Session Y06: Inference and Microbiological Physics

Inferring collective dynamical states from subsampled systems

When studying the dynamics of complex systems, one can rarely sample the state of all components. We show that this spatial subsampling typically leads to severe underestimation of the risk of instability in systems with propagation of events. We analytically derived a subsampling-invariant estimator and applied it to non-linear network simulations and case reports of various diseases, recovering a close relation between vaccination rate and spreading behavior. The estimator can be particularly useful in countries with unreliable case reports, and promises early warning if e.g. antibiotic resistant bacteria increase their infectiousness. In neuroscience, subsampling has led to contradictory hypotheses about the collective spiking dynamics: asynchronous-irregular or critical. With the novel estimator, we demonstrated for rat, cat and monkey that collective dynamics lives in a narrow subspace between the two. Functionally, this subspace can combine the different computational properties associated with the two states.   

On the learnability of probability distributions

Organisms and algorithms learn stimulus distributions from previous observations, either over evolutionary time or on the fly. If discrete events are what is observed, then the probability distribution is a list of numbers, one for each possible outcome; in the absence of regularities, estimating the underlying distribution from data requires an organism to observe each possible outcome many times. The number of possible outcomes is astronomical, even in small systems. In a binary image with just N = 100 pixels, the number of possible images (2^N~ 10³⁰) is larger than the age of the universe in seconds. Learning requires discovery of regularities in the data, and exploitation of these regularities by formulating simplified models. Here we show that two conditions support efficient learning. First, the mutual information between two partitions of the system should be sub-extensive. Second, this shared information should be compressible, so that it can be represented by a number of bits equal to the information rather than the sub-systems' entropy. We argue that, under these conditions, the distribution can be learned with a number of parameters that grows linearly with N.   

Investigating neuronal populations that are truly large – can we keep our models small?

Recent technological breakthroughs in large-scale neural recordings have ushered in a new era, in which we can simultaneously monitor the activity of thousands of neurons. To write down minimal models for the collective behavior of these large populations of cells, we seek theoretical approaches that will help us simplify the rich dynamics. We focus on the neural activity underlying the behavior of mice running in a virtual environment, and model the complex activity exhibited by more than a thousand neurons simultaneously active in hippocampus. First, we show that we can reliably build minimal (maximum entropy) models for different subsets of neurons out of the whole population. These models of smaller networks tend to have more predictive power and behave more similarly to one another if the participating cells are in spatial proximity. Next, we look at the correlation matrix across the system as a whole, and explore methods from random matrix theory that may allow us to recover estimates of the true eigenvalue spectrum for these correlations. Finally, we use different coarse graining methods, in the spirit of the renormalization group, to uncover macroscopic features of the large network. We find hints that the behavior of the system is controlled by a non-trivial fixed point.   

A Step Forward in the Analysis of Confocal Fluorescence Spectroscopy Measurements

Fluorescence signals are commonly measured in modern microscopy experiments including confocal fluorescence spectroscopy. Typically, these signals are analyzed by well-established methods, e.g. FCS and FRAP. Although these methods provide accurate estimation of the dynamical properties of the targeted molecules, for example diffusion coefficients and photon emission rates, they require (i) long signals and (ii) high molecule concentrations which limit the scope of most recent experimental techniques, especially those probing live cells. In this presentation, we introduce a novel approach for the analysis of fluorescence signals that relaxes the requirements of existing methods and, in particular, avoids signal correlation. Specifically, our method achieves the same level of accuracy with signals that (i) are several orders shorter and (ii) produced by very low molecule concentrations. We test our method on synthetic and experimental fluorescence intensity signals from confocal microscopy. The results demonstrate the ability and accuracy of our approach to extract realistic estimates of diffusion coefficients and of other quantities of biophysical interest.   

Group symmetries in the lineage trees of single cells

Fate maps on lineage trees have been a defining conceptual framework for understanding development in multicellular organisms. Yet the heterogeneity that is increasingly observed in single-cell lineage data across a variety of living systems has been difficult to reconcile with traditional notions of fate determination and differentiation. Examination of the group symmetries of a binary tree has revealed a set of orthogonal components for describing variation in a lineage. These provide a natural way to aggregate tree-structured data and suggest a statistical definition of fate determination and differentiation that allows for noisy variation from each division and at each generation. This new type of harmonic analysis has been applied to data on CD8+ T cell lineages. As benchmarks, the analysis has been applied to previously-published data on C. Elegans, a lineage with clear determination stages, and to a simulated branching process, which has none. The results demonstrate how group representation theory can be used to improve inference in, and extract scientific meaning from, complex structured data.   

