Session Q40: Focus Session: Systems Biology and Biochemical Networks III

Fold-change detection and scalar symmetry of sensory input fields

Recent studies suggest that certain cellular sensory systems display fold-change detection (FCD): a response whose entire shape, including amplitude and duration, depends only on fold-changes in input, and not on absolute changes. We show that FCD is necessary and sufficient for sensory search to depend only on the spatial profile of the input, and not on its amplitude. Such amplitude scalar symmetry occurs in a wide range of sensory inputs, such as source strength multiplying diffusing chemical fields sensed in chemotaxis, ambient light multiplying the contrast field in vision, and protein concentrations multiplying the output in cellular signaling systems. We present a wide class of mechanisms that have FCD, including certain nonlinear feedback and feedforward loops. In addition, we find that bacterial chemotaxis displays feedback within the present class, and has indeed recently been shown to exhibit FCD. This can explain experiments in which chemotaxis searches are insensitive to attractant source levels. This study thus suggests a connection between properties of biological sensory systems and scalar symmetry stemming from physical properties of their input fields.   

Network architectural conditions for prominent and robust stochastic oscillations

Understanding relationship between noisy dynamics and biological network architecture is a fundamentally important question, particularly in order to elucidate how cells encode and process information. We analytically and numerically investigate general network architectural conditions that are necessary to generate stochastic amplified and coherent oscillations. We enumerate all possible topologies of coupled negative feedbacks in the underlying biochemical networks with three components, negative feedback loops, and mass action kinetics. Using the linear noise approximation to analytically obtain the time-dependent solution of the master equation and derive the algebraic expression of power spectra, we find that (a) all networks with coupled negative feedbacks are capable of generating stochastic amplified and coherent oscillations; (b) networks with a single negative feedback are better stochastic amplified and coherent oscillators than those with multiple coupled negative feedbacks; (c) multiple timescale difference among the kinetic rate constants is required for stochastic amplified and coherent oscillations.   

Properties of gene expression including the non-functional binding of transcription factors to DNA

Many eukaryotic transcription factors bind to DNA sequences with a remarkable lack of specificity. This suggests that non-functional binding between transcription factors and DNA might not have the detrimental effect on regulation one would naively assume results from competition for binding. In fact, if binding to DNA protects transcription factors from degradation, the number and binding affinity of these 'decoy' binding sites should have no influence on the copy number of transcription factors available for regulation. We calculate the influence of adding decoy binding sites on several important aspects of gene expression including the noise, the time to reach steady state, and bimodal switch rates. Analyzing these effects could shed some light on how a gene functions in the 'dressed' environment of a genomic background.   

Single promoters as regulatory network motifs

At eukaryotic promoters, chromatin can influence the relationship between a gene's expression and transcription factor (TF) activity. This additional complexity might allow single promoters to exhibit dynamical behavior commonly attributed to regulatory motifs involving multiple genes. We investigate the role of promoter chromatin architecture in the kinetics of gene activation using a previously described set of promoter variants based on the phosphate-regulated PHO5 promoter in S. cerevisiae. Accurate quantitative measurement of transcription activation kinetics is facilitated by a controllable and observable TF input to a promoter of interest leading to an observable expression output in single cells. We find the particular architecture of these promoters can result in a significant delay in activation, filtering of noisy TF signals, and a memory of previous activation -- dynamical behaviors reminiscent of a feed-forward loop but only requiring a single promoter. We suggest this is a consequence of chromatin transactions at the promoter, likely passing through a long-lived ``primed'' state between its inactive and competent states. Finally, we show our experimental setup can be generalized as a ``gene oscilloscope'' to probe the kinetics of heterologous promoter architectures.   

Towards a principled way of making kinetic models from data

Kinetic model extraction from noisy data is the basic route to mechanistic insight in biology. I will show how the tools of Maximum Caliber (the dynamical analog of Maximum Entropy) can be used to infer -and not fit- models in a way which is driven by the structure and limitations of the data. For instance, the typical output of an experiment in systems biology is the stochastic expression of one reporter gene. Master equations used to model the regulatory process underlying the stochastic gene expression require knowledge of a circuit topology and rates. However rates and topology are often fit as these are rarely all independently determinable from the limited data. Our goal is to build a kinetic model from the data available with no adjustable parameter using the tools of Maximum Caliber. We apply our method to infer the statistics of rare stochastic switching events in the genetic toggle switch from fluctuations on shorter measurable timescales. In addition, we discuss how these tools can be used to infer kinetic models from real single molecule data drawn from anomalous folding kinetics of phosphoglycerate kinase and RNA hairpin zipping-unzipping time traces.   

Reaction kinetics in the cell membrane: confining domains lead to reaction bursts

Our goal is to reveal the effects of confining domains such as those observed in cell membranes on the kinetics of reversible reactions in two-dimensions. During the last two decades, single molecule tracking experiments showed that proteins and lipids are temporarily confined in the compartments of a meshwork induced by the actin cytoskeleton, while diffusing laterally in the plasma membrane. It has been clearly demonstrated that the presence of these compartments significantly hinders the diffusion of membrane molecules. Nevertheless, how confinement affects the interaction between membrane molecules and the regulation of signaling has still not been clarified. Using Monte Carlo simulations and the mathematical theory of diffusion, we showed that the presence of compartments leads to reaction bursts, during which the number of reactions an individual molecule experiences rises sharply, but briefly. Surprisingly, we found that the mean reaction rate does not depend on whether compartments exist or not. However, our results show that the variance of the rate depends strongly on the presence of confinement effects, which turns out to be an indicator of a profound change in the temporal pattern of reaction events: bursts of reactions instead of constant but low yield.   

