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.

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 characteristics and adaptability of mouse vestibulo-ocular and optokinetic response eye movements and the role of the flocculo-olivary system revealed by chemical lesions

The dynamic characteristics of reflex eye movements were measured in two strains of chronically prepared mice by using an infrared television camera system. The horizontal vestibulo-ocular reflex (HVOR) and horizontal optokinetic response (HOKR) were induced by sinusoidal oscillations of a turntable, in darkness, by 10° (peak to peak) at 0.11–0.50 Hz and of a checked-pattern screen, in light, by 5–20°at 0.11–0.17 Hz, respectively. The gains and phases of the HVOR and HOKR of the C57BL/6 mice were nearly equivalent to those of rabbits and rats, whereas the 129/Sv mice exhibited very low gains in the HVOR and moderate phase lags in the HOKR, suggesting an inherent sensory-motor anomaly. Adaptability of the HOKR was examined in C57BL/6 mice by sustained screen oscillation. When the screen was oscillated by 10° at 0.17 Hz, which induced sufficient retinal slips, the gain of the HOKR increased by 0.08 in 1 h on average, whereas the stimuli that induced relatively small or no retinal slips affected the gain very little. Lesions of the flocculi induced by local applications of 0.1% ibotenic acid and lesions of the inferior olivary nuclei induced by i.p. injection of 3-acetylpyridine in C57BL/6 mice little affected the dynamic characteristics of the HVOR and HOKR, but abolished the adaptation of the HOKR. These results indicate that the olivo-floccular system plays an essential role in the adaptive control of the ocular reflex in mice, as suggested in other animal species. The data presented provide the basis for analyzing the reflex eye movements of genetically engineered mice.

Unusual Centrosome Cycle in Dictyostelium: Correlation of Dynamic Behavior and Structural Changes

Centrosome duplication and separation are of central importance for cell division. Here we provide a detailed account of this dynamic process in Dictyostelium. Centrosome behavior was monitored in living cells using a γ-tubulin–green fluorescent protein construct and correlated with morphological changes at the ultrastructural level. All aspects of the duplication and separation process of this centrosome are unusual when compared with, e.g., vertebrate cells. In interphase the Dictyostelium centrosome is a box-shaped structure comprised of three major layers, surrounded by an amorphous corona from which microtubules emerge. Structural duplication takes place during prophase, as opposed to G1/S in vertebrate cells. The three layers of the box-shaped core structure increase in size. The surrounding corona is lost, an event accompanied by a decrease in signal intensity of γ-tubulin–green fluorescent protein at the centrosome and the breakdown of the interphase microtubule system. At the prophase/prometaphase transition the separation into two mitotic centrosomes takes place via an intriguing lengthwise splitting process where the two outer layers of the prophase centrosome peel away from each other and become the mitotic centrosomes. Spindle microtubules are now nucleated from surfaces that previously were buried inside the interphase centrosome. Finally, at the end of telophase, the mitotic centrosomes fold in such a way that the microtubule-nucleating surface remains on the outside of the organelle. Thus in each cell cycle the centrosome undergoes an apparent inside-out/outside-in reversal of its layered structure.

Tubulin Polyglycylation: Differential Posttranslational Modification of Dynamic Cytoplasmic and Stable Axonemal Microtubules in Paramecium

Polyglycylation, a posttranslational modification of tubulin, was discovered in the highly stable axonemal microtubules of Paramecium cilia where it involves the lateral linkage of up to 34 glycine units per tubulin subunit. The observation of this type of posttranslational modification mainly in axonemes raises the question as to its relationship with axonemal organization and with microtubule stability. This led us to investigate the glycylation status of cytoplasmic microtubules that correspond to the dynamic microtubules in Paramecium. Two anti-glycylated tubulin monoclonal antibodies (mAbs), TAP 952 and AXO 49, are shown here to exhibit different affinities toward mono- and polyglycylated synthetic tubulin peptides. Using immunoblotting and mass spectrometry, we show that cytoplasmic tubulin is glycylated. In contrast to the highly glycylated axonemal tubulin, which is recognized by the two mAbs, cytoplasmic tubulin reacts exclusively with TAP 952, and the α- and β- tubulin subunits are modified by only 1–5 and 2–9 glycine units, respectively. Our analyses suggest that most of the cytoplasmic tubulin contains side chain lengths of 1 or 2 glycine units distributed on several glycylation sites. The subcellular partition of distinct polyglycylated tubulin isoforms between cytoplasmic and axonemal compartments implies the existence of regulatory mechanisms for glycylation. By following axonemal tubulin immunoreactivity with anti-glycylated tubulin mAbs upon incubation with a Paramecium cellular extract, the presence of a deglycylation enzyme is revealed in the cytoplasm of this organism. These observations establish that polyglycylation is reversible and indicate that, in vivo, an equilibrium between glycylating and deglycylating enzymes might be responsible for the length of the oligoglycine side chains of tubulin.

