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PubMed1998

A polymer model for the structural organization of chromatin loops and minibands in interphase chromosomes.

A quantitative model of interphase chromosome higher-order structure is presented based on the isochore model of the genome and results obtained in the field of copolymer research. G1 chromosomes are approximated in the model as multiblock copolymers of the 30-nm chromatin fiber, which alternately contain two types of 0.5- to 1-Mbp blocks (R and G minibands) differing in GC content and DNA-bound proteins. A G1 chromosome forms a single-chain string of loop clusters (micelles), with each loop approximately 1-2 Mbp in size. The number of approximately 20 loops per micelle was estimated from the dependence of geometrical versus genomic distances between two points on a G1 chromosome. The greater degree of chromatin extension in R versus G minibands and a difference in the replication time for these minibands (early S phase for R versus late S phase for G) are explained in this model as a result of the location of R minibands at micelle cores and G minibands at loop apices. The estimated number of micelles per nucleus is close to the observed number of replication clusters at the onset of S phase. A relationship between chromosomal and nuclear sizes for several types of higher eukaryotic cells (insects, plants, and mammals) is well described through the micelle structure of interphase chromosomes. For yeast cells, this relationship is described by a linear coil configuration of chromosomes.

Animals↗
PubMed2003

Modelling cereal root systems for water and nitrogen capture: towards an economic optimum.

A quantitative model of wheat root systems is developed that links the size and distribution of the root system to the capture of water and nitrogen (which are assumed to be evenly distributed with depth) during grain filling, and allows estimates of the economic consequences of this capture to be assessed. A particular feature of the model is its use of summarizing concepts, and reliance on only the minimum number of parameters (each with a clear biological meaning). The model is then used to provide an economic sensitivity analysis of possible target characteristics for manipulating root systems. These characteristics were: root distribution with depth, proportional dry matter partitioning to roots, resource capture coefficients, shoot dry weight at anthesis, specific root weight and water use efficiency. From the current estimates of parameters it is concluded that a larger investment by the crop in fine roots at depth in the soil, and less proliferation of roots in surface layers, would improve yields by accessing extra resources. The economic return on investment in roots for water capture was twice that of the same amount invested for nitrogen capture.

Models, Theoretical↗
PubMed2004

A simulation model of Escherichia coli osmoregulatory switch using E-CELL system.

BACKGROUND: Bacterial signal transduction mechanism referred to as a "two component regulatory systems" contributes to the overall adaptability of the bacteria by regulating the gene expression. Osmoregulation is one of the well-studied two component regulatory systems comprising of the sensor, EnvZ and the cognate response regulator, OmpR, which together control the expression of OmpC and OmpF porins in response to the osmolyte concentration. RESULTS: A quantitative model of the osmoregulatory switch operative in Escherichia coli was constructed by integrating the enzyme rate equations using E-CELL system. Using the substance reactor logic of the E-CELL system, a total of 28 reactions were defined from the injection of osmolyte till the regulated expression of porins by employing the experimental kinetic constants as reported in literature. In the case of low osmolarity, steady state production of OmpF and repression of OmpC was significant. In this model we show that the steady state - production of OmpF is dramatically reduced in the high osmolarity medium. The rate of OmpC production increased after sucrose addition, which is comparable with literature results. The relative porin production seems to be unaltered with changes in cell volume changes, ATP, EnvZ and OmpR at low and high osmolarity conditions. But the reach of saturation was rapid at high and low osmolarity with altered levels of the above components. CONCLUSIONS: The E-CELL system allows us to perform virtual experiments on the bacterial osmoregulation model. This model does not take into account interaction with other networks in the cell. It suggests that the regulation of OmpF and OmpC is a direct consequence of the level of OmpRP in the cell and is dependent on the way in which OmpRP interacts with ompF and ompC regulatory regions. The preliminary simulation experiment indicates that both reaching steady state expression and saturation is delayed in the case of OmpC compared to OmpF. Experimental analysis will help improve the model. The model captures the basic features of the generally accepted view of EnvZ-OmpR signaling and is a reasonable starting point for building sophisticated models and explaining quantitative features of the system.

Computer Simulation↗
PubMed1993

Models of the mechanism for crossbridge attachment in smooth muscle.

