Abstract: Because of the limited processing capacity of eyes, retinal networks must adapt constantly to best present the ever changing visual world to the brain. However, we still know little about how adaptation in retinal networks shapes neural encoding of changing information. To study this question, we recorded voltage responses from photoreceptors (R1-R6) and their output neurons (LMCs) in the Drosophila eye to repeated patterns of contrast values, collected from natural scenes. By analyzing the continuous photoreceptor-to-LMC transformations of these graded-potential neurons, we show that the efficiency of coding is dynamically improved by adaptation. In particular, adaptation enhances both the frequency and amplitude distribution of LMC output by improving sensitivity to under-represented signals within seconds. Moreover, the signal-to-noise ratio of LMC output increases in the same time scale. We suggest that these coding properties can be used to study network adaptation using the genetic tools in Drosophila, as shown in a companion paper (Part II).

Abstract: Retinal networks must adapt constantly to best present the ever changing visual world to the brain. Here we test the hypothesis that adaptation is a result of different mechanisms at several synaptic connections within the network. In a companion paper (Part I), we showed that adaptation in the photoreceptors (R1-R6) and large monopolar cells (LMC) of the Drosophila eye improves sensitivity to under-represented signals in seconds by enhancing both the amplitude and frequency distribution of LMCs' voltage responses to repeated naturalistic contrast series. In this paper, we show that such adaptation needs both the light-mediated conductance and feedback-mediated synaptic conductance. A faulty feedforward pathway in histamine receptor mutant flies speeds up the LMC output, mimicking extreme light adaptation. A faulty feedback pathway from L2 LMCs to photoreceptors slows down the LMC output, mimicking dark adaptation. These results underline the importance of network adaptation for efficient coding, and as a mechanism for selectively regulating the size and speed of signals in neurons. We suggest that concert action of many different mechanisms and neural connections are responsible for adaptation to visual stimuli. Further, our results demonstrate the need for detailed circuit reconstructions like that of the Drosophila lamina, to understand how networks process information.

Abstract: In cortical neurones, analogue dendritic potentials are thought to be encoded into patterns of digital spikes. According to this view, neuronal codes and computations are based on the temporal patterns of spikes: spike times, bursts or spike rates. Recently, we proposed an 'action potential waveform code' for cortical pyramidal neurones in which the spike shape carries information. Broader somatic action potentials are reliably produced in response to higher conductance input, allowing for four times more information transfer than spike times alone. This information is preserved during synaptic integration in a single neurone, as back-propagating action potentials of diverse shapes differentially shunt incoming postsynaptic potentials and so participate in the next round of spike generation. An open question has been whether the information in action potential waveforms can also survive axonal conduction and directly influence synaptic transmission to neighbouring neurones. Several new findings have now brought new light to this subject, showing cortical information processing that transcends the classical models.

Abstract: Wiring cost minimization has successfully explained many structures of nervous systems. However, in the nematode Caenorhabditis elegans, for which anatomical data are most detailed, wiring economy is thought to play only a partial role and alone has failed to account for the grouping of neurons into ganglia [Chen BL, Hall DH, Chklovskii DB (2006) Proc Natl Acad Sci USA 103:4723-4728; Kaiser M, Hilgetag CC (2006) PLoS Comput Biol 2:e95; Ahn Y-Y, Jeong H, Kim BJ (2006) Physica A 367:531-537]. Here, we test the hypothesis that optimally wired subnetworks can exist within nonoptimal networks, thus allowing wiring economy to give an improved prediction of spatial structure. We show in C. elegans that the small subnetwork of wires connecting sensory and motor neurons with sensors and muscles, comprising only 15% of connections, is close to optimal and alone predicts the main features of the spatial segregation of neurons into ganglia and encephalization. Moreover, a method to dissect networks into optimal and nonoptimal components is shown to find a large near-optimal subnetwork of 84% of neurons with a very low position error of 5.4%, and that explains clustering of neurons into ganglia and encephalization to fine detail. In general, we expect realistic networks not to be globally optimal in wire cost. We thus propose the strategy of using near-optimal subnetworks to understand neuroanatomical structure.

