resembles that found experimentally. The model indicates that several synaptic properties, in particular postsynaptic inhibition and presynaptic facilitation, play a key role in the discrimination of wind direction.

Animals↗
PubMedDate not supplied

A biologically plausible model of thickening of arterial intima under shear.

A biologically plausible model of the early thickening of the arterial intima has been developed to interpret experimental data relating hemodynamic shear to human intimal morphology. The model included many processes known or commonly believed to take place in the vascular intima, including: smooth muscle cell migration, proliferation, metabolism, and expression of extracellular matrix; lipoprotein kinetics and binding; and monocyte chemotaxis, conversion to macrophage, and foam cell formation. Certain of these processes were allowed to be shear-dependent. The best fit to the data was obtained when smooth muscle cell accumulation was more rapid, and extracellular matrix expression proceeded more slowly where the fluid shear was relatively high and unidirectional. This result is consistent with the earlier inference that competing shear-dependent processes take place in the wall; it is also consistent with the notion that intimal thickening might be part of an adaptive mechanism by which the artery maintains a favorable shear environment.

Arteries↗
PubMed2003

Expanding comparative-advantage biological market models: contingency of mutualism on partners' resource requirements and acquisition trade-offs.

We expand the comparative-advantage biological market-modelling framework to show how differences between partners, both in their abilities to acquire two resources and in their requirements for those resources, can affect the net benefit of participating in interspecific resource exchange. In addition, the benefits derived from resource trading depend strongly on the nature of the trade-off between the acquisition of one resource and the acquisition of another, described here by the shape (linear, convex or concave) of the resource acquisition constraints of the individuals involved. Combined with previous results, these analyses provide a suite of predictions about whether or not resource exchange is beneficial for two heterospecific individuals relative to a strategy of non-interaction. The benefit derived from resource exchange depends on three factors: (i) relative differences between the partners in their resource acquisition abilities; (ii) relative differences between the partners in their resource requirements; and (iii) variation in the shape of resource acquisition trade-offs. We find that such an explicit consideration of resource requirements and acquisition abilities can provide useful and sometimes non-intuitive predictions about the benefits of resource exchange, and also which resources should be traded by which species.

Animals↗
PubMed2001

Non-local concepts and models in biology.

In this paper, we consider local and non-local spatially explicit mathematical models for biological phenomena. We show that, when rate differences between fast and slow local dynamics are great enough, non-local models are adequate simplifications of local models. Non-local models thus avoid describing fast processes in mechanistic detail, instead describing the effects of fast processes on slower ones. As a consequence, non-local models are helpful to biologists because they describe biological systems on scales that are convenient to observation, data collection, and insight. We illustrate these arguments by comparing local and non-local models for the aggregation of hypothetical organisms, and we support theoretical ideas with concrete examples from cell biology and animal behavior.

Animal Communication↗
PubMed1998

Photochromic polypeptides as synthetic models of biological photoreceptors: a spectroscopic study.

L-Glutamic acid polypeptides containing photochromic nitrospiropyran bound to the side chains at various percentages ("local" concentration) have been synthesized and investigated as possible artificial models of biological photoreceptors. Absorption and fluorescence spectroscopy have been utilized to investigate the photophysical and photochemical properties of nitrospiropyrans, both inserted in the polypeptide chain and in solution as "free" dye. Conformational variations produced by dark storage and light exposure of the photochromic polypeptides have been studied by means of circular dichroism. Dark-kept "free" dyes in hexafluoro-2-propanol solution in the merocyanine form ("open" form) give rise to molecular aggregates, which have been characterized as merocyanine dimers. The equilibrium constant between the monomer and the dimer, K, and their molar extinction coefficients, epsilon, at several wavelengths have been determined. Fluorescence measurements on "free" and polypeptide-bound nitrospiropyrans suggest that the dimerization process between merocyanines is favored when the photochromic units are inserted in the polypeptide chain and that under these conditions an efficient energy transfer from the monomer (donor) to the dimer (acceptor) occurs. By varying "local" as well as total nitrospiropyran concentration, it has been shown that the dimeric species result from intermolecular interactions between photochromic groups inserted in the same polypeptide chain. The alpha-helix --> random coil transition of the polypeptide structure after dark storage has eventually been shown to be the result of the dimerization process and not of the dark isomerization per se from the "closed" spiropyran form to the "open" merocyanine form of the dye.