The mechanism responsible for formation of attached, dephosphorylated crossbridges (latchbridges) in smooth muscle is controversial. Myosin light chain phosphorylation may be obligatory for crossbridge attachment; if this were the case, latchbridges would arise solely by dephosphorylation of attached, phosphorylated crossbridges. Alternatively, the presence of attached crossbridges could induce cooperative activation by allowing dephosphorylated crossbridges to attach to the thin filament. We evaluated whether four-state models based on dephosphorylation and/or cooperativity-regulated attachment could quantitatively predict smooth muscle contractile behaviour. Five quantitative models for transitions between crossbridge states were developed. Mechanisms for latchbridge formation included: (1) dephosphorylation, (2) cooperativity-regulated attachment dependent only on attached, phosphorylated crossbridges, (3) cooperativity-regulated attachment dependent on all attached crossbridges, (4) dephosphorylation and cooperativity-regulated attachment dependent only on attached, phosphorylated crossbridges, and (5) dephosphorylation and cooperativity-regulated attachment dependent on all attached crossbridges. All five models approximated the time course of contraction and the dependence of steady-state stress on myosin phosphorylation in the swine carotid artery. In the two models that had cooperative attachment regulated by all attached crossbridges, small increases in the rate constant for cooperativity-regulated attachment resulted in positive feedback and irreversible contraction. We suggest that a number of four-state crossbridge models can predict contractile behaviour in arterial smooth muscle. Potentially, latchbridges could be formed by both dephosphorylation and cooperativity-regulated attachment. If cooperativity-regulated latchbridge attachment does exist in smooth muscle, we suggest that it should be dependent only on the number of phosphorylated crossbridges rather than all attached crossbridges.

Actomyosin↗
PubMed2000

A mathematical analysis for the Brownian dynamics of a DNA tether.

In the single-particle tracking experiment, the internal motion of a single DNA or polymer molecule whose one end is attached to a microsphere (optical marker) and the other end is anchored to a substratum is studied (Finzi and Gelles, 1995). The stochastic Brownian dynamics of the sphere reflect the spontaneous fluctuations, thus the physical characteristics, of the DNA or polymer molecule (Qian and Elson, 1999, Qian, 2000). In this paper, two continuous models of polymer molecules, a flexible elastic string and a weakly bendable elastic rod, are analyzed. Both models are cast mathematically in terms of linear stochastic differential equations. Based on Fourier analyses, we calculate the mean square displacement (MSD) of the particle motion, the key observable in the experiment. We obtain for both models the short-time asymptomatics for the MSD, as well as the long-time behavior in terms of the smallest non-zero eigenvalues. It is shown that: (i) the long-time dynamics of continuous elastic string model quantitatively agree with that of the discrete bead-spring model. (ii) The short-time MSD of both models are controlled by the tethered particle, with linear dependence on t. (iii) The two models show characteristic difference for long-time behavior: The longest relaxation time is proportional to L2 for long elastic string and to L for short elastic string, but is proportional to L4 for both long and short weakly bendable rod.

DNA↗
PubMed2006

Random sampling-high dimensional model representation (RS-HDMR) and orthogonality of its different order component functions.

High dimensional model representation is under active development as a set of quantitative model assessment and analysis tools for capturing high-dimensional input-output system behavior based on a hierarchy of functions of increasing dimensions. The HDMR component functions are optimally constructed from zeroth order to higher orders step-by-step. This paper extends the definitions of HDMR component functions to systems whose input variables may not be independent. The orthogonality of the higher order terms with respect to the lower order ones guarantees the best improvement in accuracy for the higher order approximations. Therefore, the HDMR component functions are constructed to be mutually orthogonal. The RS-HDMR component functions are efficiently constructed from randomly sampled input-output data. The previous introduction of polynomial approximations for the component functions violates the strictly desirable orthogonality properties. In this paper, new orthonormal polynomial approximation formulas for the RS-HDMR component functions are presented that preserve the orthogonality property. An integrated exposure and dose model as well as ionospheric electron density determined from measured ionosonde data are used as test cases, which show that the new method has better accuracy than the prior one.

Algorithms↗
PubMed2004

Using models of the myocyte for functional interpretation of cardiac proteomic data.

