Dynamic modeling of gene expression data

We describe the time evolution of gene expression levels by using a time translational matrix to predict future expression levels of genes based on their expression levels at some initial time. We deduce the time translational matrix for previously published DNA microarray gene expression data sets by modeling them within a linear framework by using the characteristic modes obtained by singular value decomposition. The resulting time translation matrix provides a measure of the relationships among the modes and governs their time evolution. We show that a truncated matrix linking just a few modes is a good approximation of the full time translation matrix. This finding suggests that the number of essential connections among the genes is small.

Dynamic regulation of the tryptophan operon: A modeling study and comparison with experimental data

A mathematical model for regulation of the tryptophan operon is presented. This model takes into account repression, feedback enzyme inhibition, and transcriptional attenuation. Special attention is given to model parameter estimation based on experimental data. The model's system of delay differential equations is numerically solved, and the results are compared with experimental data on the temporal evolution of enzyme activity in cultures of Escherichia coli after a nutritional shift (minimal + tryptophan medium to minimal medium). Good agreement is obtained between the numeric simulations and the experimental results for wild-type E. coli, as well as for two different mutant strains.

Dynamic mapping at the laminar level of odor-elicited responses in rat olfactory bulb by functional MRI

We have applied functional MRI (fMRI) based on blood oxygenation level-dependent (BOLD) image-contrast to map odor-elicited olfactory responses at the laminar level in the rat olfactory bulb (OB) elicited by iso-amyl acetate (10−2 dilution of saturated vapor) with spatial and temporal resolutions of 220×220×1,000 μm and 36 s. The laminar structure of the OB was clearly depicted by high-resolution in vivo anatomical MRI with spatial resolution of 110×110×1,000 μm. In repeated BOLD fMRI measurements, highly significant (P < 0.001) foci were located in the outer layers of both OBs. The occurrence of focal OB activity within a domain at the level of individual glomeruli or groups of glomeruli was corroborated on an intra- and inter-animal basis under anesthetized conditions with this noninvasive method. The dynamic studies demonstrated that the odor-elicited BOLD activations were highly reproducible on a time scale of minutes, whereas over tens of minutes the activations sometimes varied slowly. We found large BOLD signal (ΔS/S = 10–30%) arising from the olfactory nerve layer, which is devoid of synapses and composed of unmyelinated fibers and glial cells. Our results support previous studies with other methods showing that odors elicit activity within glomerular layer domains in the mammalian OB, and extend the analysis to shorter time periods at the level of individual glomeruli or groups of glomeruli. With further improvement, BOLD fMRI should be ideal for systematic analysis of the functional significance of individual glomeruli in olfactory information encoding and of spatiotemporal processing within the olfactory system.

Modeling the dynamics of human hair cycles by a follicular automaton

The hair follicle cycle successively goes through the anagen, catagen, telogen, and latency phases, which correspond, respectively, to hair growth, arrest, shedding, and absence before a new anagen phase is initiated. Experimental observations collected over a period of 14 years in a group of 10 male volunteers, alopecic and nonalopecic, allowed us to determine the characteristics of scalp hair follicle cycles. On the basis of these observations, we propose a follicular automaton model to simulate the dynamics of human hair cycles. The automaton model is defined by a set of rules that govern the stochastic transitions of each follicle between the successive states anagen, telogen, and latency, and the subsequent return to anagen. The transitions occur independently for each follicle, after time intervals given stochastically by a distribution characterized by a mean and a variance. The follicular automaton model accounts both for the dynamical transitions observed in a single follicle and for the behavior of an ensemble of independently cycling follicles. Thus, the model successfully reproduces the evolution of the fractions of follicle populations in each of the three phases, which fluctuate around steady-state or slowly drifting values. We apply the follicular automaton model to the study of spatial patterns of follicular growth that result from a spatially heterogeneous distribution of parameters such as the mean duration of anagen phase. When considering that follicles die or miniaturize after going through a critical number of successive cycles, the model can reproduce the evolution to hair patterns similar to well known types of diffuse or androgenetic alopecia.

Assessment and discrimination of odor stimuli in rat olfactory bulb by dynamic functional MRI

Dynamic blood oxygenation level-dependent functional MRI was applied at 7 T in the rat olfactory bulb (OB) with pulsed delivery of iso-amyl acetate (IAA) and limonene. Acquisition times for single-slice and whole OB data were 8 and 32 s, respectively, with spatial resolution of 220 × 220 × 250 μm. On an intrasubject basis, short IAA exposures of 0.6 min separated by 3.5-min intervals induced reproducible spatial activity patterns (SAPs) in the olfactory nerve layer, glomerular layer, and external plexiform layer. During long exposures (≈10 min), the initially dominant dorsal SAPs declined in intensity and area, whereas in some OB regions, the initially weak ventral/lateral SAPs increased first and then decreased. The SAPs of different concentrations were topologically similar, which implies that whereas an odor at various concentrations activates the same subsets of receptor cells, different concentrations are assessed and discriminated by variable magnitudes of laminarspecific activations. IAA and limonene reproducibly activated different subsets of receptor cells with some overlaps. Whereas qualitative topographical agreement was observed with results from other methods, the current dynamic blood oxygenation level-dependent functional MRI results can provide quantitative SAPs of the entire OB.

