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Variability is a prominent feature of any biological system. Random variability poses a fundamental problem for information processing and therefore affects all aspects of nervous system function. We know much about the molecular mechanisms which govern neuronal function. Yet, the impact of the inherent molecular variability ("noise") on neural function has only recently been addressed in a quantitative manner by the use of stochastic models and simulations.
We will focus here on the action potentials, the fundamental signal used by neurons to transmit information along the connections of our brain's networks. We will show how thermodynamic fluctuations in signaling proteins (voltage-gated ion channels) that mediate the action potential set hard limits and constraints on the way the brain can be wired. We place this finding into the context of other physical constraints on the brain's networks. This approach will enable us to make predictions about basic properties of neural network connectivity from first biophysical principles.
Collective dynamics are widely observed during development of multicellular bodies and emerge as a result of communication among individual cells via signaling molecules. However, little is known experimentally of the fundamental features that describe how the highly nonlinear spatio-temporal dynamics at the single-cell level can give rise to coherent dynamics at the population level. Here a FRET-based sensor protein, combined with live-imaging is used to monitor cytosolic levels of cAMP which serves as the messenger molecule in developing cells of social amoebae Dictyostelium discoideum to allow individual cells to aggregate to form fruiting bodies. Timelapse recordings of cell populations during the first 10 hours of development reveal the very onset of periodic spike-like signaling and sequential changes in the frequency at single cell level resolution. Collective cAMP oscillations in populations of cells under perfusion reveal a sharp phase transition between a decoupled and a synchronized state for a range of cell densities and dilution rates. These observations suggest that the intact population is able to drive itself to this transition spontaneously during development.
Many biological systems require precise positional information to function correctly. A prominent example is the determination of cell fate during embryonic development. This positional information is often encoded in concentration gradients. A specific protein is often produced only within a small region, and subsequently spreads into the surrounding space. This leads to a spatial concentration gradient, with the highest protein concentration near the source. By switching on a signal only where the local concentration is above a certain threshold, this gradient can provide positional information. However, intrinsic randomness in biochemical reactions and diffusion will lead to unavoidable fluctuations in the concentration profile, which in turn will lead to fluctuations in the identified position. We therefore investigated how precisely a noisy concentration gradient can specify positional information. We found that both the kinetic parameters and the overall functional form of a concentration gradient can be optimised to generate maximally precise positional information.
How do multipotent stem cells establish, with such stunning reliability, the correct transcriptome of a cell fate that is specified by the expression state of 1000s of genes to generate the discrete cell types of the metazoan body? Given the unfathomable combinatorial possibilities for the expression of ten thousands of genes, obviously the answer lies in the gene regulatory network that orchestrates the improbable yet inevitable establishment of each of the cell type-specific gene expression configurations. The key idea is that cell fates correspond to high-dimensional attractor states, as Stuart Kauffman proposed in 1969. However, cell fate decision is also stochastic. In this talk, I will present an integration of the high-dimensional determination and the stochasticity of cell fates. Experimental evidence will be presented in support of the ideas (i) that cell fates are "attractors" of the network; (ii) that cell fate decisions correspond to bifurcation-driven destabilization of the stem cell attractors; and (iii) that transcriptome-wide gene expression fluctuations are at the core of multipotency, allowing multipotent stem cells to vacillate in the state of indeterminacy before making fate decisions.
