SUMMARY Loss of FMRP causes Fragile X syndrome (FXS), but the physiological functions of FMRP remain highly debatable. Here we show that FMRP regulates neurotransmitter release in CA3 pyramidal neurons by modulating action potential (AP) duration. Loss of FMRP leads to excessive AP broadening during repetitive activity, enhanced presynaptic calcium influx and elevated neurotransmitter release. The AP broadening defects caused by FMRP loss have a cell-autonomous presynaptic origin and can be acutely rescued in postnatal neurons. These presynaptic actions of FMRP are translation-independent and are mediated selectively by BK channels via interaction of FMRP with BK channel’s regulatory β4 subunits. Information-theoretical analysis demonstrates that loss of these FMRP functions causes marked dysregulation of synaptic information transmission. FMRP-dependent AP broadening is not limited to the hippocampus, but also occurs in cortical pyramidal neurons. Our results thus suggest major translation-independent presynaptic functions of FMRP that may have important implications for understanding FXS neuropathology.

Measurements of action potential duration in Figures 1, 3, 5G, 6D, and S1 display an apparent three-point periodicity. We clarify that this effect results from using 60 Hz stimulus trains that have fractional 16.67 ms interstimulus intervals (ISIs). Because of software rounding of submillisecond timing to a whole millisecond, every third ISI is 1 ms shorter in these stimulus trains, causing periodicity in the data. This periodicity was no longer apparent when 58.8 Hz trains (with a constant 17 ms ISIs) were used instead in the same neurons (see Figure E1 shown here). Because of the precision of AP duration determination and its strong dependence on ISI, this periodicity is apparent in all recordings of AP duration at 60 Hz, but not in recordings of synaptic transmission, in which the noise is dominated by the intrinsic stochasticity of release. This effect is very small (<2%) and is present in all recordings. This clarification is now presented in the figure shown here. In addition, two units of measure have been corrected on page 10 of the Supplemental Information.

Synaptic vesicle exo- and endocytosis are usually driven by neuronal activity but can also occur spontaneously. The identity and differences between vesicles supporting evoked and spontaneous neurotransmission remain highly debated. Here we combined nanometer-resolution imaging with a transient motion analysis approach to examine the dynamics of individual synaptic vesicles in hippocampal terminals under physiological conditions. We found that vesicles undergoing spontaneous and stimulated endocytosis differ in their dynamic behavior, particularly in the ability to engage in directed motion. Our data indicate that such motional differences depend on the myosin family of motor proteins, particularly myosin II. Analysis of synaptic transmission in the presence of myosin II inhibitor confirmed a specific role for myosin II in evoked, but not spontaneous, neurotransmission and also suggested a functional role of myosin II-mediated vesicle motion in supporting vesicle mobilization during neural activity.

Short-term synaptic plasticity (STP) is widely thought to play an important role in information processing. This major function of STP has recently been challenged, however, by several computational studies indicating that transmission of information by dynamic synapses is broadband, i.e., frequency independent. Here we developed an analytical approach to quantify time-and rate-dependent synaptic information transfer during arbitrary spike trains using a realistic model of synaptic dynamics in excitatory hippocampal synapses. We found that STP indeed increases information transfer in a wide range of input rates, which corresponds well to the naturally occurring spike frequencies at these synapses. This increased information transfer is observed both during Poisson-distributed spike trains with a constant rate and during naturalistic spike trains recorded in hippocampal place cells in exploring rodents. Interestingly, we found that the presence of STP in low release probability excitatory synapses leads to optimization of information transfer specifically for short high-frequency bursts, which are indeed commonly observed in many excitatory hippocampal neurons. In contrast, more reliable high release probability synapses that express dominant short-term depression are predicted to have optimal information transmission for single spikes rather than bursts. This prediction is verified in analyses of experimental recordings from high release probability inhibitory synapses in mouse hippocampal slices and fits well with the observation that inhibitory hippocampal interneurons do not commonly fire spike bursts. We conclude that STP indeed contributes significantly to synaptic information transfer and may serve to maximize information transfer for specific firing patterns of the corresponding neurons.

For a large class of repulsive interaction models, the Mayer cluster integrals can be transformed into a tridiagonal real symmetric matrix R_{mn} , whose elements converge to two constants. This allows for an effective extrapolation of the equation of state for these models. Due to a nearby (nonphysical) singularity on the negative real z axis, standard methods (e.g., Padé approximants based on the cluster integrals expansion) fail to capture the behavior of these models near the ordering transition, and, in particular, do not detect the critical point. A recent work [E. Eisenberg and A. Baram, Proc. Natl. Acad. Sci. U.S.A. 104, 5755 (2007)] has shown that the critical exponents sigma and sigma;{'} , characterizing the singularity of the density as a function of the activity, can be exactly calculated if the decay of the R matrix elements to their asymptotic constant follows a 1/n;{2} law. Here we employ renormalization group (RG) arguments to extend this result and analyze cases for which the asymptotic approach of the R matrix elements toward their limiting value is of a more general form. The relevant asymptotic correction terms (in RG sense) are identified, and we then present a corrected exact formula for the critical exponents. We identify the limits of usage of the formula and demonstrate one physical model, which is beyond its range of validity. The formula is validated numerically and then applied to analyze a number of concrete physical models.

The supercooled N3 model exhibits an increasingly slow dynamics as density approaches the random closest packing density. Here, we present a direct measurement of the dynamical correlation function G4(r,t), showing the emergence of a growing length scale ξ(4) across which the dynamics is correlated. The correlation length measured, up to 120 lattice sites, power law diverges as the density approaches ρ(t), the density at which the fluid phase of the model is predicted to terminate. The four-point susceptibility, often used as an agent to estimate ξ(4), does not depend simply on the latter. Rather, it depends strongly on the short-range behavior of G4(r,t). Consequently, χ(4) peaks before ξ(4) reaches its maximal value. The two quantities should therefore be studied independently.

Temporal codes are believed to play important roles in neuronal representation of information. Neuronal ability to classify and learn temporal spiking patterns is thus essential for successful extraction and processing of information. Understanding neuronal learning of temporal code has been complicated, however, by the intrinsic stochasticity of synaptic transmission. Using a computational model of a learning neuron, the tempotron, we studied the effects of synaptic unreliability and short-term dynamics on the neuron's ability to learn spike timing rules. Our results suggest that such a model neuron can learn to classify spike timing patterns even with unreliable synapses, albeit with a significantly reduced success rate. We explored strategies to improve correct spike timing classification and found that firing clustered spike bursts significantly improves learning performance. Furthermore, rapid activity-dependent modulation of synaptic unreliability, implemented with realistic models of dynamic synapses, further improved classification of different burst properties and spike timing modalities. Neuronal models with only facilitating or only depressing inputs exhibited preference for specific types of spike timing rules, but a mixture of facilitating and depressing synapses permitted much improved learning of multiple rules. We tested applicability of these findings to real neurons by considering neuronal learning models with the naturally distributed input release probabilities found in excitatory hippocampal synapses. Our results suggest that spike bursts comprise several encoding modalities that can be learned effectively with stochastic dynamic synapses, and that distributed release probabilities significantly improve learning performance. Synaptic unreliability and dynamics may thus play important roles in the neuron's ability to learn spike timing rules during decoding.

We consider a tiling model of the two-dimensional square-lattice, where each site is tiled with one of the sixteen Wang tiles. The ground states of this model are all quasi-periodic. The systems undergoes a disorder to quasi-periodicity phase transition at finite temperature. Introducing a proper order-parameter, we study the system at criticality, and extract the critical exponents characterizing the transition. The exponents obtained are consistent with hyper-scaling.