Making sense of AMPA receptor trafficking by modeling molecular mechanisms of synaptic plasticity.

Synaptic plasticity involves a complex molecular machinery with various protein interactions but it is not yet clear how its components give rise to the different aspects of synaptic plasticity. Here we ask whether it is possible to mathematically model synaptic plasticity by making use of known substances only. We present a model of a multistable biochemical reaction system and use it to simulate the plasticity of synaptic transmission in long-term potentiation (LTP) or long-term depression (LTD) after repeated excitation of the synapse. According to our model, we can distinguish between two phases: first, a "viscosity" phase after the first excitation, the effects of which like the activation of NMDA receptors and CaMKII fade out in the absence of further excitations. Second, a "plasticity" phase actuated by an identical subsequent excitation that follows after a short time interval and causes the temporarily altered concentrations of AMPA subunits in the postsynaptic membrane to be stabilized. We show that positive feedback is the crucial element in the core chemical reaction, i.e. the activation of the short-tail AMPA subunit by NEM-sensitive factor, which allows generating multiple stable equilibria. Three stable equilibria are related to LTP, LTD and a third unfixed state called ACTIVE. Our mathematical approach shows that modeling synaptic multistability is possible by making use of known substances like NMDA and AMPA receptors, NEM-sensitive factor, glutamate, CaMKII and brain-derived neurotrophic factor. Furthermore, we could show that the heteromeric combination of short- and long-tail AMPA receptor subunits fulfills the function of a memory tag.

MORM--a Petri net based model for assessing OH&S risks in industrial processes: modeling qualitative aspects.

Because of the increase in workplace automation and the diversification of industrial processes, workplaces have become more and more complex. The classical approaches used to address workplace hazard concerns, such as checklists or sequence models, are, therefore, of limited use in such complex systems. Moreover, because of the multifaceted nature of workplaces, the use of single-oriented methods, such as AEA (man oriented), FMEA (system oriented), or HAZOP (process oriented), is not satisfactory. The use of a dynamic modeling approach in order to allow multiple-oriented analyses may constitute an alternative to overcome this limitation. The qualitative modeling aspects of the MORM (man-machine occupational risk modeling) model are discussed in this article. The model, realized on an object-oriented Petri net tool (CO-OPN), has been developed to simulate and analyze industrial processes in an OH&S perspective. The industrial process is modeled as a set of interconnected subnets (state spaces), which describe its constitutive machines. Process-related factors are introduced, in an explicit way, through machine interconnections and flow properties. While man-machine interactions are modeled as triggering events for the state spaces of the machines, the CREAM cognitive behavior model is used in order to establish the relevant triggering events. In the CO-OPN formalism, the model is expressed as a set of interconnected CO-OPN objects defined over data types expressing the measure attached to the flow of entities transiting through the machines. Constraints on the measures assigned to these entities are used to determine the state changes in each machine. Interconnecting machines implies the composition of such flow and consequently the interconnection of the measure constraints. This is reflected by the construction of constraint enrichment hierarchies, which can be used for simulation and analysis optimization in a clear mathematical framework. The use of Petri nets to perform multiple-oriented analysis opens perspectives in the field of industrial risk management. It may significantly reduce the duration of the assessment process. But, most of all, it opens perspectives in the field of risk comparisons and integrated risk management. Moreover, because of the generic nature of the model and tool used, the same concepts and patterns may be used to model a wide range of systems and application fields.

Measurements of glial metabolic fluxes with C-11-acetate using positron emission and an adapted NMR-based metabolic modeling approach