Abstract: Pump activity is a homeostatic mechanism that maintains ionic gradients. Here we examined whether the slow reduction in excitability induced by sodium-pump activity that has been seen in many neuronal types is also involved in neuronal coding. We took intracellular recordings from a spike-bursting sensory neuron in the leech Hirudo medicinalis in response to naturalistic tactile stimuli with different statistical distributions. We show that regulation of excitability by sodium pumps is necessary for the neuron to make different responses depending on the statistical context of the stimuli. In particular, sodium-pump activity allowed spike-burst sizes and rates to code not for stimulus values per se, but for their ratio with the standard deviation of the stimulus distribution. Modeling further showed that sodium pumps can be a general mechanism of adaptation to statistics on the time scale of 1 min. These results implicate the ubiquitous pump activity in the adaptation of neural codes to statistics.

Abstract: At the layer of first visual synapses, information from photoreceptors is processed and transmitted towards the brain. In fly compound eye, output from photoreceptors (R1-R6) that share the same visual field is pooled and transmitted via histaminergic synapses to two classes of interneuron, large monopolar cells (LMCs) and amacrine cells (ACs). The interneurons also feed back to photoreceptor terminals via numerous ligand-gated synapses, yet the significance of these connections has remained a mystery. We investigated the role of feedback synapses by comparing intracellular responses of photoreceptors and LMCs in wild-type Drosophila and in synaptic mutants, to light and current pulses and to naturalistic light stimuli. The recordings were further subjected to rigorous statistical and information-theoretical analysis. We show that the feedback synapses form a negative feedback loop that controls the speed and amplitude of photoreceptor responses and hence the quality of the transmitted signals. These results highlight the benefits of feedback synapses for neural information processing, and suggest that similar coding strategies could be used in other nervous systems.

Abstract: One of the basic operations in sensory processing is the computation of the temporal order of excitation of sensors. Motivated by the discrepancy between models and experiments at high signal contrast, we obtain families of algorithms by solutions of a general set of equations that define temporal order detection as an input-to-output relationship. Delays and nonlinear operations are the basis of all algorithms found, but different algorithmic structures exist when the operations are multiplications, OR gates, different types of AND-NOT logical gates, or concatenated AND-NOT gates. Among others, we obtain the Hassenstein-Reichardt model, a network using a multiplicative operation that has been proposed to explain fly optomotor behavior. We also find extensions of the Barlow-Levick model (based on an AND-NOT gate with delayed inhibition and nondelayed excitation as inputs), originally proposed to explain the bipolar cell response of the rabbit retina to motion stimuli. In the extended models, there are two more steps, another AND-NOT gate, and a subtraction or two subtractions that make the model responsive only to motion. In response to low-contrast inputs, the concatenated AND-NOT gates or the AND-NOT gate followed by a subtraction in these new models act as the multiplicative operation in the Hassenstein-Reichardt model. At high contrast, the new models behave like the Hassenstein-Reichardt model except that they are independent of contrast as observed experimentally.

Abstract: Synapses are specialized communication points between neurons, and their number is a major determinant of cognitive abilities. These dynamic structures undergo developmental- and activity-dependent changes. During brain aging and certain diseases, synapses are gradually lost, causing mental decline. It is, thus, critical to identify the molecular mechanisms controlling synapse number. We show here that the levels of phosphoinositide 3 kinase (PI3K) regulate synapse number in both Drosophila larval motor neurons and adult brain projection neurons. The supernumerary synapses induced by PI3K overexpression are functional and elicit changes in behavior. Remarkably, PI3K activation induces synaptogenesis in aged adult neurons as well. We demonstrate that persistent PI3K activity is necessary for synapse maintenance. We also report that PI3K controls the expression and localization of synaptic markers in human neuroblastoma cells, suggesting that PI3K synaptogenic activity is conserved in humans. Thus, we propose that PI3K stimulation can be applied to prevent or delay synapse loss in normal aging and in neurological disorders.

Abstract: Neural variability in the presence of noise has been studied mainly in resonator neurons, such as Hodgkin-Huxley or FitzHugh-Nagumo models. Here we investigate this variability for integrator neurons, whose excitability is due to a saddle-node bifurcation of the rest state instead of a Hopf bifurcation. Using simple theoretical expressions for the interspike times distributions, we obtain coefficients of variation in good agreement with numerical calculations in realistic neuron models. The main features of this coefficient as a function of noise depend on the refractory period and on the presence of bistability. The bistability is responsible for the existence of two different time scales in the spiking behavior giving an antiresonance effect.

