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1.  Dissection of a Krox20 positive feedback loop driving cell fate choices in hindbrain patterning 
A positive autoregulatory loop required for the expression of the transcription factor Krox20 was dissected using in vivo quantitative data and biophysical modelling to demonstrate how Krox20 controls cell fate decision and rhombomere size in the hindbrain.
Positive autoregulation of Krox20 underpins a bistable switch that turns a transient input signal into cell fate commitment, as demonstrated in single cell analyses.The duration and strength of the input signal control the size of the hindbrain segments by modulating the distribution between two cell fates.The progressive extinction of Krox20 expression involves a destabilization of the loop by repressor molecules.
Although feedback loops are essential in development, their molecular implementation and precise functions remain elusive. Using enhancer knockout in mice, we demonstrate that a direct, positive autoregulatory loop amplifies and maintains the expression of Krox20, a transcription factor governing vertebrate hindbrain segmentation. By combining quantitative data collected in the zebrafish with biophysical modelling that accounts for the intrinsic stochastic molecular dynamics, we dissect the loop at the molecular level. We find that it underpins a bistable switch that turns a transient input signal into cell fate commitment, as we observe in single cell analyses. The stochasticity of the activation process leads to a graded input–output response until saturation is reached. Consequently, the duration and strength of the input signal controls the size of the hindbrain segments by modulating the distribution between the two cell fates. Moreover, segment formation is buffered from severe variations in input level. Finally, the progressive extinction of Krox20 expression involves a destabilization of the loop by repressor molecules. These mechanisms are of general significance for cell type specification and tissue patterning.
PMCID: PMC3792346  PMID: 24061538
Fgf; Krox20; rhombomere; stochastic model; transcriptional enhancer
2.  Spatial telomere organization and clustering in yeast Saccharomyces cerevisiae nucleus is generated by a random dynamics of aggregation–dissociation 
Molecular Biology of the Cell  2013;24(11):1791-1800.
The 32 telomeres of budding yeast form clusters, yet whether clusters are due to random localization or telomeric interactions is unclear. Data from live-cell imaging are compared with a biophysical model of telomere dynamics. Direct molecular interaction between telomeres is the key parameter that regulates telomere clustering.
Spatial and temporal behavior of chromosomes and their regulatory proteins is a key control mechanism in genomic function. This is exemplified by the clustering of the 32 budding yeast telomeres that form foci in which silencing factors concentrate. To uncover the determinants of telomere distribution, we compare live-cell imaging with a stochastic model of telomere dynamics that we developed. We show that random encounters alone are inadequate to produce the clustering observed in vivo. In contrast, telomere dynamics observed in vivo in both haploid and diploid cells follows a process of dissociation–aggregation. We determine the time that two telomeres spend in the same cluster for the telomere distribution observed in cells expressing different levels of the silencing factor Sir3 protein, limiting for telomere clustering. We conclude that telomere clusters, their dynamics, and their nuclear distribution result from random motion, aggregation, and dissociation of telomeric regions, specifically determined by the amount of Sir3.
PMCID: PMC3667730  PMID: 23576549
3.  The Length of the Shortest Telomere as the Major Determinant of the Onset of Replicative Senescence 
Genetics  2013;194(4):847-857.
The absence of telomerase in many eukaryotes leads to the gradual shortening of telomeres, causing replicative senescence. In humans, this proliferation barrier constitutes a tumor suppressor mechanism and may be involved in cellular aging. Yet the heterogeneity of the senescence phenotype has hindered the understanding of its onset. Here we investigated the regulation of telomere length and its control of senescence heterogeneity. Because the length of the shortest telomeres can potentially regulate cell fate, we focus on their dynamics in Saccharomyces cerevisiae. We developed a stochastic model of telomere dynamics built on the protein-counting model, where an increasing number of protein-bound telomeric repeats shift telomeres into a nonextendable state by telomerase. Using numerical simulations, we found that the length of the shortest telomere is well separated from the length of the others, suggesting a prominent role in triggering senescence. We evaluated this possibility using classical genetic analyses of tetrads, combined with a quantitative and sensitive assay for senescence. In contrast to mitosis of telomerase-negative cells, which produces two cells with identical senescence onset, meiosis is able to segregate a determinant of senescence onset among the telomerase-negative spores. The frequency of such segregation is in accordance with this determinant being the length of the shortest telomere. Taken together, our results substantiate the length of the shortest telomere as being the key genetic marker determining senescence onset in S. cerevisiae.