Objectives: Acetate brain metabolism has the particularity to occur specifically in glial cells. Labeling studies, using acetate labeled either with 13C (NMR) or 11C (PET), are governed by the same biochemical reactions and thus follow the same mathematical principles. In this study, the objective was to adapt an NMR acetate brain metabolism model to analyse [1-11C]acetate infusion in rats. Methods: Brain acetate infusion experiments were modeled using a two-compartment model approach used in NMR.1-3 The [1-11C]acetate labeling study was done using a beta scintillator.4 The measured radioactive signal represents the time evolution of the sum of all labeled metabolites in the brain. Using a coincidence counter in parallel, an arterial input curve was measured. The 11C at position C-1 of acetate is metabolized in the first turn of the TCA cycle to the position 5 of glutamate (Figure 1A). Through the neurotransmission process, it is further transported to the position 5 of glutamine and the position 5 of neuronal glutamate. After the second turn of the TCA cycle, tracer from [1-11C]acetate (and also a part from glial [5-11C]glutamate) is transferred to glial [1-11C]glutamate and further to [1-11C]glutamine and neuronal glutamate through the neurotransmission cycle. Brain poster session: oxidative mechanisms S460 Journal of Cerebral Blood Flow & Metabolism (2009) 29, S455-S466 Results: The standard acetate two-pool PET model describes the system by a plasma pool and a tissue pool linked by rate constants. Experimental data are not fully described with only one tissue compartment (Figure 1B). The modified NMR model was fitted successfully to tissue time-activity curves from 6 single animals, by varying the glial mitochondrial fluxes and the neurotransmission flux Vnt. A glial composite rate constant Kgtg=Vgtg/[Ace]plasma was extracted. Considering an average acetate concentration in plasma of 1 mmol/g5 and the negligible additional amount injected, we found an average Vgtg = 0.08±0.02 (n = 6), in agreement with previous NMR measurements.1 The tissue time-activity curve is dominated by glial glutamate and later by glutamine (Figure 1B). Labeling of neuronal pools has a low influence, at least for the 20 mins of beta-probe acquisition. Based on the high diffusivity of CO2 across the blood-brain barrier; 11CO2 is not predominant in the total tissue curve, even if the brain CO2 pool is big compared with other metabolites, due to its strong dilution through unlabeled CO2 from neuronal metabolism and diffusion from plasma. Conclusion: The two-compartment model presented here is also able to fit data of positron emission experiments and to extract specific glial metabolic fluxes. 11C-labeled acetate presents an alternative for faster measurements of glial oxidative metabolism compared to NMR, potentially applicable to human PET imaging. However, to quantify the relative value of the TCA cycle flux compared to the transmitochondrial flux, the chemical sensitivity of NMR is required. PET and NMR are thus complementary.

Brain lactate kinetics: Modeling evidence for neuronal lactate uptake upon activation.

A critical issue in brain energy metabolism is whether lactate produced within the brain by astrocytes is taken up and metabolized by neurons upon activation. Although there is ample evidence that neurons can efficiently use lactate as an energy substrate, at least in vitro, few experimental data exist to indicate that it is indeed the case in vivo. To address this question, we used a modeling approach to determine which mechanisms are necessary to explain typical brain lactate kinetics observed upon activation. On the basis of a previously validated model that takes into account the compartmentalization of energy metabolism, we developed a mathematical model of brain lactate kinetics, which was applied to published data describing the changes in extracellular lactate levels upon activation. Results show that the initial dip in the extracellular lactate concentration observed at the onset of stimulation can only be satisfactorily explained by a rapid uptake within an intraparenchymal cellular compartment. In contrast, neither blood flow increase, nor extracellular pH variation can be major causes of the lactate initial dip, whereas tissue lactate diffusion only tends to reduce its amplitude. The kinetic properties of monocarboxylate transporter isoforms strongly suggest that neurons represent the most likely compartment for activation-induced lactate uptake and that neuronal lactate utilization occurring early after activation onset is responsible for the initial dip in brain lactate levels observed in both animals and humans.

Toxicokinetic modeling of folpet fungicide and its ring-biomarkers of exposure in humans.

A human in vivo toxicokinetic model was built to allow a better understanding of the toxicokinetics of folpet fungicide and its key ring biomarkers of exposure: phthalimide (PI), phthalamic acid (PAA) and phthalic acid (PA). Both PI and the sum of ring metabolites, expressed as PA equivalents (PAeq), may be used as biomarkers of exposure. The conceptual representation of the model was based on the analysis of the time course of these biomarkers in volunteers orally and dermally exposed to folpet. In the model, compartments were also used to represent the body burden of folpet and experimentally relevant PI, PAA and PA ring metabolites in blood and in key tissues as well as in excreta, hence urinary and feces. The time evolution of these biomarkers in each compartment of the model was then mathematically described by a system of coupled differential equations. The mathematical parameters of the model were then determined from best fits to the time courses of PI and PAeq in blood and urine of five volunteers administered orally 1 mg kg(-1) and dermally 10 mg kg(-1) of folpet. In the case of oral administration, the mean elimination half-life of PI from blood (through feces, urine or metabolism) was found to be 39.9 h as compared with 28.0 h for PAeq. In the case of a dermal application, mean elimination half-life of PI and PAeq was estimated to be 34.3 and 29.3 h, respectively. The average final fractions of administered dose recovered in urine as PI over the 0-96 h period were 0.030 and 0.002%, for oral and dermal exposure, respectively. Corresponding values for PAeq were 24.5 and 1.83%, respectively. Finally, the average clearance rate of PI from blood calculated from the oral and dermal data was 0.09 ± 0.03 and 0.13 ± 0.05 ml h(-1) while the volume of distribution was 4.30 ± 1.12 and 6.05 ± 2.22 l, respectively. It was not possible to obtain the corresponding values from PAeq data owing to the lack of blood time course data.

