Maximum entropy models are the least structured probability distributions that exactly reproduce a chosen set of statistics measured in an interacting network. Here we use this principle to construct probabilistic models which describe the correlated spiking activity of populations of up to 120 neurons in the salamander retina as it responds to natural movies. Already in groups as small as 10 neurons, interactions between spikes can no longer be regarded as small perturbations in an otherwise independent system; for 40 or more neurons pairwise interactions need to be supplemented by a global interaction that controls the distribution of synchrony in the population. Here we show that such “K-pairwise” models—being systematic extensions of the previously used pairwise Ising models—provide an excellent account of the data. We explore the properties of the neural vocabulary by: 1) estimating its entropy, which constrains the population's capacity to represent visual information; 2) classifying activity patterns into a small set of metastable collective modes; 3) showing that the neural codeword ensembles are extremely inhomogenous; 4) demonstrating that the state of individual neurons is highly predictable from the rest of the population, allowing the capacity for error correction.
Sensory neurons encode information about the world into sequences of spiking and silence. Multi-electrode array recordings have enabled us to move from single units to measuring the responses of many neurons simultaneously, and thus to ask questions about how populations of neurons as a whole represent their input signals. Here we build on previous work that has shown that in the salamander retina, pairs of retinal ganglion cells are only weakly correlated, yet the population spiking activity exhibits large departures from a model where the neurons would be independent. We analyze data from more than a hundred salamander retinal ganglion cells and characterize their collective response using maximum entropy models of statistical physics. With these models in hand, we can put bounds on the amount of information encoded by the neural population, constructively demonstrate that the code has error correcting redundancy, and advance two hypotheses about the neural code: that collective states of the network could carry stimulus information, and that the distribution of neural activity patterns has very nontrivial statistical properties, possibly related to critical systems in statistical physics.
Previous studies have shown that motion onset is very effective at capturing attention and is more salient than smooth motion. Here, we find that this salience ranking is present already in the firing rate of retinal ganglion cells. By stimulating the retina with a bar that appears, stays still, and then starts moving, we demonstrate that a subset of salamander retinal ganglion cells, fast OFF cells, responds significantly more strongly to motion onset than to smooth motion. We refer to this phenomenon as an alert response to motion onset. We develop a computational model that predicts the time-varying firing rate of ganglion cells responding to the appearance, onset, and smooth motion of a bar. This model, termed the adaptive cascade model, consists of a ganglion cell that receives input from a layer of bipolar cells, represented by individual rectified subunits. Additionally, both the bipolar and ganglion cells have separate contrast gain control mechanisms. This model captured the responses to our different motion stimuli over a wide range of contrasts, speeds, and locations. The alert response to motion onset, together with its computational model, introduces a new mechanism of sophisticated motion processing that occurs early in the visual system.
Many biological systems perform computations on inputs that have very large dimensionality. Determining the relevant input combinations for a particular computation is often key to understanding its function. A common way to find the relevant input dimensions is to examine the difference in variance between the input distribution and the distribution of inputs associated with certain outputs. In systems neuroscience, the corresponding method is known as spike-triggered covariance (STC). This method has been highly successful in characterizing relevant input dimensions for neurons in a variety of sensory systems. So far, most studies used the STC method with weakly correlated Gaussian inputs. However, it is also important to use this method with inputs that have long range correlations typical of the natural sensory environment. In such cases, the stimulus covariance matrix has one (or more) outstanding eigenvalues that cannot be easily equalized because of sampling variability. Such outstanding modes interfere with analyses of statistical significance of candidate input dimensions that modulate neuronal outputs. In many cases, these modes obscure the significant dimensions. We show that the sensitivity of the STC method in the regime of strongly correlated inputs can be improved by an order of magnitude or more. This can be done by evaluating the significance of dimensions in the subspace orthogonal to the outstanding mode(s). Analyzing the responses of retinal ganglion cells probed with Gaussian noise, we find that taking into account outstanding modes is crucial for recovering relevant input dimensions for these neurons.