All biological systems have a certain level of robustness to some ranges of disturbances and changes in the noisy environment. Robustness is a fundamental property for any system to function properly. Therefore, it has been studied intensively in the control engineering community for last 20 years. Although nonlinear relations are general properties of biomolecular networks, in many cases some basic principles and structures can be understood from linear analysis. ?Even for the linear formulations, however, there are several fundamental difficulties in the robustness analysis. In this talk, two very different aspects of robustness analysis are discussed: deterministic and stochastic. The significant effect of stochastic noise in biomolecular network will be highlighted and some modelling and analysis methods will be presented. Firstly, an extreme fragility of cAMP oscillations of Dictyostelium during the aggregation phase is found based on a deterministic robustness analysis. Secondly, it will be shown that the fragility is disappeared with stochastic noises and the source of robust cAMP oscillation is indeed the noise itself. Thirdly, from a computational aspect, an efficient algorithm to check the stochastic effects will be presented. It will be shown that checking any qualitative change by noise will be equivalent to check the Nyquist stability criteria, which has been a major analysis tool in control engineering. Finally, a new modelling approach in order to include not only stochastic but also spatial effects without increasing the required computational cost too much will be presented.
Genetic information is encoded in the nucleotide sequence of the DNA. This sequence contains the instruction code of the cell - determining protein structure and function, and hence cell function and fate.
Transcription is a vital stage in the process of gene expression and a major contributor to fluctuations in gene expression levels. It is typically modelled as a single step process with Poisson statistics. However, recent single molecule experiments raise questions about the validity of such a simple single step picture. I will present a molecular multi-step model of transcription elongation that demonstrates that transcription times are in general non-Poisson distributed. In particular, we model transcriptional pauses due to backtracking of the RNA polymerase as a first passage process. When transcriptional pauses result in long transcription times, I will demonstrate that this naturally leads to bursts of mRNA production and non-Poisson statistics of mRNA levels.
The viability and endurance of organisms crucially depend on the fidelity with which genetic information is transcribed/translated (during mRNA and protein production) and replicated (during DNA replication). However, thermodynamics introduces significant fluctuations which would incur large error rates if efficient proofreading mechanisms were not in place. I will examine a putative mechanism for error correction during DNA transcription, which relies on backtracking of the RNA polymerase (RNAP). This model will be used to calculate the error fraction as a function of the relevant rates (translocation, cleavage, backtracking and polymerization) and show that the its theoretical limit is equivalent to that accomplished by a multiple-step kinetic proofreading mechanism.
Cellular Ca2+ signals are generated across broad spatial and temporal ranges – spanning nanometers to centimeters, and from microseconds to daily fluctuations in basal cytoplasmic Ca2+ concentration. In this talk, I will discuss two examples taken from these extremes to illustrate the importance of basal variability - in first, local Ca2+ channel activity and second, macroscopic Ca2+ levels - in regulating appropriate physiological outcomes. First, at the subcellular level, current knowledge of the in situ organization and properties of inositol trisphosphate receptors (IP3Rs) within the the endoplasmic reticulum will be summarized from an experimentalist’s perspective and showcased using examples from the malleable functional architecture of IP3Rs observed during oocyte maturation. Second, at the whole organism level, variability in basal Ca2+ levels as a positional cue during axis specification will be discussed in the context of regenerative patterning. The key theme from both examples is to highlight the need for the next generation of modeling studies to consider the functional ramifications of variable Ca2+ channel activity resulting from Ca2+ channel localization and socialization within diverse and dynamic biological architectures.
The sequential formation of somites along the elongating zebrafish body axis is a model system for understanding the patterning of a growing tissue as well as the control of biological timing. We have used a combination of live imaging, gene expression analysis, and physical theory to explore the organization and function of the segmentation clock, the synchronized oscillating gene network that underlies the dynamics of somitogenesis. I will discuss new experimental results identifying the first somitogenesis period mutants, and corresponding theoretical approaches that explain the collective control of cellular oscillations at the tissue level in terms of the delays in the coupling between cells. Such effects should be important in any biological clock where communication between oscillators is slow relative to the period of the clock.