Modeling morphogen gradient formation from arbitrary realistically shaped sources.

Much of the analytical modeling of morphogen profiles is based on simplistic scenarios, where the source is abstracted to be point-like and fixed in time, and where only the steady state solution of the morphogen gradient in one dimension is considered. Here we develop a general formalism allowing to model diffusive gradient formation from an arbitrary source. This mathematical framework, based on the Green's function method, applies to various diffusion problems. In this paper, we illustrate our theory with the explicit example of the Bicoid gradient establishment in Drosophila embryos. The gradient formation arises by protein translation from a mRNA distribution followed by morphogen diffusion with linear degradation. We investigate quantitatively the influence of spatial extension and time evolution of the source on the morphogen profile. For different biologically meaningful cases, we obtain explicit analytical expressions for both the steady state and time-dependent 1D problems. We show that extended sources, whether of finite size or normally distributed, give rise to more realistic gradients compared to a single point-source at the origin. Furthermore, the steady state solutions are fully compatible with a decreasing exponential behavior of the profile. We also consider the case of a dynamic source (e.g. bicoid mRNA diffusion) for which a protein profile similar to the ones obtained from static sources can be achieved.

Implicit methods for qualitative modeling of gene regulatory networks.

Advancements in high-throughput technologies to measure increasingly complex biological phenomena at the genomic level are rapidly changing the face of biological research from the single-gene single-protein experimental approach to studying the behavior of a gene in the context of the entire genome (and proteome). This shift in research methodologies has resulted in a new field of network biology that deals with modeling cellular behavior in terms of network structures such as signaling pathways and gene regulatory networks. In these networks, different biological entities such as genes, proteins, and metabolites interact with each other, giving rise to a dynamical system. Even though there exists a mature field of dynamical systems theory to model such network structures, some technical challenges are unique to biology such as the inability to measure precise kinetic information on gene-gene or gene-protein interactions and the need to model increasingly large networks comprising thousands of nodes. These challenges have renewed interest in developing new computational techniques for modeling complex biological systems. This chapter presents a modeling framework based on Boolean algebra and finite-state machines that are reminiscent of the approach used for digital circuit synthesis and simulation in the field of very-large-scale integration (VLSI). The proposed formalism enables a common mathematical framework to develop computational techniques for modeling different aspects of the regulatory networks such as steady-state behavior, stochasticity, and gene perturbation experiments.

A mathematical model to describe fat oxidation kinetics during graded exercise.

PURPOSE: The purpose of this study was to develop a mathematical model (sine model, SIN) to describe fat oxidation kinetics as a function of the relative exercise intensity [% of maximal oxygen uptake (%VO2max)] during graded exercise and to determine the exercise intensity (Fatmax) that elicits maximal fat oxidation (MFO) and the intensity at which the fat oxidation becomes negligible (Fatmin). This model included three independent variables (dilatation, symmetry, and translation) that incorporated primary expected modulations of the curve because of training level or body composition. METHODS: Thirty-two healthy volunteers (17 women and 15 men) performed a graded exercise test on a cycle ergometer, with 3-min stages and 20-W increments. Substrate oxidation rates were determined using indirect calorimetry. SIN was compared with measured values (MV) and with other methods currently used [i.e., the RER method (MRER) and third polynomial curves (P3)]. RESULTS: There was no significant difference in the fitting accuracy between SIN and P3 (P = 0.157), whereas MRER was less precise than SIN (P < 0.001). Fatmax (44 +/- 10% VO2max) and MFO (0.37 +/- 0.16 g x min(-1)) determined using SIN were significantly correlated with MV, P3, and MRER (P < 0.001). The variable of dilatation was correlated with Fatmax, Fatmin, and MFO (r = 0.79, r = 0.67, and r = 0.60, respectively, P < 0.001). CONCLUSIONS: The SIN model presents the same precision as other methods currently used in the determination of Fatmax and MFO but in addition allows calculation of Fatmin. Moreover, the three independent variables are directly related to the main expected modulations of the fat oxidation curve. SIN, therefore, seems to be an appropriate tool in analyzing fat oxidation kinetics obtained during graded exercise.

