Mean-field method for generic conductance-based integrate-and-fire neurons with finite timescales.

The construction of transfer functions in theoretical neuroscience plays an important role in determining the spiking rate behavior of neurons in networks. These functions can be obtained through various fitting methods, but the biological relevance of the parameters is not always clear. However, for stationary inputs, such functions can be obtained without the adjustment of free parameters by using mean-field methods. In this work, we expand current Fokker-Planck approaches to account for the concurrent influence of colored and multiplicative noise terms on generic conductance-based integrate-and-fire neurons. We reduce the resulting stochastic system through the application of the diffusion approximation to a one-dimensional Langevin equation. An effective Fokker-Planck is then constructed using Fox Theory, which is solved numerically using a newly developed double integration procedure to obtain the transfer function and the membrane potential distribution. The solution is capable of reproducing the transfer function and the stationary voltage distribution of simulated neurons across a wide range of parameters. The method can also be easily extended to account for different sources of noise with various multiplicative terms, and it can be used in other types of problems in principle.

The maturational characteristics of the GABA input in the anterior piriform cortex may also contribute to the rapid learning of the maternal odor during the sensitive period.

During the first ten postnatal days (P), infant rodents can learn olfactory preferences for novel odors if they are paired with thermo-tactile stimuli that mimic components of maternal care. After P10, the thermo-tactile pairing becomes ineffective for conditioning. The current explanation for this change in associative learning is the alteration in the norepinephrine (NE) inputs from the locus coeruleus (LC) to the olfactory bulb (OB) and the anterior piriform cortex (aPC). By combining patch-clamp electrophysiology and computational simulations, we showed in a recent work that a transitory high responsiveness of the OB-aPC circuit to the maternal odor is an alternative mechanism that could also explain early olfactory preference learning and its cessation after P10. That result relied solely on the maturational properties of the aPC pyramidal cells. However, the GABAergic system undergoes important changes during the same period. To address the importance of the maturation of the GABAergic system for early olfactory learning, we incorporated data from the GABA inputs, obtained from in vitro patch-clamp experiment in the aPC of rat pups aged P5-P7 reported here, to the model proposed in our previous publication. In the younger than P10 OB-aPC circuit with GABA synaptic input, the number of responsive aPC pyramidal cells to the conditioned maternal odor was amplified in 30% compared to the circuit without GABAergic input. When compared with the circuit with other younger than P10 OB-aPC circuit with adult GABAergic input profile, this amplification was 88%. Together, our results suggest that during the olfactory preference learning in younger than P10, the GABAergic synaptic input presumably acts by depolarizing the aPC pyramidal neurons in such a way that it leads to the amplification of the pyramidal neurons response to the conditioned maternal odor. Furthermore, our results suggest that during this developmental period, the aPC pyramidal cells themselves seem to resolve the apparent lack of GABAergic synaptic inhibition by a strong firing adaptation in response to increased depolarizing inputs.

Maturation of pyramidal cells in anterior piriform cortex may be sufficient to explain the end of early olfactory learning in rats.

Studies have shown that neonate rodents exhibit high ability to learn a preference for novel odors associated with thermo-tactile stimuli that mimics maternal care. Artificial odors paired with vigorous strokes in rat pups younger than 10 postnatal days (P), but not older, rapidly induce an orientation-approximation behavior toward the conditioned odor in a two-choice preference test. The olfactory bulb (OB) and the anterior olfactory cortex (aPC), both modulated by norepinephrine (NE), have been identified as part of a neural circuit supporting this transitory olfactory learning. One possible explanation at the neuronal level for why the odor-stroke pairing induces consistent orientation-approximation behavior in P10, is the coincident activation of prior existent neurons in the aPC mediating this behavior. Specifically, odor-stroke conditioning in P10 pups, promoting orientation-approximation behavior in the former but not in the latter. In order to test this hypothesis, we performed in vitro patch-clamp recordings of the aPC pyramidal neurons from rat pups from two age groups (P5-P8 and P14-P17) and built computational models for the OB-aPC neural circuit based on this physiological data. We conditioned the P5-P8 OB-aPC artificial circuit to an odor associated with NE activation (representing the process of maternal odor learning during mother-infant interactions inside the nest) and then evaluated the response of the OB-aPC circuit to the presentation of the conditioned odor. The results show that the number of responsive aPC neurons to the presentation of the conditioned odor in the P14-P17 OB-aPC circuit was lower than in the P5-P8 circuit, suggesting that at P14-P17, the reduced number of responsive neurons to the conditioned (maternal) odor might not be coincident with the responsive neurons for a second conditioned odor.

How the Brain Represents Language and Answers Questions? Using an AI System to Understand the Underlying Neurobiological Mechanisms.

To understand the computations that underlie high-level cognitive processes we propose a framework of mechanisms that could in principle implement START, an AI program that answers questions using natural language. START organizes a sentence into a series of triplets, each containing three elements (subject, verb, object). We propose that the brain similarly defines triplets and then chunks the three elements into a spatial pattern. A complete sentence can be represented using up to 7 triplets in a working memory buffer organized by theta and gamma oscillations. This buffer can transfer information into long-term memory networks where a second chunking operation converts the serial triplets into a single spatial pattern in a network, with each triplet (with corresponding elements) represented in specialized subregions. The triplets that define a sentence become synaptically linked, thereby encoding the sentence in synaptic weights. When a question is posed, there is a search for the closest stored memory (having the greatest number of shared triplets). We have devised a search process that does not require that the question and the stored memory have the same number of triplets or have triplets in the same order. Once the most similar memory is recalled and undergoes 2-level dechunking, the sought for information can be obtained by element-by-element comparison of the key triplet in the question to the corresponding triplet in the retrieved memory. This search may require a reordering to align corresponding triplets, the use of pointers that link different triplets, or the use of semantic memory. Our framework uses 12 network processes; existing models can implement many of these, but in other cases we can only suggest neural implementations. Overall, our scheme provides the first view of how language-based question answering could be implemented by the brain.

Retrieval-time properties of the Little-Hopfield model and their physiological relevance.

We perform an extensive numerical investigation on the retrieval dynamics of the synchronous Hopfield model, also known as Little-Hopfield model, up to sizes of 2(18) neurons. Our results correct and extend much of the early simulations on the model. We find that the average convergence time has a power law behavior for a wide range of system sizes, whose exponent depends both on the network loading and the initial overlap with the memory to be retrieved. Surprisingly, we also find that the variance of the convergence time grows as fast as its average, making it a non-self-averaging quantity. Based on the simulation data we differentiate between two definitions for memory retrieval time, one that is mathematically strict, tau(c), the number of updates needed to reach the attractor whose properties we just described, and a second definition correspondent to the time tau(eta) when the network stabilizes within a tolerance threshold eta such that the difference of two consecutive overlaps with a stored memory is smaller that eta. We show that the scaling relationships between tau(c) and tau(eta) and the typical network parameters as the memory load alpha or the size of the network N vary greatly, being tau(eta) relatively insensitive to system sizes and loading. We propose tau(eta) as the physiological realistic measure for the typical attractor network response.