SOLAR-STORM: Fast and Robust 3D Localization of Fluorophores in Dense Clusters

Stochastic switching-based super-resolution microscopy provides an order of magnitude resolution improvement to conventional diffraction-limited microscopy by separating fluorophores in the time domain and localizing them with high precision. This trade-off between spatial and temporal resolution can be mitigated by increasing the density of fluorophores in each frame. However, conventional algorithms can only detect well-separated single emitter events, rejecting many fluorophores in dense clusters.
Here, we introduce a fast and precise algorithm that localizes fluorophores in dense clusters in 3D, namely Spline-fitting and Orthogonal matching pursuit (OMP) based Localization Algorithm for Reconstructing STORM images (SOLAR-STORM). SOLAR-STORM provides the 3D coordinates of fluorophores in dense scenes on a continuous space by Taylor-expanding the spline-fitted point spread function (PSF). It contains an inherent parallel structure that allows significant acceleration when implemented on GPUs. This approach provides fast and robust 3D reconstruction with any given PSF, suggesting that this method can be widely used for different fluorescence microscopy techniques for imaging biological systems.
  

DISSIPATION IN A SEQUENCE OF RELAXATIONS: THE LADDER THEOREM

We consider one relaxation: the complete equilibration of a system to a bath. We show that replacing one relaxation with two relaxations starting and ending at the same states but reaching an intermediate equilibrium along the way always produces less entropy than the single relaxation. We present a completely general proof of this Ladder Theorem, which asserts that the entropy production in a relaxation process is decreased when the relaxation proceeds via intermediate steps.
This is indeed what is observed in the central carbon metabolism of the microbes in coral ecosystems. The microbes in the coral- dominated, energy-limited environments have an enrichment in genes encoding for the Embden Meyerhoff Parnas (EMP) pathway, a central carbon catabolic pathway that has 12 steps involved in the breakdown of sugars to pyruvate. On the other hand, microbes in algal dominated, energy surplus environments have an enrichment for alternative central carbon metabolism pathways such as the Pentose Phosphate (PP) pathway and the Entner Doudoroff (ED) pathway, which contain fewer steps than the EMP pathway.
  

Exploring viscoelastic properties of Myxococcus xanthus fruiting bodies with AFM measurements

When nutrients are scarce, the soil-dwelling bacteria Myxococcus xanthus aggregates into multicellular structures to form massive 3D clusters called fruiting bodies, where cells sporulate as a self-preservation mechanism. While our previous studies have explained the initiation of such a behavior in 2D as a motility induced phase separation process, the mechanical properties and cell dynamics within a maturing fruiting body remain unclear. In this study, we use atomic force microscopy (AFM) to explore the viscoelastic properties of a M. xanthus fruiting body. Treating M. xanthus aggregates as an active gel, our measurements provide insights on the hydrodynamic properties of such an out-of-equilibrium soft system. Mechanical measurements will also offer details about both cell-cell and cell-substrate interaction rules that can eventually lead to the understanding of the physics of long-range and self-organizing behaviors in M. xanthus.   

Volvox barberi flocks actively, forming near-optimal, two-dimensional, polydisperse lattice packings

Volvox barberi are multicellular protists forming spherical colonies of 10000-50000 differentiated somatic and germ cells. Here, I show that these colonies actively self-organize over minutes into “flocks” that can contain more than 100 colonies moving and rotating collectively for hours. The colonies in flocks form two-dimensional, irregular, “active crystals”, with lattice angles and colony diameters both following log-normal distributions. Comparison with a molecular dynamics simulation of soft spheres with diameters matched to the Volvox, and a weak long-range attractive force, show that the Volvox flocks achieve optimal random close-packing. A dye tracer in the Volvox medium reveals large hydrodynamic vortices generated by colony and flock rotations, providing a likely source of the forces leading to flocking and optimal packing.   