Ab initio modeling and molecular dynamics simulation of the alpha 1b-adrenergic receptor activation.

This work describes the ab initio procedure employed to build an activation model for the alpha 1b-adrenergic receptor (alpha 1b-AR). The first version of the model was progressively modified and complicated by means of a many-step iterative procedure characterized by the employment of experimental validations of the model in each upgrading step. A combined simulated (molecular dynamics) and experimental mutagenesis approach was used to determine the structural and dynamic features characterizing the inactive and active states of alpha 1b-AR. The latest version of the model has been successfully challenged with respect to its ability to interpret and predict the functional properties of a large number of mutants. The iterative approach employed to describe alpha 1b-AR activation in terms of molecular structure and dynamics allows further complications of the model to allow prediction and interpretation of an ever-increasing number of experimental data.

Modeling sequencing errors by combining Hidden Markov models.

Among the largest resources for biological sequence data is the large amount of expressed sequence tags (ESTs) available in public and proprietary databases. ESTs provide information on transcripts but for technical reasons they often contain sequencing errors. Therefore, when analyzing EST sequences computationally, such errors must be taken into account. Earlier attempts to model error prone coding regions have shown good performance in detecting and predicting these while correcting sequencing errors using codon usage frequencies. In the research presented here, we improve the detection of translation start and stop sites by integrating a more complex mRNA model with codon usage bias based error correction into one hidden Markov model (HMM), thus generalizing this error correction approach to more complex HMMs. We show that our method maintains the performance in detecting coding sequences.

Modeling of in-situ crystallization processes in the Permian mafic layered intrusion of Mont Collon (Dent Blanche nappe, western Alps)

The Mont Collon mafic complex is one of the best preserved examples of the Early Permian magmatism in the Central Alps, related to the intra-continental collapse of the Variscan belt. It mostly consists (> 95 vol.%) of ol+hy-nonnative plagioclase-wehrlites, olivine- and cpx-gabbros with cumulitic structures, crosscut by acid dikes. Pegmatitic gabbros, troctolites and anorthosites outcrop locally. A well-preserved cumulative, sequence is exposed in the Dents de Bertol area (center of intrusion). PT-calculations indicate that this layered magma chamber emplaced at mid-crustal levels at about 0.5 GPa and 1100 degrees C. The Mont Collon cumulitic rocks record little magmatic differentiation, as illustrated by the restricted range of clinopyroxene mg-number (Mg#(cpx)=83-89). Whole-rock incompatible trace-element contents (e.g. Nb, Zr, Ba) vary largely and without correlation with major-element composition. These features are characteristic of an in-situ crystallization process with variable amounts of interstitial liquid L trapped between the cumulus mineral phases. LA-ICPMS measurements show that trace-element distribution in the latter is homogeneous, pointing to subsolidus re-equilibration between crystals and interstitial melts. A quantitative modeling based on Langmuir's in-situ crystallization equation successfully duplicated the REE concentrations in cumulitic minerals of all rock facies of the intrusion. The calculated amounts of interstitial liquid L vary between 0 and 35% for degrees of differentiation F of 0 to 20%, relative to the least evolved facies of the intrusion. L values are well correlated with the modal proportions of interstitial amphibole and whole-rock incompatible trace-element concentrations (e.g. Zr, Nb) of the tested samples. However, the in-situ crystallization model reaches its limitations with rock containing high modal content of REE-bearing minerals (i.e. zircon), such as pegmatitic gabbros. Dikes of anorthositic composition, locally crosscutting the layered lithologies, evidence that the Mont Collon rocks evolved in open system with mixing of intercumulus liquids of different origins and possibly contrasting compositions. The proposed model is not able to resolve these complex open systems, but migrating liquids could be partly responsible for the observed dispersion of points in some correlation diagrams. Absence of significant differentiation with recurrent lithologies in the cumulitic pile of Dents de Bertol points to an efficiently convective magma chamber, with possible periodic replenishment, (c) 2005 Elsevier B.V. All rights reserved.