TBC
Gamma oscillations, in the frequency range of 30 to 80 Hz, are a prominent kind of synchronized activity in the awake cortex, and are widely believed to play a role in neurocognitive functions, including feature binding, selective attention, and consciousness. The phasic firing of neurons during gamma oscillations suggests the possibility of encoding information by the spike times of individual cells, relative to the gamma "clock" signal of the concerted activity in the surrounding network. Such an encoding must operate against a background of highly variable synaptic input from the network. In this talk, I describe our studies on the responses of cortical neurons to controlled conductance stimulation, reproducing the local network synaptic input during gamma oscillations. I discuss how the intrinsic biophysical properties and synaptic connections of different types of cortical neuron allow us to understand how oscillations cohere and disperse, and what determines the timing and reliability of action potential firing during the gamma cycle.
I present a discrete model of stochastic excitability by a low-dimensional set of delayed integral equations governing the probability in the rest state, the excited state and the refractory state. The process is a random walk with discrete states and non-exponential waiting time distributions, which lead to the incorporation of memory kernels in the integral equations. We extend the equations of a single unit to the system of equations for an ensemble of globally coupled oscillators, derive the mean field equations and investigate bifurcations of steady states. Conditions of destabilization are found, which imply oscillations of the mean fields in the stochastic ensemble. The relation between the mean field equations and the paradigmatic Kuramoto-model is shown.
Literature: H. Leohardt, M.A. Zaks, M. Falcke, and L. Schimansky-Geier, JOURNAL OF BIOLOGICAL PHYSICS Volume: 34 , 521-538 ()2008).
T. Prager, M. Falcke, L. Schimansky-Geier, and M.A. Zaks, PHYSICAL REVIEW E 76, 011118 (2007).
Biochemical networks have two sources of stochasticity: intrinsic fluctuations, inherent in the biochemistry and enhanced by low numbers of molecules, and extrinsic fluctuations, generated by interactions of the system of interest with other stochastic systems in the cell or its environment. I will discuss the definitions of intrinsic and extrinsic stochasticity and their interdependencies. I will describe ways to mathematically model and simulate both types of fluctuations and illustrate how stochasticity can be important for understanding the 'design' of some simple biochemical networks.
Inositol 1,4,5-trisphosphate receptors (IP3R) are widely expressed intracellular Ca2+ channels. Their large conductance and ability to conduct both Ca2+ and K+ allows IP3R to mediate large and relatively sustained release of Ca2+ from intracellular stores. Slow diffusion of cytosolic Ca2+ restricts these Ca2+ signals to the immediate vicinity of each open IP3R, but regulation of IP3R by Ca2+ allows regenerative propagation of Ca2+ signals. The ability of IP3R to evoke either local or global Ca2+ signals increases the versatility of this signalling pathway. Underpinning this spatial complexity is the precise subcellular targeting of IP3R and the dynamic regulation of IP3R assembly into small clusters of interacting IP3R. Residues within the six transmembrane domains of each IP3R subunit mediate targeting of IP3R to the endoplasmic reticulum (ER) and their retention within the ER. Most IP3R in most cells remain within the ER, but in DT40 cells small numbers (typically 2 IP3R/cell) are inserted into the plasma membrane (PM), where they convey about half the Ca2+ entry evoked by activation of the B cell receptor. The mechanisms responsible for reliably counting so few IP3R into the PM are unresolved, but require neither IP3 binding nor transport of cations through the pore. Patch-clamp recording from the outer nuclear envelope, which is continuous with the ER, demonstrates that IP3 causes IP3R rapidly and reversibly to assemble into small clusters of about 4 IP3R. Lone and clustered IP3R respond very differently to Ca2+ and IP3. This dynamically regulated clustering serves not only to drive IP3R into the assemblies that allow Ca2+-mediated interactions between them, but also retunes their behaviour so as to exaggerate the effects of Ca2+. We suggest that lone and clustered IP3R are the fundamental units of IP3-mediated signalling, and that IP3 controls both assembly of these units and gating of IP3R within them.
Markus Owen
Stephen Coombes
Martin Falcke
Alfonso Martinez-Arias
Nick Monk
Jordi Garcia Ojalvo
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