Abstract: Action potentials have been shown to shunt synaptic charge to a degree that depends on their waveform. In this way, they participate in synaptic integration, and thus in the probability of generating succeeding action potentials, in a shape-dependent way. Here we test whether the different action potential waveforms produced during dynamical stimulation in a single cortical neuron carry information about the conductance stimulus history. When pyramidal neurons in rat visual cortex were driven by a conductance stimulus that resembles natural synaptic input, somatic action potential waveforms showed a large variability that reliably signaled the history of the input for up to 50 ms before the spike. The correlation between stimulus history and action potential waveforms had low noise, resulting in information rates that were three to four times larger than for the instantaneous spike rate. The reliable correlation between stimulus history and spike waveforms then acts as a local encoding at the single-cell level. It also directly affects neuronal communication as different waveforms influence the production of succeeding spikes via differential shunting of synaptic charge. Modeling was used to show that slow conductances can implement memory of the stimulus history in cortical neurons, encoding this information in the spike shape.

Abstract: Communication in biological systems must deal with noise and metabolic or temporal constraints. We include these constraints into information theory to obtain the distributions of signal usage corresponding to a maximal rate of information transfer given any noise structure and any constraints. Generalized versions of the Boltzmann, Gaussian, or Poisson distributions are obtained for linear, quadratic and temporal constraints, respectively. These distributions are shown to imply that biological transformations must dedicate a larger output range to the more probable inputs and less to the outputs with higher noise and higher participation in the constraint. To show the general theory of reliable communication at work, we apply these results to biochemical and neuronal signaling. Noncooperative enzyme kinetics is shown to be suited for transfer of a high signal quality when the input distribution has a maximum at low concentrations while cooperative kinetics for near-Gaussian input statistics. Neuronal codes based on spike rates, spike times or bursts have to balance signal quality and cost-efficiency and at the network level imply sparseness and uncorrelation within the limits of noise, cost, and processing operations.

Abstract: Auditory pattern recognition by the CNS is a fundamental process in acoustic communication. Because crickets communicate with stereotyped patterns of constant frequency syllables, they are established models to investigate the neuronal mechanisms of auditory pattern recognition. Here we provide evidence that for the neural processing of amplitude-modulated sounds, the instantaneous spike rate rather than the time-averaged neural activity is the appropriate coding principle by comparing both coding parameters in a thoracic interneuron (Omega neuron ON1) of the cricket (Gryllus bimaculatus) auditory system. When stimulated with different temporal sound patterns, the analysis of the instantaneous spike rate demonstrates that the neuron acts as a low-pass filter for syllable patterns. The instantaneous spike rate is low at high syllable rates, but prominent peaks in the instantaneous spike rate are generated as the syllable rate resembles that of the species-specific pattern. The occurrence and repetition rate of these peaks in the neuronal discharge are sufficient to explain temporal filtering in the cricket auditory pathway as they closely match the tuning of phonotactic behavior to different sound patterns. Thus temporal filtering or "pattern recognition" occurs at an early stage in the auditory pathway.

Abstract: We present a method to measure the rate of information transfer for any continuous signals of finite duration without assumptions. After testing the method with simulated responses, we measure the encoding performance of Calliphora photoreceptors. We find that especially for naturalistic stimulation the responses are nonlinear and noise is nonadditive, and show that adaptation mechanisms affect signal and noise differentially depending on the time scale, structure, and speed of the stimulus. Different signaling strategies for short- and long-term and dim and bright light are found for this graded system when stimulated with naturalistic light changes.

Abstract: Reduction of costs in biological signalling seems an evolutionary advantage, but recent experiments have shown signalling codes shifted to signals of high cost with an underutilization of low-cost signals. Here I derive a theory for efficient signalling that includes both errors and costs as constraints and I show that errors in the efficient translation of biological states into signals can shift codes to higher costs, effectively performing a quality control. The statistical structure of signal usage is predicted to be of a generalized Boltzmann form that penalizes signals that are costly and sensitive to errors. This predicted distribution of signal usage against signal cost has two main features: an exponential tail required for cost efficiency and an underutilization of the low-cost signals required to protect the signalling quality from the errors. These predictions are shown to correspond quantitatively to the experiments in which gathering signal statistics is feasible as in visual cortex neurons.