The activity of neurons is influenced by random fluctuations and can be strongly modulated by firing rate adaptation, particularly in sensory systems. Still, there is ongoing debate about the characteristics of neuronal noise and the mechanisms of adaptation, and even less is known about how exactly they affect perception. Noise and adaptation are critical in binocular rivalry, a visual phenomenon where two images compete for perceptual dominance. Here, we investigated the effects of different noise processes and adaptation mechanisms on visual perception by simulating a model of binocular rivalry with Gaussian white noise, Ornstein-Uhlenbeck noise, and pink noise, in variants with divisive adaptation, subtractive adaptation, and without adaptation. By simulating the nine models in parameter space, we find that white noise only produces rivalry when paired with subtractive adaptation and that subtractive adaptation reduces the influence of noise intensity on rivalry strength and introduces convergence of the mean percept duration, an important metric of binocular rivalry, across all noise processes. In sum, our results show that white noise is an insufficient description of background activity in the brain and that subtractive adaptation is a stronger and more general switching mechanism in binocular rivalry than divisive adaptation, with important noise-filtering properties.

*f*and 1/

*f*

^{2}(Baranauskas et al., 2012; Dehghani, Bédard, Cash, Halgren, & Destexhe, 2010; Zarahn, Aguirre, & D'Esposito, 1997). The statistics of spontaneous activity are at the heart of the debate on whether information is encoded by the precise timing of spikes or the average firing activity of neurons. Poisson statistics are associated with a rate code, whereas non-Poisson statistics, with a temporal correlation between successive spikes, are associated with a temporal code. Neurons may operate in both regimes (Biederlack et al., 2006; Rudolph & Destexhe, 2003). Furthermore, temporally uncorrelated spike trains can give rise to temporally correlated activity measures through the nonlinear filtering properties of both dendrites (Brunel, Chance, Fourcaud, & Abbott, 2001; Lindén, Pettersen, & Einevoll, 2010) and extracellular space (Bédard, Kröger, & Destexhe, 2006). As a result, computational models have included neuronal noise as a synaptic current of zero-mean Gaussian white noise (an approximation to a Poisson process), pink or Brownian noise (power spectra weighted as 1/

*f*and 1/

*f*

^{2}, respectively), and Ornstein-Uhlenbeck noise (a low-pass filtered version of white noise, which is related to Brownian noise).

*I*is:

*F*are the firing rates of the

_{b}*N*presynaptic input neurons, with

_{u}*w*the weights of these inputs and τ

_{b}_{s}the time constant of the synapse-to-soma process. The architecture of the network determines the input sum. Monocular neurons receive sensory input which is added to the right-hand side (RHS) of the equation as input contrast,

*c*.

*F*is thus described by:

*A*(

*I*) an activation function, usually nonlinear, that describes the input-output function of the neuron and τ

_{r}the time constant of this process, determining how closely

*F*can follow fluctuations in

*I*.

*s*is a semi-saturation constant, which can be different for each type of neuron, and the weighted sum over

*k*is the sum of the synaptic currents of the neurons in the normalization pool.

_{s}and the firing rate time constant τ

_{r}are significantly different, the system formed by Equations 1 and 2 can be replaced by only one differential equation (Dayan & Abbott, 2001). For instance, if τ

_{r}≪ τ

_{s}, the firing rate

*F*follows

*I*almost instantaneously and

*F*(

*t*) =

*A*(

*I*(

*t*)), leaving only the differential equation for the synaptic current

*I*. If τ

_{r}≫ τ

_{s}, the synaptic current reaches equilibrium faster than the firing rate and one can make the replacement \(I = \mathop \sum \nolimits_b^{{N_u}} {w_b}{F_b}\), working only with the equation for the firing rate

*F*. This last simplification is common and done in models of binocular rivalry by Shpiro et al. (2009), Li et al. (2017) and Wilson (2003), who use time constants τ

_{r}of 10 ms or 20 ms, thus assuming τ

_{s}≪ 10 ms. In contrast, Said and Heeger (2013) use both equations with equal time constants τ

_{s}= τ

_{r}= 50 ms. This is also our approach.