Inference of Mechanical Network Parameters in Epithelial Tissue Development

Mechanical stress in cells has been linked to biochemical networks that influence cell structure and function. Yet direct \emph{in vivo} measurements of mechanical forces in epithelial tissues remain a serious experimental challenge. I will present an alternative approach based on a computational analysis of high resolution images of epithelial tissues. Assuming that epithelial cell layers are close to mechanical equilibrium, we use the observed geometry of the two dimensional cell array to infer interfacial tensions and intracellular pressures. I will present applications of this mechanical parameter inference algorithm in the context of several developmental processes involving epithelial cell layers.   

Regulatory dynamics and stability in discrete and continuous models

Biological processes such as cell deviation, cell differentiation and so on are regulated dynamics. These dynamics are often described by continuous rate equations for continuously varying chemical concentrations. Binary discretization of state space and time leads to another class of models, Boolean dynamics, which are dealing with larger systems, higher complexity and less computational details. Here we study the reaction of discrete and continuous dynamics to perturbations. When asking if a gene-regulatory system reproduces a prescribed trajectory despite noise, large perturbations are to be considered in the case of low copy numbers of regulatory molecules and bursty stochastic response. Small perturbations, however, are more appropriate when modelling systems with large copy numbers and an integrative response to filter out bursts. In Boolean networks, the dynamics has been called unstable if flip perturbations lead to damage spreading. We find that this stability classification strongly differs from the stability properties of the original continuous dynamics under small perturbations of the state vector. In particular, random networks of nodes with large sensitivity yield stable dynamics under small perturbations and chaotic regime disappears.   

Polarization and molecular information transmission in the cell

During chemotaxis, pseudopodia are extended at the leading edge and retracted at the back of the cell. Efficient chemotaxis is the result of a refined interplay between signaling modules to transmit and integrate spatial information such as PtdIns(3,4,5)P3. The localization of PtdIns(3,4,5)P3 is expected to depend on the distributions or activities of PI3Ks, PTEN, and 5-phosphatases. The spatial signals spread relatively slowly so that high local concentrations of PIP3 in the plasma membrane appear in patches. These gradients induce localization of PIP3 and PTEN to the front and back of the cell, respectively. To simulate this polarization process that involves the action of seven reaction-channels inside the cell we carried out extensive stochastic simulations using Gilliespie algorithm. The simulations were done on a square cell with ten thousand sites $(100\times100)$ emulating a square cell with side $10\>\mu m$ long. We found that there are localized patches of PIP3 at the active receptors and segregation of PTEN on the opposite side of the cell. When we block the reaction-channel, $PTEN + PIP3 \rightarrow PIP2$ that involves the production of PIP2 we obtained a five-fold increase in the concentration of PIP3. This finding appears to be consistent with the o   

Energy Flow in Neuronal Systems

We will present results from a computational model designed to investigate the physical underpinnings of neuronal systems. Most neuronal models assume that the ionic flow across neuronal membranes is to small to effect the ionic composition inside and outside of cells. However neurons exhibiting high levels of activity can produce ionic redistributions large enough to cause significant changes to cellular excitability. Furthermore, physically-accurate neuronal models must obey conservation of mass and energy. Energy is injected into these cells through the consumption of atp, stored in electrochemical gradients, and dissipated through ionic flow down these gradients. Our model incorporates essential biological mechanisms required to reproduce this energy flow and storage. We will discuss the advantages and limitations of this dynamic system in the context of neuronal function.   

Rhythm-Induced Spike-Timing Patterns Characterized by 1D Firing Map

A basic problem in neuroscience is to understand how the dynamic mechanisms that govern the responses of nerve cells to stimuli, which are both non-linear and noisy, still produce reliable collective activity. We study patterning in the responses of neurons subjected to periodic rhythms. These patterns are governed by simple, low-dimensional mathematical structures independent of modeling detail. We show both theoretically and in whole-cell recordings that the 1D map generated from successive spike times is such a construct. As expected, the stable periodic points of this 1D map cause a neuron's entrainment or phase-locking to a periodic rhythm. But our work has also revealed a complementary and unexpected patterning in the spike-timing of un-entrained neurons in the form of repeated sequences of reliable spike-phase advances, which cannot be characterized simply as a noisy perturbation near the stable periodic points of the noise-free return map. This new patterning appears to require both noise and a sufficiently steep return map.   

The Effects of Intrinsic Noise on an Inhomogeneous Lattice of Chemical Oscillators

Intrinsic or demographic noise has been shown to play an important role in the dynamics of a variety of systems including biochemical reactions within cells, predator-prey populations, and oscillatory chemical reaction systems, and is known to give rise to oscillations and pattern formation well outside the parameter range predicted by standard mean-field analysis. Motivated by an experimental model of cells and tissues where the cells are represented by chemical reagents isolated in emulsion droplets, we study the stochastic Brusselator, a simple activator-inhibitor chemical reaction model. Our work extends the results of recent studies on the zero and one dimensional system to the case of a non-uniform one dimensional lattice using a combination of analytical techniques and Monte Carlo simulations.