There has been significant progress towards the development of highly integrative computational models of the cardiac myocyte over the past decade. Models now incorporate descriptions of voltage-gated ionic currents and membrane transporters, mechanisms of calcium-induced calcium release and intracellular calcium cycling, mitochondrial ATP production and its coupling to energy-requiring membrane transport processes and mechanisms of force generation. There is an extensive literature documenting both the reconstructive and predictive abilities of these models and there is no question that an interplay between quantitative modelling and experimental investigation has become a central component of modern cardiovascular research. As data regarding the cardiovascular proteome in both health and disease emerge, integrative models of the myocyte are becoming useful tools for interpreting the functional significance of changes in protein expression and post-translational modifications (PTMs). Data of particular importance include information on: (a) changes of expressed protein level, (b) changes of protein PTMs, (c) protein localization, and (d) protein-protein interactions, as it is often possible to incorporate and interpret the functional significance of such findings using computational models. We provide two examples of how models may be used in this fashion. In the first example, we show how information on altered expression of the sarcoplasmic reticulum Ca2+-ATPase, when interpreted through the use of a computational model, has provided key insights into fundamental mechanisms regulating cardiac action potential duration. In the second example, we show how information on the effects of phosphorylation of L-type Ca2+ channels, when interpreted through the use of a model, provides insights on how this post-translational modification alters the properties of excitation-contraction coupling and risk for arrhythmia.

Animals↗
PubMed2006

Dual diffusion model for single-cell recording data from the superior colliculus in a brightness-discrimination task.

Monkeys made saccades to one of two peripheral targets based on the brightness of a central stimulus. Task difficulty was manipulated by varying the ratio of stimulus black-and-white pixels. Correct response probability for two monkeys varied directly with difficulty. Deep layer SC neurons exhibited robust presaccadic activity the magnitude of which was unaffected by task difficulty when the stimulus specified a saccade toward a target within the neuron's response field. Activity after stimuli specifying saccades to targets outside the response field was affected by task difficulty, increasing as the task became more difficult. A quantitative model derived from studies of human decision-making was fit to the behavioral data. The model assumes that information from the stimulus drives two independent diffusion processes. Simulated paths from the model were compared with neuron activity, assuming that firing rate is linearly related to position in the accumulation process. The firing rate data show delayed availability of discriminative information for fast, intermediate, and slow decisions when activity is aligned on the stimulus and very small differences in discriminative information when aligned on the saccade. The model produces exactly these patterns of results. The accumulation process is highly variable, allowing the process both to make errors, as is the case for the behavioral performance, and also to account for the firing rate results. Thus the dual diffusion model provides a quantitative account for both the behavior in a simple decision-making task as well as the patterns of activity in competing populations of neurons.

Animals↗
PubMed1978

[An in vitro model for the quantitative study of E. histolytica virulence].

An experimental model for the quantitative study of the cytopathic effect of E. histolytica is described. Confluent cultures of the MDCK cell line, which form a monolayer with morphological and electrophysiological features of an epithelium were used. Trophozoites of the strains HM1:IMSS, HM2:IMSS and HM3:IMSS, axenic produced variable degrees of cytopathic effects of MDCK cultures each one characteristic for a given strain. The degree of damage induced by the different strains of amebas was measured quantitatively. The results demonstrate that the degree of the cytopathic effect produced in vitro by the various strains tested correlates with the virulence shown in vivo by the same strains, judged as the size of the inoculum required to induce liver cytopathic effect in newborn hamsters.

Animals↗
PubMed2003

Modelling the dynamics of LCMV infection in mice: II. Compartmental structure and immunopathology.

In this study, we develop a mathematical model for analysis of the compartmental aspects and immunopathology of lymphocytic choriomeningitis virus (LCMV) infection in mice. We used sets of original and published data on systemic (extrasplenic) virus distribution to estimate the parameters of virus growth and elimination for spleen and other anatomical compartments, such as the liver, kidney, thymus and lung as well as transfer rates between blood and the above organs. A mathematical model quantitatively integrating the virus distribution kinetics in the host, the specific cytotoxic T lymphocyte (CTL) response in spleen and the re-circulation of effector CTL between spleen, blood and liver is advanced to describe the CTL-mediated immunopathology (hepatitis) in mice infected with LCMV. For intravenous and "peripheral" routes of infection we examine the severity of the liver disease, as a function of the virus dose and the host's immune status characterized by the numbers of precursor and/or cytolytic effector CTL. The model is used to predict the efficacy of protection against virus persistence and disease in a localized viral infection as a function of the composition of CTL population. The modelling analysis suggests quantitative demands to CTL memory for maximal protection against a wide range of doses of infection with a primarily peripheral site of virus replication without the risk of favoring immunopathology. It specifies objectives for CTL vaccination to ensure virus elimination with minimal immunopathology vs. vaccination for disease.

Animals↗
PubMed1990

Model for drug uptake by brain tumors: effects of osmotic treatment and of diffusion in brain.