In many areas of computational biology, including the analyses of genetic mutations, protein stability and neural coding, as well as in economics, one of the most basic and important steps of data analysis is to find the relevant input dimensions for a particular task. In neural coding problems, the spike-triggered covariance (STC) method identifies relevant input dimensions by comparing the variance of the input distribution along different dimensions to the variance of inputs that elicited a neural response. While in theory the method can be applied to Gaussian stimuli with or without correlations, it has so far been used in studies with only weakly correlated stimuli. Here we show that to use STC with strongly correlated, -type inputs, one has to take into account that the covariance matrix of random samples from this distribution has a complex structure, with one or more outstanding modes. We use simulations on model neurons as well as an analysis of the responses of retinal neurons to demonstrate that taking the presence of these outstanding modes into account improves the sensitivity of the STC method by more than an order of magnitude.
Recording simultaneously from essentially all of the relevant neurons in a local circuit is crucial to understand how they collectively represent information. Here we show that the combination of a large, dense multi-electrode array and a novel, mostly automated spike sorting algorithm allowed us to record simultaneously from a highly overlapping population of more than 200 ganglion cells in the salamander retina. By combining these methods with labeling and imaging, we showed that up to 95% of the ganglion cells over the area of the array were recorded. By measuring the coverage of visual space by the receptive fields of the recorded cells, we concluded that our technique captured a neural population that forms an essentially complete representation of a region of visual space. This completeness allowed us to determine the spatial layout of different cell types as well as identify a novel group of ganglion cells that responded reliably to a set of naturalistic and artificial stimuli but had no measurable receptive field. Thus, our method allows unprecedented access to the complete neural representation of visual information, a crucial step for the understanding of population coding in sensory systems.
Recording simultaneously from essentially all of the relevant neurons in a local circuit is crucial to understand how they collectively represent information. Here we show that the combination of a large, dense multielectrode array and a novel, mostly automated spike-sorting algorithm allowed us to record simultaneously from a highly overlapping population of >200 ganglion cells in the salamander retina. By combining these methods with labeling and imaging, we showed that up to 95% of the ganglion cells over the area of the array were recorded. By measuring the coverage of visual space by the receptive fields of the recorded cells, we concluded that our technique captured a neural population that forms an essentially complete representation of a region of visual space. This completeness allowed us to determine the spatial layout of different cell types as well as identify a novel group of ganglion cells that responded reliably to a set of naturalistic and artificial stimuli but had no measurable receptive field. Thus, our method allows unprecedented access to the complete neural representation of visual information, a crucial step for the understanding of population coding in sensory systems.
Detailed measurement of ganglion cell receptive fields often reveals significant deviations from a smooth, Gaussian profile. We studied the effect of these irregularities on the representation of fine spatial information in the retina. We recorded from nearby clusters of ganglion cells, testing their ability to determine the location of small flashed spots, and we compared the results to the prediction of a Gaussian receptive field model derived from reverse correlation. Despite considerable receptive field overlap, almost all ganglion cell pairs signaled nearly independently. For groups of five cells with highly overlapping receptive fields, the measured light-evoked currents encoded ~33% more information than predicted by the Gaussian receptive field model. Including measured local irregularities in the receptive field model increased performance to the level observed experimentally. These results suggest that instead of being an unavoidable defect, irregularities may be a positive design feature of population neural codes.
The manner in which groups of neurons represent events in the external world is a central question in neuroscience. Estimation of the information encoded by small groups of neurons has shown that in many neural systems, cells carry mildly redundant information. These measures average over all the activity patterns of a neural population. Here, we analyze the population code of the salamander and guinea pig retinas by quantifying the information conveyed by specific multi-cell activity patterns. Synchronous spikes, even though they are relatively rare and highly informative, convey less information than the sum of either spike alone, making them redundant coding symbols. Instead, patterns of spiking in one cell and silence in others, which are relatively common and often overlooked as special coding symbols, were found to be mostly synergistic. Our results reflect that the mild average redundancy between ganglion cells that was previously reported is actually the result of redundant and synergistic multi-cell patterns, whose contributions partially cancel each other when taking the average over all patterns. We further show that similar coding properties emerge in a generic model of neural responses, suggesting that this form of combinatorial coding, in which specific compound patterns carry synergistic or redundant information, may exist in other neural circuits.