*t*) is defined by a differential equation of a low-pass filter of a white noise process, ξ(

*t*):

*t*). Ornstein-Uhlenbeck noise (Uhlenbeck & Ornstein, 1930) is thus exponentially-filtered white noise (Bibbona, Panfilo, & Tavella, 2008) and models the low-pass filtering effects of synapses (Shpiro et al., 2009). However, instead of the synaptic time constant τ

_{s}above, a much larger value for τ is usually chosen: τ = 800 ms in Said and Heeger (2013) and τ = 100 ms in Shpiro et al. (2009) and Li et al. (2017). Integrating Equation 4 along with the system equations significantly slows down the simulation. Hence, an alternative way of computing the Ornstein-Uhlenbeck process is by starting with Gaussian white noise of standard deviation σ, computed for all time steps, and convolving in time with a Gaussian kernel with standard deviation τ, as done by Said and Heeger (2013). Although an exponential kernel would be more consistent with Equation 1, a comparison of simulations with each type of kernel showed no significant differences.

*f*and phase sampled from a uniform distribution, φ ∈ [0, 2π). To obtain the specified standard deviation in the time domain, the resulting process is multiplied by a correcting factor.

*f*= 1/2πτ, with τ the noise correlation time (Bibbona, Panfilo, & Tavella, 2008). For larger frequencies, it decays as 1/

_{c}*f*

^{2}, which is the spectrum of Brownian noise.

*H*obey

_{H}is the adaptation time constant, and

*F*is the neuron's firing rate. The different formulations used are summarized in Table 1.

*w*= 2 and τ

_{H}_{H}= 2000 ms. These are the same values used by Li et al. (2017). Shpiro et al. (2009) also use τ

_{H}= 2000 ms, whereas Wilson (2003) uses τ

_{H}= 900 ms. Using the same values for subtractive and divisive adaptation allows for a fair comparison of the two mechanisms, which both represent a physiological hyperpolarization current.

*c*and correlation time τ (in the case of Ornstein-Uhlenbeck noise), the dynamics of binocular rivalry were simulated for 2500 pairs of parameters in each diagram (Table 2), with metrics of rivalry calculated for each simulation of 60 seconds and averaged over three runs. The corresponding standard deviation over the three runs was calculated. The duration of each simulation and the number of repetitions were chosen to obtain enough variability (an adequate number of perceptual alternations and different seeds of the stochastic process, respectively) without significantly slowing the simulations since 7500 simulations were performed to obtain each diagram. The list of parameter values kept constant and equal to the original values used by Said and Heeger (2013) is shown in Table 3.

*c*), the intensity of the noise process (σ), and, for Ornstein-Uhlenbeck noise, the correlation time (τ). For each simulation we calculated the relative dominance time (RDT), a measure of rivalry strength, the mean dominant percept duration, the coefficient of variation of percept durations, and the mean mixed percept duration (see Methods). These quantities were averaged over three runs of 60 seconds for each pair of parameters, and the respective standard deviation was calculated.

*p*< 0.001 for both adaptation formulations), as is physiologically expected. Subtractive adaptation leads to a stronger reduction (

*p*< 0.001) and results in similar values of this metric for all noise processes.

*p*< 0.001), but not divisive (

*p*> 0.5), adaptation is added, whereas for pink noise adaptation reduces mixed perception (

*p*< 0.001 for both adaptation variants). The coefficient of variation of percept durations increases with divisive and subtractive adaptation for all noise processes (

*p*< 0.05 for all comparisons).

*f*

^{2}spectrum) for large frequencies (see Methods), the similarity between the two correlated processes suggests that in this model temporal correlations of 1/

*f*and 1/

*f*

^{2}are functionally equivalent. Nonetheless, our work provides some constraints: besides virtually excluding white noise, it establishes a minimum temporal correlation constant for Ornstein-Uhlenbeck noise, which should inform future computational studies on neural activity.

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