A mathematical model describing drug uptake into brain tumors, directly from blood and indirectly from neighboring tissue, is presented. The model quantitatively describes uptake into tumor, brain surrounding tumor (BST), and normal brain and uptake following reversible osmotic blood-brain barrier (BBB) and blood-tumor barrier disruption. It employs published data on the time course for reclosure of the BBB following osmotic treatment and on the brain and tumor uptake of [14C]alpha-aminoisobutyric acid by Walker 256 carcinomas and C6 gliomas implanted into the rat brain. Constant infusion and bolus injection infusion schedules are considered. In untreated brain, the BST acts as a sink, reducing the integrated exposure of the adjacent tumor to the drug, whereas following osmotic treatment, tumor exposure to drug is enhanced, not only by increased delivery from blood but also by diffusion (and bulk flow) from neighboring brain. The model provides a quantitative framework for examining the efficacy of osmotic treatment to enhance chemotherapy of brain tumors.

Aminoisobutyric Acids↗
PubMedDate not supplied

Modeling of Gibbs energy of formation of organic compounds by linear and nonlinear methods.

Two quantitative models for the prediction of the Gibbs energy of formation (DeltaGf degrees ) of 177 organic compounds were developed. These molecules contain elements such as H, C, N, O, F, S, Cl, and Br, with the molecular weight in the range of 16.04-202.25. The molecules were represented by six selected 2D-structure descriptors. At first, the complex relationship between DeltaGf degrees and the six selected input descriptors was depicted by a two-dimensional Kohonen's self-organizing neural network (KohNN) map; on the basis of the KohNN map, the whole data set was split into a training set consisting of 130 compounds and a test set (or a validation set and a test set) including 47 compounds. Then, DeltaGf degrees was predicted using a multilinear regression (MLR) analysis and a back-propagation (BPG) neural network. For 177 organic compounds, root-mean-square deviations of 17.8 and 15.4 kcal mol-1 were achieved by MLR and the BPG neural network, respectively.

Algorithms↗
PubMed2003

Identification of nucleocytoplasmic cycling as a remote sensor in cellular signaling by databased modeling.

Considerable progress has been made in identifying the molecular composition of complex signaling networks controlling cell proliferation, differentiation, and survival. However, to discover general building principles and predict the dynamic behavior of signaling networks, it is necessary to develop quantitative models based on experimental observations. Here we report a mathematical model of the core module of the Janus family of kinases (JAK)-signal transducer and activator of transcription (STAT) signaling pathway based on time-resolved measurements of receptor and STAT5 phosphorylation. Applying the fitted model, we can determine the quantitative behavior of STAT5 populations not accessible to experimental measurement. By in silico investigations, we identify the parameters of nuclear shuttling as the most sensitive to perturbations and verify experimentally the model prediction that inhibition of nuclear export results in a reduced transcriptional yield. The model reveals that STAT5 undergoes rapid nucleocytoplasmic cycles, continuously coupling receptor activation and target gene transcription, thereby forming a remote sensor between nucleus and receptor. Thus, dynamic modeling of signaling pathways can promote functional understanding at the systems level.

Animals↗
PubMed2002

Probabilistic code for DNA recognition by proteins of the EGR family.

A recognition code for protein-DNA interactions would allow for the prediction of binding sites based on protein sequence, and the identification of binding proteins for specific DNA targets. Crystallographic studies of protein-DNA complexes showed that a simple, deterministic recognition code does not exist. Here, we present a probabilistic recognition code (P-code) that assigns energies to all possible base-pair-amino acid interactions for the early growth response factor (EGR) family of zinc-finger transcription factors. The specific energy values are determined by a maximum likelihood method using examples from in vitro randomisation experiments (namely, SELEX and phage display) reported in the literature. The accuracy of the model is tested in several ways, including the ability to predict in vivo binding sites of EGR proteins and other non-EGR zinc-finger proteins, and the correlation between predicted and measured binding affinities of various EGR proteins to several different DNA sites. We also show that this model improves significantly upon the prediction capabilities of previous qualitative and quantitative models. The probabilistic code we develop uses information about the interacting positions between the protein and DNA, but we show that such information is not necessary, although it reduces the number of parameters to be determined. We also employ the assumption that the total binding energy is the sum of the energies of the individual contacts, but we describe how that assumption can be relaxed at the cost of additional parameters.

Algorithms↗
PubMedDate not supplied

Recent advances in mathematical modeling of developmental abnormalities using mechanistic information.