Dynamic localization of a cytoplasmic signal transduction response regulator controls morphogenesis during the Caulobacter cell cycle

We present evidence that a bacterial signal transduction cascade that couples morphogenesis with cell cycle progression is regulated by dynamic localization of its components. Previous studies have implicated two histidine kinases, DivJ and PleC, and the response regulator, DivK, in the regulation of morphogenesis in the dimorphic bacterium Caulobacter crescentus. Here, we show that the cytoplasmic response regulator, DivK, exhibits a dynamic, cyclical localization that culminates in asymmetric distribution of DivK within the two cell types that are characteristic of the Caulobacter cell cycle; DivK is dispersed throughout the cytoplasm of the progeny swarmer cell and is localized to the pole of the stalked cell. The membrane-bound DivJ and PleC histidine kinases, which are asymmetrically localized at the opposite poles of the predivisional cell, control the temporal and spatial localization of DivK. DivJ mediates DivK targeting to the poles whereas PleC controls its release from one of the poles at times and places that are consistent with the activities and location of DivJ and PleC in the late predivisional cell. Thus, dynamic changes in subcellular location of multiple components of a signal transduction cascade may constitute a novel mode of prokaryotic regulation to generate and maintain cellular asymmetry.

The neural development and organization of letter recognition: Evidence from functional neuroimaging, computational modeling, and behavioral studies

Although much of the brain’s functional organization is genetically predetermined, it appears that some noninnate functions can come to depend on dedicated and segregated neural tissue. In this paper, we describe a series of experiments that have investigated the neural development and organization of one such noninnate function: letter recognition. Functional neuroimaging demonstrates that letter and digit recognition depend on different neural substrates in some literate adults. How could the processing of two stimulus categories that are distinguished solely by cultural conventions become segregated in the brain? One possibility is that correlation-based learning in the brain leads to a spatial organization in cortex that reflects the temporal and spatial clustering of letters with letters in the environment. Simulations confirm that environmental co-occurrence does indeed lead to spatial localization in a neural network that uses correlation-based learning. Furthermore, behavioral studies confirm one critical prediction of this co-occurrence hypothesis, namely, that subjects exposed to a visual environment in which letters and digits occur together rather than separately (postal workers who process letters and digits together in Canadian postal codes) do indeed show less behavioral evidence for segregated letter and digit processing.

Dynamic contrast-enhanced magnetic resonance imaging reveals stress-induced angiogenesis in MCF7 human breast tumors.

The mechanism of contrast enhancement of tumors using magnetic resonance imaging was investigated in MCF7 human breast cancer implanted in nude mice. Dynamic contrast-enhanced images recorded at high spatial resolution were analyzed by an image analysis method based on a physiological model, which included the blood circulation, the tumor, the remaining tissues, and clearance via the kidneys. This analysis enabled us to map in rapidly enhancing regions within the tumor, the capillary permeability factor (capillary permeability times surface area per voxel volume) and the fraction of leakage space. Correlation of these maps with T2-weighted spin echo images, with histopathology, and with immunohistochemical staining of endothelial cells demonstrated the presence of dense permeable microcapillaries in the tumor periphery and in intratumoral regions that surrounded necrotic loci. The high leakage from the intratumoral permeable capillaries indicated an induction of a specific angiogenic process associated with stress conditions that cause necrosis. This induction was augmented in tumors responding to tamoxifen treatment. Determination of the distribution and extent of this stress-induced angiogenic activity by contrast-enhanced MRI might be of diagnostic and of prognostic value.

Spatial integration and cortical dynamics.

Cells in adult primary visual cortex are capable of integrating information over much larger portions of the visual field than was originally thought. Moreover, their receptive field properties can be altered by the context within which local features are presented and by changes in visual experience. The substrate for both spatial integration and cortical plasticity is likely to be found in a plexus of long-range horizontal connections, formed by cortical pyramidal cells, which link cells within each cortical area over distances of 6-8 mm. The relationship between horizontal connections and cortical functional architecture suggests a role in visual segmentation and spatial integration. The distribution of lateral interactions within striate cortex was visualized with optical recording, and their functional consequences were explored by using comparable stimuli in human psychophysical experiments and in recordings from alert monkeys. They may represent the substrate for perceptual phenomena such as illusory contours, surface fill-in, and contour saliency. The dynamic nature of receptive field properties and cortical architecture has been seen over time scales ranging from seconds to months. One can induce a remapping of the topography of visual cortex by making focal binocular retinal lesions. Shorter-term plasticity of cortical receptive fields was observed following brief periods of visual stimulation. The mechanisms involved entailed, for the short-term changes, altering the effectiveness of existing cortical connections, and for the long-term changes, sprouting of axon collaterals and synaptogenesis. The mutability of cortical function implies a continual process of calibration and normalization of the perception of visual attributes that is dependent on sensory experience throughout adulthood and might further represent the mechanism of perceptual learning.

Modeling and optimization of populations subject to time-dependent mutation.

It has become clear that many organisms possess the ability to regulate their mutation rate in response to environmental conditions. So the question of finding an optimal mutation rate must be replaced by that of finding an optimal mutation schedule. We show that this task cannot be accomplished with standard population-dynamic models. We then develop a "hybrid" model for populations experiencing time-dependent mutation that treats population growth as deterministic but the time of first appearance of new variants as stochastic. We show that the hybrid model agrees well with a Monte Carlo simulation. From this model, we derive a deterministic approximation, a "threshold" model, that is similar to standard population dynamic models but differs in the initial rate of generation of new mutants. We use these techniques to model antibody affinity maturation by somatic hypermutation. We had previously shown that the optimal mutation schedule for the deterministic threshold model is phasic, with periods of mutation between intervals of mutation-free growth. To establish the validity of this schedule, we now show that the phasic schedule that optimizes the deterministic threshold model significantly improves upon the best constant-rate schedule for the hybrid and Monte Carlo models.