PMCID: PMC3730915  PMID: 23733785
telomere distribution; replicative senescence; Saccharomyces cerevisiae; genetic determinism; stochastic modeling
4.  Unraveling novel features hidden in superresolution microscopy data 
Stochastic analysis of superresolution microscopy data obtained from receptor trafficking on neurons reveals novel organized molecular assembly generating long range forces. Would that have been possible with single particle tracking? How have we characterized these molecular assemblies?
PMCID: PMC3656019  PMID: 23710279
analysis; nano-domains; potential wells; stochastic; super-resolution
5.  Synaptic transmission in neurological disorders dissected by a quantitative approach 
Synaptic transmission depends on several molecular and geometric components, such as the location of vesicular release, the number of released neurotransmitter molecules, the number and type of receptors, as well as the synapse organization. Our goal here is to illustrate how synaptic modeling allows extracting quantitative information in the context of neurological diseases and associated therapies. Combining electrophysiology with simulation tools, we first evaluate the reduction in synaptically released glutamate molecules induced by a ketogenic diet. In a second part, because the scaffolding molecule Shank3 is disrupted at the postsynaptic density in Autism Spectral Disorders, we present a numerical simulation of the synaptic response where this disruption leads to an alteration of the excitatory AMPA receptor trafficking. The take home message is that combining recent experimental findings with modeling approaches allows obtaining precise quantitative properties of what was still unapproachable a decade ago.
PMCID: PMC3502205  PMID: 23181158
Shank3 mutation; autism; brownian simulations; glutamate dynamics; ketogenic diet; modeling; synaptic transmission
6.  Using default constraints of the spindle assembly checkpoint to estimate the associated chemical rates 
BMC Biophysics  2012;5:1.
Default activation of the spindle assembly checkpoint provides severe constraints on the underlying biochemical activation rates: on one hand, the cell cannot divide before all chromosomes are aligned, but on the other hand, when they are ready, the separation is quite fast, lasting a few minutes. Our purpose is to use these opposed constraints to estimate the associated chemical rates.
To analyze the above constraints, we develop a markovian model to describe the dynamics of Cdc20 molecules. We compute the probability for no APC/C activation before time t, the distribution of Cdc20 at equilibrium and the mean time to complete APC/C activation after all chromosomes are attached.
By studying Cdc20 inhibition and the activation time, we obtain a range for the main chemical reaction rates regulating the spindle assembly checkpoint and transition to anaphase.
PMCID: PMC3368725  PMID: 22260411
7.  Diffusion laws in dendritic spines 
Dendritic spines are small protrusions on a neuronal dendrite that are the main locus of excitatory synaptic connections. Although their geometry is variable over time and along the dendrite, they typically consist of a relatively large head connected to the dendritic shaft by a narrow cylindrical neck. The surface of the head is connected smoothly by a funnel or non-smoothly to the narrow neck, whose end absorbs the particles at the dendrite. We demonstrate here how the geometry of the neuronal spine can control diffusion and ultimately synaptic processes. We show that the mean residence time of a Brownian particle, such as an ion or molecule inside the spine, and of a receptor on its membrane, prior to absorption at the dendritic shaft depends strongly on the curvature of the connection of the spine head to the neck and on the neck's length. The analytical results solve the narrow escape problem for domains with long narrow necks.
PMCID: PMC3365919  PMID: 22655862
8.  Barriers to Diffusion in Dendrites and Estimation of Calcium Spread Following Synaptic Inputs 
PLoS Computational Biology  2011;7(10):e1002182.
The motion of ions, molecules or proteins in dendrites is restricted by cytoplasmic obstacles such as organelles, microtubules and actin network. To account for molecular crowding, we study the effect of diffusion barriers on local calcium spread in a dendrite. We first present a model based on a dimension reduction approach to approximate a three dimensional diffusion in a cylindrical dendrite by a one-dimensional effective diffusion process. By comparing uncaging experiments of an inert dye in a spiny dendrite and in a thin glass tube, we quantify the change in diffusion constants due to molecular crowding as Dcyto/Dwater = 1/20. We validate our approach by reconstructing the uncaging experiments using Brownian simulations in a realistic 3D model dendrite. Finally, we construct a reduced reaction-diffusion equation to model calcium spread in a dendrite under the presence of additional buffers, pumps and synaptic input. We find that for moderate crowding, calcium dynamics is mainly regulated by the buffer concentration, but not by the cytoplasmic crowding, dendritic spines or synaptic inputs. Following high frequency stimulations, we predict that calcium spread in dendrites is limited to small microdomains of the order of a few microns (<5 μm).