A fundamental task of the brain is detecting patterns in the environment that enable predictions about the future. Here, we show that the salamander and mouse retinas can recognize a wide class of periodic temporal patterns, such that a subset of ganglion cells fire strongly and specifically in response to a violation of the periodicity. This sophisticated retinal processing may provide a substrate for hierarchical pattern detection in subsequent circuits.
We show that when a moving object suddenly reverses direction, there is a brief, synchronous burst of firing within a population of retinal ganglion cells. This burst can be driven by either the leading or trailing edge of the object. The latency is constant for movement at different speeds, objects of different size, and bright versus dark contrasts. The same ganglion cells that signal a motion reversal also respond to smooth motion. We show that the brain can build a pure reversal detector using only a linear filter that reads out synchrony from a group of ganglion cells. These results indicate that not only can the retina anticipate the location of a smoothly moving object, but that it can also signal violations in its own prediction. We show that the reversal response cannot be explained by models of the classical receptive field and suggest that nonlinear receptive field subunits may be responsible.
Chronic obstructive pulmonary disease (COPD) patients have lower levels of physical activity compared to age-matched controls, and they limit physical activities requiring normal exertion. Our purpose was to compare the effectiveness of a traditional exercise therapy (TET) program with a behavioral lifestyle activity program (LAP) in promoting physical activity.
Moderate physical activity (kcal/week) was assessed in 176 COPD patients using the Community Health Activities Model for Seniors questionnaire. Patients were randomized to either a three month TET program that meet thrice weekly or a LAP. The LAP was designed to teach behavioral skills that encouraged the daily accumulation of self-selected physical activities of at least moderate intensity. Interventionist contact was similar (36 hours) between the two groups. Patients were assessed at baseline and 3, 6 and 12 months.
Compared to baseline values, self-reported moderate physical activity increased three months post-randomization with no significant difference (p = 0.99) found between the TET (2,501 ± 197 kcal/week) and the LAP (2,498 ± 211 kcal/week). At 6 and 12 months post-randomization, there were no significant differences (p = 0.37 and 0.69, respectively) in self-reported levels of moderate physical activity between the TET (2,210 ± 187 and 2,213 ± 218 kcal/week, respectively) and the LAP (2,456 ± 198 and 2,342 ± 232 kcal/week, respectively).
Although there was no difference between treatment groups, the TET and the LAP were both effective at in increasing moderate levels of physical activity at 3 months and maintaining moderate physical activity levels 12 months post-randomization.
Chronic obstructive pulmonary disease; Exercise; Physical activity; Behavioral intervention
Pattern recognition is one of the most important tasks of the visual system, and uncovering the neural mechanisms underlying recognition phenomena has been a focus of researchers for decades. Surprisingly, at the earliest stages of vision, the retina is capable of highly sophisticated temporal pattern recognition. We stimulated the retina of tiger salamander (Ambystoma tigrinum) with periodic dark flash sequences and found that retinal ganglion cells had a wide variety of different responses to a periodic flash sequence with many firing when a flash was omitted. The timing of the omitted stimulus response (OSR) depended on the period, with individual cells tracking the stimulus period down to increments of 5 ms. When flashes occurred earlier than expected, cells updated their expectation of the next flash time by as much as 50 ms. When flashes occurred later than expected, cells fired an OSR and reset their temporal expectation to the average time interval between flashes. Using pharmacology to investigate the retinal circuitry involved, we found that inhibitory transmission from amacrine cells was not required, but on bipolar cells were required. The results suggest a mechanism in which the intrinsic resonance of on bipolars leads to the OSR in ganglion cells. We discuss the implications of retinal pattern recognition on the neural code of the retina and visual processing in general.