Circular Dichroism↗
PubMed2026

Biological Foundation Models for Complex Disease Research and Clinical Translation.

Complex diseases, including cancer, rare genetic disorders, neurodevelopmental and psychiatric conditions, and neurodegenerative diseases, arise from interactions among genetic variation, gene regulation, and cellular states that are difficult to capture using a single data type or biological scale. Biological foundation models address this challenge by treating nucleotides and genes as tokens and learning representations that can be transferred to downstream biomedical and clinical tasks. In this review, we examine two major model classes, genomic sequence foundation models and cell foundation models, and compare their tokenization strategies, model architectures, pretraining objectives, and adaptation methods. We summarize their emerging applications in regulatory variant interpretation, disease-associated cell-state analysis, drug-response prediction, and therapeutic target discovery across complex diseases. We distinguish applications supported by experimental or retrospective validation from those that remain primarily computational or conceptual. We further discuss key challenges to clinical translation, including multimodal data integration, model interpretability, benchmarking, patient-specific prediction, and privacy protection. We highlight future opportunities to integrate biological foundation models with emerging frameworks of medical digital twins, agentic AI, and federated learning. By linking model design to translational goals, this review provides a practical framework for evaluating biological foundation models and their readiness for complex disease research and clinical use.

biological foundation model↗
PubMed1992

A branching process model of gene amplification following chromosome breakage.

We have devised a mathematical model of gene amplification utilizing recent experimental observations concerning dihydrofolate reductase (DHFR) gene amplification in CHO cells. The mathematical model, based on a biological model which proposes that acentric elements are the initial intermediates in gene amplification, includes the following features: (1) initiation of amplification by chromosomal breakage to produce an acentric structure; (2) replication of acentric DNA, once per cell cycle; (3) dissociation of replicated acentric DNA; (4) unequal segregation of acentric DNA fragments to daughter cells at mitosis; (5) subsequent reintegration of acentric fragments into chromosomes. These processes are assumed to be independent for each element present in a cell at a given time. Thus, processes of unequal segregation and integration may occur in parallel, not necessarily in a unique sequence, and may be reiterated in one or multiple cell cycles. These events are described mathematically as a Galton-Watson branching process with denumerable infinity of object types. This mathematical model qualitatively and quantitatively reproduces the major elements of the dynamical behavior of DHFR genes observed experimentally. The agreement between the mathematical model and the experimental data lends credence to the biological model proposed by Windle et al. (1991), including the importance of chromosome breakage and subsequent gene deletion resulting from resection of the broken chromosome ends as initial events in gene amplification.

Animals↗
PubMed1992

The continuous Sir Philip Sidney game: a simple model of biological signalling.

An analysis of Maynard Smith's two-player, ESS model of biological signalling, the "Sir Philip Sidney game", is presented. The stable strategies of the players in this game are shown to satisfy the conditions of Zahavi's handicap principle. At equilibrium, signals are honest, costly, and costly in a way that is related to the true quality revealed. Further analysis reveals that the level of cost required to maintain stability is inversely related to the degree of relatedness between the players. It therefore seems likely that stable biological signalling systems will feature lower signalling costs when communication occurs between relatives. A three-player, extended version of the model is investigated, in which signals are passed via an intermediate, or "messenger". It is shown that this destabilizes the signalling system, and leads to increased signalling costs. This result suggests that "kin conflict" theories of the evolution of the endosperm in flowering plants require further refinement. The introduction of a novel resource acquisition tissue, which mediates parent-offspring interaction during development, cannot be assumed to limit parent-offspring conflict simply because it carries an extra copy of the maternally inherited genes. The ability to add such complications to the Sir Philip Sidney game and still obtain solutions makes it a very useful modelling tool.

Animals↗
PubMed2005

Model of biologically active apolipoprotein E bound to dipalmitoylphosphatidylcholine.

Apolipoprotein (apo)E plays a critical role in cholesterol transport, through high affinity binding to the low density lipoprotein receptor. This interaction requires apoE to be associated with a lipoprotein particle. To determine the structure of biologically active apoE on a lipoprotein particle, we crystallized dipalmitoylphosphatidylcholine particles containing two apoE molecules and determined the molecular envelope of apoE at 10 Angstroms resolution. On the basis of the molecular envelope and supporting biochemical evidence, we propose a model in which each apoE molecule is folded into a helical hairpin with the binding region for the low density lipoprotein receptor at its apex.

1,2-Dipalmitoylphosphatidylcholine↗