Sensory stimulation can systematically bias the perceived passage of time, but why and how this happens is mysterious. In this report, we provide evidence that such biases may ultimately derive from an innate and adaptive use of stochastically evolving dynamic stimuli to help refine estimates derived from internal timekeeping mechanisms. A simplified statistical model based on probabilistic expectations of stimulus change derived from the second-order temporal statistics of the natural environment makes three predictions. First, random noise-like stimuli whose statistics violate natural expectations should induce timing bias. Second, a previously unexplored obverse of this effect is that similar noise stimuli with natural statistics should reduce the variability of timing estimates. Finally, this reduction in variability should scale with the interval being timed, so as to preserve the overall Weber law of interval timing. All three predictions are borne out experimentally. Thus, in the context of our novel theoretical framework, these results suggest that observers routinely rely on sensory input to augment their sense of the passage of time, through a process of Bayesian inference based on expectations of change in the natural environment.

The representation of acoustic stimuli in the brainstem forms the basis for higher auditory processing. While some characteristics of this representation (e.g. tuning curve) are widely accepted, it remains a challenge to predict the firing rate at high temporal resolution in response to complex stimuli. In this study we explore models for in vivo, single cell responses in the medial nucleus of the trapezoid body (MNTB) under complex sound stimulation. We estimate a family of models, the multilinear models, encompassing the classical spectrotemporal receptive field and allowing arbitrary input-nonlinearities and certain multiplicative interactions between sound energy and its short-term auditory context. We compare these to models of more traditional type, and also evaluate their performance under various stimulus representations. Using the context model, 75% of the explainable variance could be predicted based on a cochlear-like, gamma-tone stimulus representation. The presence of multiplicative contextual interactions strongly reduces certain inhibitory/suppressive regions of the linear kernels, suggesting an underlying nonlinear mechanism, e.g. cochlear or synaptic suppression, as the source of the suppression in MNTB neuronal responses. In conclusion, the context model provides a rich and still interpretable extension over many previous phenomenological models for modeling responses in the auditory brainstem at submillisecond resolution.

The relationship between a sound and its neural representation in the auditory cortex remains elusive. Simple measures such as the frequency response area or frequency tuning curve provide little insight into the function of the auditory cortex in complex sound environments. Spectrotemporal receptive field (STRF) models, despite their descriptive potential, perform poorly when used to predict auditory cortical responses, showing that nonlinear features of cortical response functions, which are not captured by STRFs, are functionally important. We introduce a new approach to the description of auditory cortical responses, using multilinear modeling methods. These descriptions simultaneously account for several nonlinearities in the stimulus-response functions of auditory cortical neurons, including adaptation, spectral interactions, and nonlinear sensitivity to sound level. The models reveal multiple inseparabilities in cortical processing of time lag, frequency, and sound level, and suggest functional mechanisms by which auditory cortical neurons are sensitive to stimulus context. By explicitly modeling these contextual influences, the models are able to predict auditory cortical responses more accurately than are STRF models. In addition, they can explain some forms of stimulus dependence in STRFs that were previously poorly understood.

Many perceptual processes and neural computations, such as speech recognition, motor control and learning, depend on the ability to measure and mark the passage of time. However, the processes that make such temporal judgements possible are unknown. A number of different hypothetical mechanisms have been advanced, all of which depend on the known, temporally predictable evolution of a neural or psychological state, possibly through oscillations or the gradual decay of a memory trace. Alternatively, judgements of elapsed time might be based on observations of temporally structured, but stochastic processes. Such processes need not be specific to the sense of time; typical neural and sensory processes contain at least some statistical structure across a range of time scales. Here, we investigate the statistical properties of an estimator of elapsed time which is based on a simple family of stochastic process.

We describe a class of models that predict how the instantaneous firing rate of a neuron depends on a dynamic stimulus. The models utilize a learnt pointwise nonlinear transform of the stimulus, followed by a linear filter that acts on the sequence of transformed inputs. In one case, the nonlinear transform is the same at all filter lag-times. Thus, this "input nonlinearity" converts the initial numerical representation of stimulus value to a new representation that provides optimal input to the subsequent linear model. We describe algorithms that estimate both the input nonlinearity and the linear weights simultaneously; and present techniques to regularise and quantify uncertainty in the estimates. In a second approach, the model is generalized to allow a different nonlinear transform of the stimulus value at each lag-time. Although more general, this model is algorithmically more straightforward to fit. However, it has many more degrees of freedom than the first approach, thus requiring more data for accurate estimation. We test the feasibility of these methods on synthetic data, and on responses from a neuron in rodent barrel cortex. The models are shown to predict responses to novel data accurately, and to recover several important neuronal response properties.

Biophysically accurate multicompartmental models of individual neurons have significantly advanced our understanding of the input-output function of single cells. These models depend on a large number of parameters that are difficult to estimate. In practice, they are often hand-tuned to match measured physiological behaviors, thus raising questions of identifiability and interpretability. We propose a statistical approach to the automatic estimation of various biologically relevant parameters, including 1) the distribution of channel densities, 2) the spatiotemporal pattern of synaptic input, and 3) axial resistances across extended dendrites. Recent experimental advances, notably in voltage-sensitive imaging, motivate us to assume access to: i) the spatiotemporal voltage signal in the dendrite and ii) an approximate description of the channel kinetics of interest. We show here that, given i and ii, parameters 1-3 can be inferred simultaneously by nonnegative linear regression; that this optimization problem possesses a unique solution and is guaranteed to converge despite the large number of parameters and their complex nonlinear interaction; and that standard optimization algorithms efficiently reach this optimum with modest computational and data requirements. We demonstrate that the method leads to accurate estimations on a wide variety of challenging model data sets that include up to about 10(4) parameters (roughly two orders of magnitude more than previously feasible) and describe how the method gives insights into the functional interaction of groups of channels.

Our understanding of the input-output function of single cells has been substantially advanced by biophysically accurate multi-compartmental models. The large number of parameters needing hand tuning in these models has, however, somewhat hampered their applicability and interpretability. Here we propose a simple and well-founded method for automatic estimation of many of these key parameters: 1) the spatial distribution of channel densities on the cell’s membrane; 2) the spatiotemporal pattern of synaptic input; 3) the channels’ reversal potentials; 4) the intercompartmental conductances; and 5) the noise level in each compartment. We assume experimental access to: a) the spatiotemporal voltage signal in the dendrite (or some contiguous subpart thereof, e.g. via voltage sensitive imaging techniques), b) an approximate kinetic description of the channels and synapses present in each compartment, and c) the morphology of the part of the neuron under investigation. The key observation is that, given data a)-c), all of the parameters 1)-4) may be simultaneously inferred by a version of constrained linear regression; this regression, in turn, is efficiently solved using standard algorithms, without any “local minima” problems despite the large number of parameters and complex dynamics. The noise level 5) may also be estimated by standard techniques. We demonstrate the method’s accuracy on several model datasets, and describe techniques for quantifying the uncertainty in our estimates.