Chronic subclinical inflammation may contribute to impaired physical function in older adults; however, more data are needed to determine whether inflammation is a common mechanism for functional decline, independent of disease or health status.
We examined associations between physical function and inflammatory biomarkers in 542 older men and women enrolled in four clinical studies at Wake Forest University between 2001 and 2006. All participants were at least 55 years and had chronic obstructive pulmonary disease, congestive heart failure, high cardiovascular risk, or self-reported physical disability. Uniform clinical assessments were used across studies, including grip strength; a Short Physical Performance Battery (SPPB; includes balance, 4-m walk, and repeated chair stands); inflammatory biomarker assays for interleukin-6 (IL-6), tumor necrosis factor alpha (TNF-α), and C-reactive protein (CRP); and anthropometric measures.
Higher levels of CRP and IL-6, but not TNF-α, were associated with lower grip strength and SPPB scores and longer times to complete the 4-m walk and repeated chair stands tests, independent of age, gender, and race. More importantly, these relationships were generally independent of disease status. Further adjustment for fat mass, lean mass, or percent body fat altered some of these relationships but did not significantly change the overall results.
Elevated CRP and IL-6 levels are associated with poorer physical function in older adults with various comorbidities, as assessed by a common battery of clinical assessments. Chronic subclinical inflammation may be a marker of functional limitations in older persons across several diseases/health conditions.
Inflammation; Physical function; Aging; Comorbidities
To examine whether adaptations in physical activity energy expenditure (PAEE) and resting metabolic rate (RMR) during weight loss were associated with future weight regain in overweight/obese, older women.
Research Methods and Procedures
Thirty-four overweight/obese (BMI=25–40 kg/m2), postmenopausal women underwent a 20-week weight loss intervention of hypocaloric diet with (low- or high-intensity) or without treadmill walking (weekly caloric deficit was ~11760 kJ), with a subsequent 12-month follow-up. RMR (via indirect calorimetry), PAEE (by RT3 accelerometer) and body composition (by DXA) were measured before and after intervention. Body weight and self-reported information on physical activity were collected after intervention, and at 6- and 12-months following intervention.
The intervention resulted in decreases in body weight, lean mass, fat mass, percent body fat, RMR, and PAEE (p < 0.001 for all). Weight regain was 2.9 ± 3.3 kg (−3.1 to +9.2 kg) at 6- months and 5.2 ± 5.0 kg (−2.3 to +21.7 kg) at 12-months following intervention. The amount of weight regained after 6- and 12-months was inversely associated with decreases in PAEE during the weight loss intervention (r= −0.521, p = 0.002 and r= −0.404, p = 0.018, respectively), such that women with larger declines in PAEE during weight loss experienced greater weight regain during follow-up. Weight regain was not associated with changes in RMR during intervention or with self-reported physical activity during follow-up.
This study demonstrates that, while both RMR and PAEE decreased during weight loss in postmenopausal women, maintaining high levels of daily physical activity during weight loss may be important to mitigate weight regain after weight loss.
energy expenditure; resting metabolic rate; weight loss intervention; hypocaloric diet
Neurons in diverse brain areas can respond to the interruption of a regular stimulus pattern by firing bursts of spikes. Here we describe a simple model which permits such responses to periodic stimuli over a substantial frequency range. Focusing on the omitted stimulus response (OSR) in isolated retinas subjected to periodic patterns of dark flashes, we develop a pharmacologically-based model which accounts for resonances in ON bipolar cells. The bipolar cell terminal contains an LRC oscillator whose inductance is modulated by a transient calcium concentration, thus adjusting its resonant frequency to approximately match that of the stimulus. The model reproduces ganglion cell outputs, which sum the ON and OFF bipolar pathways, and it responds to omitted flashes with approximately constant latencies, as observed experimentally.
bipolar cell; calcium tuning; ganglion cell; LRC circuit; omitted stimulus response; resonance
Previous studies have shown that motion onset is very effective at capturing attention
and is more salient than smooth motion. Here, we find that this salience ranking is present already
in the firing rate of retinal ganglion cells. By stimulating the retina with a bar that appears,
stays still, and then starts moving, we demonstrate that a subset of salamander retinal ganglion
cells, fast OFF cells, responds significantly more strongly to motion onset than to smooth motion.