Author Summary
Diffusion is one of the main transport phenomena involved in signaling mechanisms of ions and molecules in living cells, such as neurons. As the cell cytoplasmic medium is highly heterogeneous and filled with many organelles, the motion of a diffusing particle is affected by many interactions with its environment. Interestingly, the functional consequences of these interactions cannot be directly quantified. Thus, in parallel with experimental methods, we have developed a computational approach to decipher the role of crowding from binding. We first study here the diffusion of a fluorescent marker in dendrites by a one-dimensional effective diffusion equation and obtained an effective diffusion constant that accounts for the presence heterogeneity in the medium. Furthermore, comparing our experimental data with simulations of diffusion in a crowded environment, we estimate the intracellular calcium spread in dendrites after injection of calcium transients. We confirm that calcium spread is mainly regulated by fixed buffer molecules, that bind temporarily to calcium, and less by the heterogeneous structure of the surrounding medium. Finally, we find that after synaptic inputs, calcium remains restricted to a domain of 2.5 µm to each side of the input location independent of the input frequency.
PMCID: PMC3192802  PMID: 22022241
9.  Synapse Geometry and Receptor Dynamics Modulate Synaptic Strength 
PLoS ONE  2011;6(10):e25122.
Synaptic transmission relies on several processes, such as the location of a released vesicle, the number and type of receptors, trafficking between the postsynaptic density (PSD) and extrasynaptic compartment, as well as the synapse organization. To study the impact of these parameters on excitatory synaptic transmission, we present a computational model for the fast AMPA-receptor mediated synaptic current. We show that in addition to the vesicular release probability, due to variations in their release locations and the AMPAR distribution, the postsynaptic current amplitude has a large variance, making a synapse an intrinsic unreliable device. We use our model to examine our experimental data recorded from CA1 mice hippocampal slices to study the differences between mEPSC and evoked EPSC variance. The synaptic current but not the coefficient of variation is maximal when the active zone where vesicles are released is apposed to the PSD. Moreover, we find that for certain type of synapses, receptor trafficking can affect the magnitude of synaptic depression. Finally, we demonstrate that perisynaptic microdomains located outside the PSD impacts synaptic transmission by regulating the number of desensitized receptors and their trafficking to the PSD. We conclude that geometrical modifications, reorganization of the PSD or perisynaptic microdomains modulate synaptic strength, as the mechanisms underlying long-term plasticity.
PMCID: PMC3184958  PMID: 21984900
10.  A Mechanism for the Polarity Formation of Chemoreceptors at the Growth Cone Membrane for Gradient Amplification during Directional Sensing 
PLoS ONE  2010;5(2):e9243.
Accurate response to external directional signals is essential for many physiological functions such as chemotaxis or axonal guidance. It relies on the detection and amplification of gradients of chemical cues, which, in eukaryotic cells, involves the asymmetric relocalization of signaling molecules. How molecular events coordinate to induce a polarity at the cell level remains however poorly understood, particularly for nerve chemotaxis. Here, we propose a model, inspired by single-molecule experiments, for the membrane dynamics of GABA chemoreceptors in nerve growth cones (GCs) during directional sensing. In our model, transient interactions between the receptors and the microtubules, coupled to GABA-induced signaling, provide a positive-feedback loop that leads to redistribution of the receptors towards the gradient source. Using numerical simulations with parameters derived from experiments, we find that the kinetics of polarization and the steady-state polarized distribution of GABA receptors are in remarkable agreement with experimental observations. Furthermore, we make predictions on the properties of the GC seen as a sensing, amplification and filtering module. In particular, the growth cone acts as a low-pass filter with a time constant ∼10 minutes determined by the Brownian diffusion of chemoreceptors in the membrane. This filtering makes the gradient amplification resistent to rapid fluctuations of the external signals, a beneficial feature to enhance the accuracy of neuronal wiring. Since the model is based on minimal assumptions on the receptor/cytoskeleton interactions, its validity extends to polarity formation beyond the case of GABA gradient sensing. Altogether, it constitutes an original positive-feedback mechanism by which cells can dynamically adapt their internal organization to external signals.