During the last several years, significant changes in the risk assessment process for developmental toxicity of environmental contaminants have begun to emerge. The first of these changes is the development and beginning use of statistically based dose-response models [the benchmark dose (BMD) approach] that better utilize data derived from existing testing approaches. Accompanying this change is the greater emphasis placed on understanding and using mechanistic information to yield more accurate, reliable, and less uncertain risk assessments. The next stage in the evolution of risk assessment will be the use of biologically based dose-response (BBDR) models that begin to build into the statistically based models factors related to the underlying kinetic, biochemical, and/or physiologic processes perturbed by a toxicant. Such models are now emerging from several research laboratories. The introduction of quantitative models and the incorporation of biologic information into them has pointed to the need for even more sophisticated modifications for which we offer the term embryologically based dose-response (EBDR) models. Because these models would be based upon the understanding of normal morphogenesis, they represent a quantum leap in our thinking, but their complexity presents daunting challenges both to the developmental biologist and the developmental toxicologist. Implementation of these models will require extensive communication between developmental toxicologists, molecular embryologists, and biomathematicians. The remarkable progress in the understanding of mammalian embryonic development at the molecular level that has occurred over the last decade combined with advances in computing power and computational models should eventually enable these as yet hypothetical models to be brought into use.

Abnormalities, Drug-Induced↗
PubMed1977

The detection of line segments.

Many simple cells of the visual cortex have long narrow receptive fields, which are strongly excited by lines oriented along their long axis. In the present psychophysical analysis, we assume that there are similar independent 'subunits' which contribute, by probability summation, to the detection of a line. If a line segment is shorter than the subunit length, then extending the line length will increase the sensitivity of all the subunits affected by the line, and a relatively large increase in visual sensitivity will occur, corresponding to this 'physiological summation' within subunits. However, for a line segment which is much longer than the subunit length, the main effect of extending line length is to stimulate more subunits, resulting in a relatively small increase in sensitivity owing to probability summation. Thus a study of sensitivity (reciprocal threshold) as a function of line length may be used to test the subunit model and to estimate the subunit length. Here we use a quantitative model to demonstrate that sensitivity/line length data may be well fitted, assuming independent subunits having a constant length of 8-6'--in good agreement with the length of Adrews' "ff" units.

Adult↗
PubMed2002

Evaluating physicians' professionalism and humanism: the case for humanism "connoisseurs".

Physicians' professionalism and humanism have become central foci of the efforts of medical educators as the public, various accrediting and licensing agencies, and the profession itself have expressed concerns about the apparent erosion of physicians' competency in these aspects of the art, rather than the science, of medicine. Of the many obstacles to enhancing trainees' skills in these domains, one of the most significant is the difficulty in assessing competency in physicians' professionalism and humanism. The author suggests that the assessment of these aspects of the art of medicine has more in common with the approaches used in criticism of the arts than with the quantitative assessment tools appropriate to the scientific method and the medical model. Quantitative and semi-quantitative tools, so effective in elucidating the etiology, pathophysiology, and treatment of disease, are often in-appropriate and invalid when applied to evaluation of professional and humanistic competencies. The author proposes that humanism "connoisseurs" be employed to qualitatively evaluate medical trainees' professionalism and humanism. Such connoisseurs would possess expert knowledge, training, and experience in the interpersonal aspects of the art of medicine, allowing them to deconstruct concepts such as empathy, compassion, integrity, and respect into their respective key elements while evaluating physicians' behaviors as an integrated, cohesive whole. Through the use of a rich descriptive vocabulary, humanism connoisseurs would provide valid formative and summative feedback regarding competency in medical professionalism and humanism. In the process, they would serve to counteract the relative marginalization of professionalism and humanism in the informal and lived curricula of medical trainees.

Attitude of Health Personnel↗
PubMed2005

Tempo sensitivity in isochronous tone sequences: the multiple-look model revisited.

Factors affecting tempo sensitivity in isochronous tone sequences were investigated in two experiments. Participants listened to tones in sequence conditions in which the number of time intervals in isochronous standard and comparison sequences was varied, and they were asked to judge the tempo of the comparison relative to the standard. When the duration of the standard interval was held constant, tempo sensitivity was affected by the number of comparison intervals, but not by the number of standard intervals. In contrast, when the duration of the standard interval was varied randomly from trial to trial, tempo sensitivity was affected by the number of intervals in both sequences. The present findings are discussed in the context of a generalized multiple-look model that posits independent contributions of both sequences to tempo sensitivity. Quantitative model fits suggest that the relative contribution of the number of the standard intervals to tempo thresholds depends on (1) the availability of a stable long-term referent for the standard tempo and (2) a priori knowledge about the number of standard intervals.

Auditory Perception↗