Mechanics of Phycomyces growth and rotation

The growth of Phycomyces Blakesleeanus has been reported in the literature as a means to understand the mechanisms of plant growth. This giant unicellular fungus that rises as a cylindrical tube (the sporangiophore) has been observed to exhibit fluctuating rotation patterns during growth. It is hypothesized that this is a result of the orientation and stresses of cellulose microfibrils that constitute the cell wall. The biophysical processes leading to this peculiar behavior are however poorly understood. We aim here to shine a light on the molecular events leading to both growth and rotation. For this, we present a statistical framework in which the cell wall is modeled as a dynamic network of microfibrils cross-linked by tethers (hemicellulose molecules). The tethers can periodically associate and dissociate with microfibrils over time, giving the cell wall the ability to tune the elastic and rheological response with the applied stress. Combining this approach with a continuum model, we will present simulation results of the flow and reorientation of microfibrils. We will then discuss how tether dynamics and elasticity affect microfibril rheology during growth and provide new hypotheses regarding the role of molecular events on sporangiophore rotation.   

3D Motility Measurements of Myxococcus xanthus Fruiting Body Formation

Myxococcus xanthus is a rod-shaped, soil-dwelling bacterium with striking manifestations of collective behavior. When starved, cells aggregate to form 3D mound-like structures known as fruiting bodies containing hundreds of thousands of cells. The aggregation process has been previously analyzed with motility-induced phase separation (MIPS). M. xanthus induce this phase separation by tuning their speed and frequency of cell reversal. In this 2D model, cells cluster through a jamming process similar to reversing active Brownian particles, but in 3D, cells extrude from the surface and migrate into a motile layered structure, a process better described by dewetting. We present here cell motility measurements in 3D during fruiting body formation for a dewetting model. We track sparsely labelled M. xanthus in 3D using confocal microscopy during fruiting body formation (24-48h). We extract cell speed and reversal frequencies, two key motility parameters of the MIPS model, and analyze their dependencies on time after starvation to better understand the mechanism behind aggregation. Cell tracks from different regions of fruiting bodies also provide information on how cells move and organize within these structures.   

Feedback between motion and sensation provides nonlinear boost in run-and-tumble navigation

Many organisms navigate the environment by alternating straight motions (runs) with random reorientations (tumbles), transiently suppressing tumbles as attractant signal increases. This induces a feedback between motion and sensation where the current tumble rate affects future signals. Previous studies have used mean field theory, assuming small fluctuations in the internal state that passes signaling information to the motor. Here we discover a new dynamical regime where this assumption breaks down, showing large fluctuations driven by the feedback. We demonstrate how these large fluctuations emerge from transient growths caused by non-normal dynamics (non-orthogonal eigenvectors near a stable fixed point) inherent in the feedback. We further identify a nonlinearity that aymmetrically amplifies this effect. This elongates runs up-gradient and truncates those down-gradient, resulting in "ratchet-like" swimming behavior. Our results thus show that the classical drawback of run-and-tumble navigation -- wasteful runs in the wrong direction -- can be mitigated by exploiting fluctuations and non-normal dynamics implicit in the run-and-tumble strategy.   

Light-induced nanowire formation and extracellular electron transport (EET) in Shewanella oneidensis MR-1

Dissimilatory metal-reducing bacteria, such as Shewanella oneidensis MR-1, harness energy from diverse sources in the environment through the metabolic oxidation of electron donors, such as organic materials, and subsequent electron transfer to insoluble electron acceptors, such as minerals. The electron transfer from bacteria to solid-state minerals or electrodes outside the cell is referred to as extracellular electron transport (EET). Recent research has proposed a few strategies for how EET is mediated in these microbial systems, including soluble redox mediators (such as flavins) to shuttle electrons via diffusion, direct contact with membrane cytochromes to the solid surface, and production of bacterial nanowires to bridge the gap between the cell body and surface. We combine optical and fluorescence microscopy with concurrent on-chip electrochemical and electrical measurements on a epifluorescence microscope to monitor the bacteria’s motility, EET, and metabolic behavior. We show preliminary data where we directly control nanowire production and enhance EET in a subpopulation of cells.