PMCID: PMC2825272  PMID: 20179770
11.  [No title available] 
The Journal of General Physiology  2006;127(2):219-220.
PMCID: PMC2151484
12.  The Emergence of Up and Down States in Cortical Networks  
PLoS Computational Biology  2006;2(3):e23.
The cerebral cortex is continuously active in the absence of external stimuli. An example of this spontaneous activity is the voltage transition between an Up and a Down state, observed simultaneously at individual neurons. Since this phenomenon could be of critical importance for working memory and attention, its explanation could reveal some fundamental properties of cortical organization. To identify a possible scenario for the dynamics of Up–Down states, we analyze a reduced stochastic dynamical system that models an interconnected network of excitatory neurons with activity-dependent synaptic depression. The model reveals that when the total synaptic connection strength exceeds a certain threshold, the phase space of the dynamical system contains two attractors, interpreted as Up and Down states. In that case, synaptic noise causes transitions between the states. Moreover, an external stimulation producing a depolarization increases the time spent in the Up state, as observed experimentally. We therefore propose that the existence of Up–Down states is a fundamental and inherent property of a noisy neural ensemble with sufficiently strong synaptic connections.
The cerebral cortex is continuously active in the absence of sensory stimuli. An example of this spontaneous activity is the phenomenon of voltage transitions between two distinct levels, called Up and Down states, observed simultaneously when recoding from many neurons. This phenomenon could be of a critical importance for working memory and attention. Thus, uncovering its biological mechanism could reveal fundamental properties of the cortical organization. In this theoretical contribution, Holcman and Tsodyks propose a mathematical model of cortical dynamics that exhibits spontaneous transitions between Up and Down states. The model describes an activity of a network of interconnected neurons. A crucial component of the model is synaptic depression of interneuronal connections, which is a well-known effect that characterizes many types of synaptic connections in the cortex. Despite its simplicity, the model reproduces many properties of Up–Down transitions that were experimentally observed, and makes several intriguing predictions for future experiments. In particular, the model predicts that the time that a network spends in the Up state is highly variable, changing from a fraction of a second to more than ten seconds, which could have some interesting implications for the temporal characteristics of working memory.
PMCID: PMC1409813  PMID: 16557293
13.  The Limit of Photoreceptor Sensitivity 
The Journal of General Physiology  2005;125(6):641-660.
Detection threshold in cone photoreceptors requires the simultaneous absorption of several photons because single photon photocurrent is small in amplitude and does not exceed intrinsic fluctuations in the outer segment dark current (dark noise). To understand the mechanisms that limit light sensitivity, we characterized the molecular origin of dark noise in intact, isolated bass single cones. Dark noise is caused by continuous fluctuations in the cytoplasmic concentrations of both cGMP and Ca2+ that arise from the activity in darkness of both guanylate cyclase (GC), the enzyme that synthesizes cGMP, and phosphodiesterase (PDE), the enzyme that hydrolyzes it. In cones loaded with high concentration Ca2+ buffering agents, we demonstrate that variation in cGMP levels arise from fluctuations in the mean PDE enzymatic activity. The rates of PDE activation and inactivation determine the quantitative characteristics of the dark noise power density spectrum. We developed a mathematical model based on the dynamics of PDE activity that accurately predicts this power spectrum. Analysis of the experimental data with the theoretical model allows us to determine the rates of PDE activation and deactivation in the intact photoreceptor. In fish cones, the mean lifetime of active PDE at room temperature is ∼55 ms. In nonmammalian rods, in contrast, active PDE lifetime is ∼555 ms. This remarkable difference helps explain why cones are noisier than rods and why cone photocurrents are smaller in peak amplitude and faster in time course than those in rods. Both these features make cones less light sensitive than rods.
PMCID: PMC2234084  PMID: 15928405
phototransduction; phosphodiesterase; guanylate cyclase; cGMP; calcium

Results 1-13 (13)