Modeling resting-state functional networks when the cortex falls asleep: local and global changes.

The transition from wakefulness to sleep represents the most conspicuous change in behavior and the level of consciousness occurring in the healthy brain. It is accompanied by similarly conspicuous changes in neural dynamics, traditionally exemplified by the change from "desynchronized" electroencephalogram activity in wake to globally synchronized slow wave activity of early sleep. However, unit and local field recordings indicate that the transition is more gradual than it might appear: On one hand, local slow waves already appear during wake; on the other hand, slow sleep waves are only rarely global. Studies with functional magnetic resonance imaging also reveal changes in resting-state functional connectivity (FC) between wake and slow wave sleep. However, it remains unclear how resting-state networks may change during this transition period. Here, we employ large-scale modeling of the human cortico-cortical anatomical connectivity to evaluate changes in resting-state FC when the model "falls asleep" due to the progressive decrease in arousal-promoting neuromodulation. When cholinergic neuromodulation is parametrically decreased, local slow waves appear, while the overall organization of resting-state networks does not change. Furthermore, we show that these local slow waves are structured macroscopically in networks that resemble the resting-state networks. In contrast, when the neuromodulator decrease further to very low levels, slow waves become global and resting-state networks merge into a single undifferentiated, broadly synchronized network.

A musculoskeletal shoulder model based on pseudo-inverse and null-space optimization.

The goal of the present work was assess the feasibility of using a pseudo-inverse and null-space optimization approach in the modeling of the shoulder biomechanics. The method was applied to a simplified musculoskeletal shoulder model. The mechanical system consisted in the arm, and the external forces were the arm weight, 6 scapulo-humeral muscles and the reaction at the glenohumeral joint, which was considered as a spherical joint. The muscle wrapping was considered around the humeral head assumed spherical. The dynamical equations were solved in a Lagrangian approach. The mathematical redundancy of the mechanical system was solved in two steps: a pseudo-inverse optimization to minimize the square of the muscle stress and a null-space optimization to restrict the muscle force to physiological limits. Several movements were simulated. The mathematical and numerical aspects of the constrained redundancy problem were efficiently solved by the proposed method. The prediction of muscle moment arms was consistent with cadaveric measurements and the joint reaction force was consistent with in vivo measurements. This preliminary work demonstrated that the developed algorithm has a great potential for more complex musculoskeletal modeling of the shoulder joint. In particular it could be further applied to a non-spherical joint model, allowing for the natural translation of the humeral head in the glenoid fossa.

Body mass index, cigarette smoking, and alcohol consumption and cancers of the oral cavity, pharynx, and larynx: modeling odds ratios in pooled case-control data.

Odds ratios for head and neck cancer increase with greater cigarette and alcohol use and lower body mass index (BMI; weight (kg)/height(2) (m(2))). Using data from the International Head and Neck Cancer Epidemiology Consortium, the authors conducted a formal analysis of BMI as a modifier of smoking- and alcohol-related effects. Analysis of never and current smokers included 6,333 cases, while analysis of never drinkers and consumers of < or =10 drinks/day included 8,452 cases. There were 8,000 or more controls, depending on the analysis. Odds ratios for all sites increased with lower BMI, greater smoking, and greater drinking. In polytomous regression, odds ratios for BMI (P = 0.65), smoking (P = 0.52), and drinking (P = 0.73) were homogeneous for oral cavity and pharyngeal cancers. Odds ratios for BMI and drinking were greater for oral cavity/pharyngeal cancer (P < 0.01), while smoking odds ratios were greater for laryngeal cancer (P < 0.01). Lower BMI enhanced smoking- and drinking-related odds ratios for oral cavity/pharyngeal cancer (P < 0.01), while BMI did not modify smoking and drinking odds ratios for laryngeal cancer. The increased odds ratios for all sites with low BMI may suggest related carcinogenic mechanisms; however, BMI modification of smoking and drinking odds ratios for cancer of the oral cavity/pharynx but not larynx cancer suggests additional factors specific to oral cavity/pharynx cancer.