A method is provided to compute the exponent parameter λ yielding the dynamic exponents of critical slowing down in mode coupling theory. It is independent from the dynamic approach and based on the formulation of an effective static field theory. Expressions of λ in terms of third order coefficients of the action expansion or, equivalently, in terms of six point cumulants are provided. Applications are reported to a number of mean-field models: with hard and soft variables and both fully connected and dilute interactions. Comparisons with existing results for the Potts glass model, the random orthogonal model, hard and soft-spin Sherrington-Kirkpatrick, and p-spin models are presented.

In the early visual system, cells of the same type perform the same computation in different places of the visual field. How these cells code together a complex visual scene is unclear. A common assumption is that cells of a single-type extract a single-stimulus feature to form a feature map, but this has rarely been observed directly. Using large-scale recordings in the rat retina, we show that a homogeneous population of fast OFF ganglion cells simultaneously encodes two radically different features of a visual scene. Cells close to a moving object code quasilinearly for its position, while distant cells remain largely invariant to the object’s position and, instead, respond nonlinearly to changes in the object’s speed. We develop a quantitative model that accounts for this effect and identify a disinhibitory circuit that mediates it. Ganglion cells of a single type thus do not code for one, but two features simultaneously. This richer, flexible neural map might also be present in other sensory systems.

BackgroundIn Escherichia coli, overlapping rounds of DNA replication allow the bacteria to double in faster times than the time required to copy the genome. The precise timing of initiation of DNA replication is determined by a regulatory circuit that depends on the binding of a critical number of ATP-bound DnaA proteins at the origin of replication, resulting in the melting of the DNA and the assembly of the replication complex. The synthesis of DnaA in the cell is controlled by a growth-rate dependent, negatively autoregulated gene found near the origin of replication. Both the regulatory and initiation activity of DnaA depend on its nucleotide bound state and its availability.ResultsIn order to investigate the contributions of the different regulatory processes to the timing of initiation of DNA replication at varying growth rates, we formulate a minimal quantitative model of the initiator circuit that includes the key ingredients known to regulate the activity of the DnaA protein. This model describes the average-cell oscillations in DnaA-ATP/DNA during the cell cycle, for varying growth rates. We evaluate the conditions under which this ratio attains the same threshold value at the time of initiation, independently of the growth rate.ConclusionsWe find that a quantitative description of replication initiation by DnaA must rely on the dependency of the basic parameters on growth rate, in order to account for the timing of initiation of DNA replication at different cell doubling times. We isolate two main possible scenarios for this, depending on the roles of DnaA autoregulation and DnaA ATP-hydrolysis regulatory process. One possibility is that the basal rate of regulatory inactivation by ATP hydrolysis must vary with growth rate. Alternatively, some parameters defining promoter activity need to be a function of the growth rate. In either case, the basal rate of gene expression needs to increase with the growth rate, in accordance with the known characteristics of the dnaA promoter. Furthermore, both inactivation and autorepression reduce the amplitude of the cell-cycle oscillations of DnaA-ATP/DNA.

Sleep slow waves are known to participate in memory consolidation, yet slow waves occurring under anesthesia present no positive effects on memory. Here, we shed light onto this paradox, based on a combination of extracellular recordings in vivo, in vitro, and computational models. We find two types of slow waves, based on analyzing the temporal patterns of successive slow-wave events. The first type is consistently observed in natural slow-wave sleep, while the second is shown to be ubiquitous under anesthesia. Network models of spiking neurons predict that the two slow wave types emerge due to a different gain on inhibitory versus excitatory cells and that different levels of spike-frequency adaptation in excitatory cells can account for dynamical distinctions between the two types. This prediction was tested in vitro by varying adaptation strength using an agonist of acetylcholine receptors, which demonstrated a neuromodulatory switch between the two types of slow waves. Finally, we show that the first type of slow-wave dynamics is more sensitive to external stimuli, which can explain how slow waves in sleep and anesthesia differentially affect memory consolidation, as well as provide a link between slow-wave dynamics and memory diseases.

We study the finite-size corrections to the free-energy density in disordered spin systems on sparse random graphs, using both replica theory and the cavity method. We derive analytical expressions for the O(1/N) corrections in the replica symmetric phase as a linear combination of the free energies of open and closed chains. We perform a numerical check of the formulas on the random-field Ising model at zero temperature by computing finite-size corrections to the ground-state energy density. © 2013 American Physical Society

Maximum entropy models can be inferred from large datasets to uncover how collective dynamics emerge from local interactions. Here, such models are employed to investigate neurons recorded by multi-electrode arrays in the human and monkey cortex. Taking advantage of the separation of excitatory and inhibitory neuron types, we construct a model including this distinction. This approach allows us to shed light on differences between excitatory and inhibitory activity across different brain states such as wakefulness and deep sleep, in agreement with previous findings. Additionally, maximum entropy models can also unveil novel features of neuronal interactions, which are found to be dominated by pairwise interactions during wakefulness, but are population-wide during deep sleep. Overall, we demonstrate that maximum entropy models can be useful to analyze datasets with classified neuron types and to reveal the respective roles of excitatory and inhibitory neurons in organizing coherent dynamics in the cerebral cortex.

Functional coupling networks are widely used to characterize collective patterns of activity in neural populations. Here, we ask whether functional couplings reflect the subtle changes, such as in physiological interactions, believed to take place during learning. We infer functional network models reproducing the spiking activity of simultaneously recorded neurons in prefrontal cortex (PFC) of rats, during the performance of a cross-modal rule shift task (task epoch), and during preceding and following sleep epochs. A large-scale study of the 96 recorded sessions allows us to detect, in about 20% of sessions, effective plasticity between the sleep epochs. These coupling modifications are correlated with the coupling values in the task epoch, and are supported by a small subset of the recorded neurons, which we identify by means of an automatized procedure. These potentiated groups increase their coativation frequency in the spiking data between the two sleep epochs, and, hence, participate to putative experience-related cell assemblies. Study of the reactivation dynamics of the potentiated groups suggests a possible connection with behavioral learning. Reactivation is largely driven by hippocampal ripple events when the rule is not yet learned, and may be much more autonomous, and presumably sustained by the potentiated PFC network, when learning is consolidated.

Deep regions of the brain are not easily accessible to investigation at the mesoscale level in awake animals or humans. We have recently developed a functional ultrasound (fUS) technique that enables imaging hemodynamic responses to visual tasks. Using fUS imaging on two awake nonhuman primates performing a passive fixation task, we constructed retinotopic maps at depth in the visual cortex (V1, V2, and V3) in the calcarine and lunate sulci. The maps could be acquired in a single-hour session with relatively few presentations of the stimuli. The spatial resolution of the technology is illustrated by mapping patterns similar to ocular dominance (OD) columns within superficial and deep layers of the primary visual cortex. These acquisitions using fUS suggested that OD selectivity is mostly present in layer IV but with extensions into layers II/III and V. This imaging technology provides a new mesoscale approach to the mapping of brain activity at high spatiotemporal resolution in awake subjects within the whole depth of the cortex.