Publications

Network dynamics with point-process-based interactions are of paramount modeling interest. Unfortunately, most relevant dynamics involve complex graphs of interactions for which an exact computational treatment is impossible. To circumvent this difficulty, the replica-mean-field approach focuses on randomly interacting replicas of the networks of interest. In the limit of an infinite number of replicas, these networks become analytically tractable under the so-called ‘Poisson hypothesis’. However, in most applications this hypothesis is only conjectured. In this paper we establish the Poisson hypothesis for a general class of discrete-time, point-process-based dynamics that we propose to call fragmentation-interaction-aggregation processes, and which are introduced here. These processes feature a network of nodes, each endowed with a state governing their random activation. Each activation triggers the fragmentation of the activated node state and the transmission of interaction signals to downstream nodes. In turn, the signals received by nodes are aggregated to their state. Our main contribution is a proof of the Poisson hypothesis for the replica-mean-field version of any network in this class. The proof is obtained by establishing the propagation of asymptotic independence for state variables in the limit of an infinite number of replicas. Discrete-time Galves–Löcherbach neural networks are used as a basic instance and illustration of our analysis.

What factors constrain the arrangement of the multiple fields of a place cell? By modeling place cells as perceptrons that act on multiscale periodic grid-cell inputs, we analytically enumerate a place cell’s repertoire – how many field arrangements it can realize without external cues while its grid inputs are unique – and derive its capacity – the spatial range over which it can achieve any field arrangement. We show that the repertoire is very large and relatively noise-robust. However, the repertoire is a vanishing fraction of all arrangements, while capacity scales only as the sum of the grid periods so field arrangements are constrained over larger distances. Thus, grid-driven place field arrangements define a large response scaffold that is strongly constrained by its structured inputs. Finally, we show that altering grid-place weights to generate an arbitrary new place field strongly affects existing arrangements, which could explain the volatility of the place code.

Replica-mean-field models have been proposed to decipher the activity of otherwise analytically intractable neural networks via a multiply-and-conquer approach. In this approach, one considers limit networks made of infinitely many replicas with the same basic neural structure as that of the network of interest, but exchanging spikes in a randomized manner. The key point is that these replica-mean-field networks are tractable versions that retain important features of the finite structure of interest. To date, the replica framework has been discussed for first-order models, whereby elementary replica constituents are single neurons with independent Poisson inputs. Here, we extend this replica framework to allow elementary replica constituents to be composite objects, namely, pairs of neurons. As they include pairwise interactions, these pair-replica models exhibit nontrivial dependencies in their stationary dynamics, which cannot be captured by first-order replica models. Our contributions are two-fold: (i) We analytically characterize the stationary dynamics of a pair of intensity-based neurons with independent Poisson input. This analysis involves the reduction of a boundary-value problem related to a two-dimensional transport equation to a system of Fredholm integral equations—a result of independent interest. (ii) We analyze the set of consistency equations determining the full network dynamics of certain replica limits. These limits are those for which replica constituents, be they single neurons or pairs of neurons, form a partition of the network of interest. Both analyses are numerically validated by computing input/output transfer functions for neuronal pairs and by computing the correlation structure of certain pair-dominated network dynamics.

Neural computations emerge from myriad neuronal interactions occurring in intricate spiking networks. Due to the inherent complexity of neural models, relating the spiking activity of a network to its structure requires simplifying assumptions, such as considering models in the thermodynamic mean-field limit. In the thermodynamic mean-field limit, an infinite number of neurons interact via vanishingly small interactions, thereby erasing the finite size of interactions. To better capture the finite-size effects of interactions, we propose to analyze the activity of neural networks in the replica-mean-field limit. Replica-mean-field models are made of infinitely many replicas which interact according to the same basic structure as that of the finite network of interest. Here, we analytically characterize the stationary dynamics of an intensity-based neural network with spiking reset and heterogeneous excitatory synapses in the replica-mean-field limit. Specifically, we functionally characterize the stationary dynamics of these limit networks via ordinary differential equations derived from the Poisson hypothesis of queuing theory. We then reduce this functional characterization to a system of self-consistency equations specifying the stationary neuronal firing rates. Of general applicability, our approach combines rate-conservation principles from point-process theory and analytical considerations from generating-function methods. We validate our approach by demonstrating numerically that replica-mean-field models better capture the dynamics of feedforward neural networks with large, sparse connections than their thermodynamic counterparts. Finally, we explain that improved performance by analyzing the neuronal rate-transfer functions, which saturate due to finite-size effects in the replica-mean-field limit.