We refer to this phenomenon as an alert response to motion onset. We develop a computational model
that predicts the time-varying firing rate of ganglion cells responding to the appearance, onset,
and smooth motion of a bar. This model, termed the Adaptive Cascade Model (ACM), consists of a
ganglion cell that receives input from a layer of bipolar cells, represented by individual rectified
subunits. Additionally, both the bipolar and ganglion cells have separate contrast gain control
mechanisms. This model captured the responses to our different motion stimuli over a wide range of
contrasts, speeds, and locations. The alert response to motion onset, together with its
computational model, introduces a new mechanism of sophisticated motion processing that occurs early
in the visual system.
Biological networks have so many possible states that exhaustive sampling is impossible. Successful analysis thus depends on simplifying hypotheses, but experiments on many systems hint that complicated, higher-order interactions among large groups of elements have an important role. Here we show, in the vertebrate retina, that weak correlations between pairs of neurons coexist with strongly collective behaviour in the responses of ten or more neurons. We find that this collective behaviour is described quantitatively by models that capture the observed pairwise correlations but assume no higher-order interactions. These maximum entropy models are equivalent to Ising models, and predict that larger networks are completely dominated by correlation effects. This suggests that the neural code has associative or error-correcting properties, and we provide preliminary evidence for such behaviour. As a first test for the generality of these ideas, we show that similar results are obtained from networks of cultured cortical neurons.
In the classic “What the frog's eye tells the frog's brain,” Lettvin and colleagues  showed that different types of retinal ganglion cell send specific kinds of information. For example, one type responds best to a dark, convex form moving centripetally (a fly). Here we consider a complementary question: how much information does the retina send and how is it apportioned among different cell types? Recording from guinea pig retina on a multi-electrode array and presenting various types of motion in natural scenes, we measured information rates for seven types of ganglion cell. Mean rates varied across cell types (6–13 bits · s−1) more than across stimuli. Sluggish cells transmitted information at lower rates than brisk cells, but because of trade-offs between noise and temporal correlation, all types had the same coding efficiency. Calculating the proportions of each cell type from receptive field size and coverage factor, we conclude (assuming independence) that the approximately 105 ganglion cells transmit on the order of 875,000 bits · s−1. Because sluggish cells are equally efficient but more numerous, they account for most of the information. With approximately 106 ganglion cells, the human retina would transmit data at roughly the rate of an Ethernet connection.
Research suggests that patients' satisfaction with their physical functioning (SPF) is a critical component of HRQL. This study was designed to examine the extent to which perceptions of physical function and the value placed on physical function are related to satisfaction ratings. The sample consisted of older adults suffering from a progressively debilitating disease, chronic obstructive pulmonary disease (COPD).
During baseline assessments, COPD patients participating in a randomized controlled physical activity trial completed measures of SPF, perceived difficulty, and perceived importance.
An ANCOVA controlling for age and gender indicated that perceived difficulty, perceived importance, and their interaction accounted for 43% of the variance in SPF. Additionally, participants were most satisfied with important tasks that they performed with little difficulty. Participants were least satisfied with important tasks that they perceived as highly difficult.
The results of the present study indicate that not being able to perform valued tasks produces discontent that is reflected in lower rating of satisfaction with physical functioning. Clearly, the significance of loss in function to individual patients is related to the importance of the functional activities that may be compromised. These data have implications for the scope of patient assessment in clinical care and for the conceptual basis of future research in the area of physical functioning.