Catalytic mechanism of the adenylyl and guanylyl cyclases: Modeling and mutational analysis

The adenylyl and guanylyl cyclases catalyze the formation of 3′,5′-cyclic adenosine or guanosine monophosphate from the corresponding nucleoside 5′-triphosphate. The guanylyl cyclases, the mammalian adenylyl cyclases, and their microbial homologues function as pairs of homologous catalytic domains. The crystal structure of the rat type II adenylyl cyclase C2 catalytic domain was used to model by homology a mammalian adenylyl cyclase C1-C2 domain pair, a homodimeric adenylyl cyclase of Dictyostelium discoideum, a heterodimeric soluble guanylyl cyclase, and a homodimeric membrane guanylyl cyclase. Mg2+ATP or Mg2+GTP were docked into the active sites based on known stereochemical constraints on their conformation. The models are consistent with the activities of seven active-site mutants. Asp-310 and Glu-432 of type I adenylyl cyclase coordinate a Mg2+ ion. The D310S and D310A mutants have 10-fold reduced Vmax and altered [Mg2+] dependence. The NTP purine moieties bind in mostly hydrophobic pockets. Specificity is conferred by a Lys and an Asp in adenylyl cyclase, and a Glu, an Arg, and a Cys in guanylyl cyclase. The models predict that an Asp from one domain is a general base in the reaction, and that the transition state is stabilized by a conserved Asn-Arg pair on the other domain.

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.

Blood flow and oxygen delivery to human brain during functional activity: Theoretical modeling and experimental data

Coupling of cerebral blood flow (CBF) and cerebral metabolic rate for oxygen (CMRO2) in physiologically activated brain states remains the subject of debates. Recently it was suggested that CBF is tightly coupled to oxidative metabolism in a nonlinear fashion. As part of this hypothesis, mathematical models of oxygen delivery to the brain have been described in which disproportionately large increases in CBF are necessary to sustain even small increases in CMRO2 during activation. We have explored the coupling of CBF and oxygen delivery by using two complementary methods. First, a more complex mathematical model was tested that differs from those recently described in that no assumptions were made regarding tissue oxygen level. Second, [15O] water CBF positron emission tomography (PET) studies in nine healthy subjects were conducted during states of visual activation and hypoxia to examine the relationship of CBF and oxygen delivery. In contrast to previous reports, our model showed adequate tissue levels of oxygen could be maintained without the need for increased CBF or oxygen delivery. Similarly, the PET studies demonstrated that the regional increase in CBF during visual activation was not affected by hypoxia. These findings strongly indicate that the increase in CBF associated with physiological activation is regulated by factors other than local requirements in oxygen.

Dynamic friction and the origin of the complexity of earthquake sources.

We study a simple antiplane fault of finite length embedded in a homogeneous isotropic elastic solid to understand the origin of seismic source heterogeneity in the presence of nonlinear rate- and state-dependent friction. All the mechanical properties of the medium and friction are assumed homogeneous. Friction includes a characteristic length that is longer than the grid size so that our models have a well-defined continuum limit. Starting from a heterogeneous initial stress distribution, we apply a slowly increasing uniform stress load far from the fault and we simulate the seismicity for a few 1000 events. The style of seismicity produced by this model is determined by a control parameter associated with the degree of rate dependence of friction. For classical friction models with rate-independent friction, no complexity appears and seismicity is perfectly periodic. For weakly rate-dependent friction, large ruptures are still periodic, but small seismicity becomes increasingly nonstationary. When friction is highly rate-dependent, seismicity becomes nonperiodic and ruptures of all sizes occur inside the fault. Highly rate-dependent friction destabilizes the healing process producing premature healing of slip and partial stress drop. Partial stress drop produces large variations in the state of stress that in turn produce earthquakes of different sizes. Similar results have been found by other authors using the Burridge and Knopoff model. We conjecture that all models in which static stress drop is only a fraction of the dynamic stress drop produce stress heterogeneity.