Metagenomics has revealed hundreds of species in almost all microbiota. In a few well-studied cases, microbial communities have been observed to coordinate their metabolic fluxes. In principle, microbes can divide tasks to reap the benefits of specialization, as in human economies. However, the benefits and stability of an economy of microbial specialists are far from obvious. Here, we physically model the population dynamics of microbes that compete for steadily supplied resources. Importantly, we explicitly model the metabolic fluxes yielding cellular biomass production under the constraint of a limited enzyme budget. We find that population dynamics generally leads to the coexistence of different metabolic types. We establish that these microbial consortia act as cartels, whereby population dynamics pins down resource concentrations at values for which no other strategy can invade. Finally, we propose that at steady supply, cartels of competing strategies automatically yield maximum biomass, thereby achieving a collective optimum.

In nature a large number of species can coexist on a small number of shared resources, however resource competition models predict that the number of species in steady coexistence cannot exceed the number of resources. Motivated by recent studies of phytoplankton, we introduce trade-offs into a resource competition model, and find that an unlimited number of species can coexist. Our model spontaneously reproduces several features of natural ecosystems including keystone species and population dynamics/abundances characteristic of neutral theory, despite an underlying non- neutral competition for resources.

Natural auditory scenes possess highly structured statistical regularities, which are dictated by the physics of sound production in nature, such as scale-invariance. We recently identified that natural water sounds exhibit a particular type of scale invariance, in which the temporal modulation within spectral bands scales with the centre frequency of the band. Here, we tested how neurons in the mammalian primary auditory cortex encode sounds that exhibit this property, but differ in their statistical parameters. The stimuli varied in spectro-temporal density and cyclo-temporal statistics over several orders of magnitude, corresponding to a range of water-like percepts, from pattering of rain to a slow stream. We recorded neuronal activity in the primary auditory cortex of awake rats presented with these stimuli. The responses of the majority of individual neurons were selective for a subset of stimuli with specific statistics. However, as a neuronal population, the responses were remarkably stable over large changes in stimulus statistics, exhibiting a similar range in firing rate, response strength, variability and information rate, and only minor variation in receptive field parameters. This pattern of neuronal responses suggests a potentially general principle for cortical encoding of complex acoustic scenes: while individual cortical neurons exhibit selectivity for specific statistical features, a neuronal population preserves a constant response structure across a broad range of statistical parameters.

DNA combing allows the investigation of DNA replication on genomic single DNA molecules, but the lengths that can be analysed have been restricted to molecules of 200–500 kb. We have improved the DNA combing procedure so that DNA molecules can be analysed up to the length of entire chromosomes in fission yeast and up to 12 Mb fragments in human cells. Combing multi-Mb-scale DNA molecules revealed previously undetected origin clusters in fission yeast and shows that in human cells replication origins fire stochastically forming clusters of fired origins with an average size of 370 kb. We estimate that a single human cell forms around 3200 clusters at mid S-phase and fires approximately 100,000 origins to complete genome duplication. The procedure presented here will be adaptable to other organisms and experimental conditions.

Five noncoding small RNAs (sRNAs) called the Qrr1-5 sRNAs act at the heart of the Vibrio harveyi quorum-sensing cascade. The Qrr sRNAs posttranscriptionally regulate 20 mRNA targets. Here, we use a method we call RSort-Seq that is based on unbiased high-throughput screening to define the critical bases in Qrr4 that specify its function. The power of our study comes from using the screening results to pinpoint particular nucleotides for follow-up biological analyses that define function. Using this approach, we discover how Qrr4 differentially regulates two of its targets, luxO and luxR. We also show how this strategy can be used to identify intramolecular suppressor mutations. This approach can be applied to any sRNA and any mRNA target.

Bacteria regulate gene expression in response to changes in cell density in a process called quorum sensing. To synchronize their gene-expression programs, these bacteria need to glean as much information as possible about their cell density. Our study is the first to physically model the flow of information in a quorum-sensing microbial community, wherein the internal regulator of the individuals response tracks the external cell density via an endogenously generated shared signal. Combining information theory and Lagrangian formalism, we find that quorum-sensing systems can improve their information capabilities by tuning circuit feedbacks. Our analysis suggests that achieving information benefit via feedback requires dedicated systems to control gene expression noise, such as sRNA-based regulation.