Neurons in primary visual cortex (V1) are frequently classified based on their response linearity: the extent to which their visual responses to drifting gratings resemble a linear replica of the stimulus. This classification is supported by the finding that response linearity is bimodally distributed across neurons in area V1 of anesthetized animals. However, recent studies suggest that such bimodal distribution may not reflect two neuronal types but a nonlinear relationship between the membrane potential and the spike output. A main limitation of these previous studies is that they measured response linearity in anesthetized animals, where the distance between the neuronal membrane potential and the spike threshold is artificially increased by anesthesia. Here, we measured V1 response linearity in the awake brain and its correlation with the neuronal spontaneous firing rate, which is related to the distance between membrane potential and threshold. Our results demonstrate that response linearity is bimodally distributed in awake V1 but that it is poorly correlated with spontaneous firing rate. In contrast, the spontaneous firing rate is best correlated to the response selectivity and response latency to stimuli.

*Response linearity (F1/F0):*The response linearity was calculated from the visual responses to drifting gratings presented at different spatial frequencies. The visual response was quantified from peristimulus time histograms (PSTHs) obtained with 10-msec time bins over a time period of 1.8 sec (we discarded the initial 0.2 sec to eliminate the response to the stimulus onset). We used Fourier analysis to measure the amplitude of the first harmonic (F1) and mean firing rate (F0) from PSTHs obtained for each spatial frequency tested (both F1 and F0 have units of spikes/second). This procedure is equivalent to fitting a sinusoid to the PSTH (with the same temporal frequency of the drifting grating) to obtain F1 and then averaging the firing rate across the entire drifting grating stimulation to obtain F0.

*p*= 0.5009, Hartigan test). However, a significant bimodal distribution was obtained if the spontaneous firing rate was subtracted directly from the PSTH (

*p*= 0.039, Hartigan test; Figure 2d). That is, the PSTH was rectified by a constant value equal to the mean spontaneous activity, and then we calculated F1 and F0 from the rectified PSTH. Therefore, in this paper, F0b is the mean firing rate under visual stimulation and F0 is the mean firing rate minus the spontaneous activity obtained by rectifying the PSTH. In neurons with PSTHs resembling a sinusoid, like neurons in Figures 1b and 1c, F1 was larger than F0b because the amplitude of the sinusoid was larger than the mean firing rate. In neurons with PSTHs resembling a step function, like the neuron in Figure 1d, F0b > F1 because the amplitude of the sinusoid fitted to the PSTH was small in comparison to the mean firing rate.

*r*

^{2}) were calculated. For distributions fitted with two Gaussian functions, we divided the F1/F0 distribution into two groups (first group with F1/F0 < 1 and second group with F1/F0 > 1) and then we calculated the average

*r*

^{2}value. Significant differences between single- and double-Gaussian fits were calculated by performing a bootstrap analysis to obtain 20

*r*

^{2}values per fit and then comparing the

*r*

^{2}values from single and double Gaussian fits with a Mann–Whitney test. The distribution of F1/F0 ratios was also tested for bimodality with the Hartigan test (Hartigan & Hartigan, 1985).

*Spatial frequency*: The spatial frequency tuning curves were fitted with Gaussian functions, and these functions were used to extract the spatial frequency peak, defined as the spatial frequency that elicited maximum response. For each cell, we also selected the half of the spatial frequency tuning curve that had the overall strongest response and defined spatial frequency half-bandwidth as the half width at half height of the tuning curve.

*R*∣, where

*R*is:

*r*

_{k}is the mean spike rate in response to a drifting grating and

*θ*

_{k}the angle of the drifting grating expressed in radians. The values of circular variance range from 0 to 1. Cells with sharp orientation tuning have values of circular variance close to zero and those with broad orientation tuning have values close to one. The direction selectivity (DS) was measured at the preferred orientation of the cell as DS = 1 −

*R*

_{NPD}/

*R*

_{PD}, where

*R*

_{PD}and

*R*

_{NPD}are the neuronal responses to gratings moving in preferred and nonpreferred direction. A neuron was classified as directional selective if the direction selectivity exceeded 0.5.

*S*), as:

*S*= 1 − ((CV + (1 − DS) + SFs) / 3), where CV is circular variance (CV), DS is direction selectivity, and SFs is spatial frequency selectivity. The spatial frequency selectivity was calculated as (SFw / maximum SFw in the total cell population), where SFw is the spatial frequency half-bandwidth (in octaves) obtained from the spatial frequency tuning. The values of response selectivity also ranged from 0 to 1. Cells that were very selective for orientation tuning (sharp tuning), direction (stronger response to preferred direction than the opposite), and spatial frequency tuning (sharp tuning) had values close to 1 and those that were not selective had values closer to 0.

*V*

_{m}is the membrane potential,

*V*

_{rest}is the resting membrane potential (taken from response from a blank stimulus),

*k*is the gain factor, and

*p*is the exponent. The subscript “+” indicates rectification (i.e., that values below zero are set to zero; Priebe et al., 2004). We used the values of firing rate to obtain F1 and F0b values and plot the expected relationship between F1 and F1/F0b (see Figure 3a). Note that the equation from Priebe et al. (2004) is similar to the equation from Mechler and Ringach (2002) to model the F1/F0b distribution. We chose the equation from Priebe et al. because it uses the resting potential as a parameter.

*R*

_{ON}and

*R*

_{OFF}) in each receptive field map at time windows where the visual response was significantly different from noise (>3 times the noise standard deviation,

*n*= 108). Neurons that responded poorly to sparse noise were not included in this analysis (

*n*= 16). We calculated the spatial relationship between

*R*

_{ON}and

*R*

_{OFF}by performing five different measurements, as in (Mata & Ringach, 2005): discreteness, correlation coefficient, normalized distance, overlap index, and relative phase. The

*discreteness*was computed as Σ∣

*R*

_{ON}−

*R*

_{OFF}∣ / (Σ∣

*R*

_{ON}∣ + Σ∣

*R*

_{OFF}∣), and it is ≈0 for complex cells and ≈1 for simple cells (Dean & Tolhurst, 1983). The

*correlation coefficient*was computed as the correlation between

*R*

_{ON}and

*R*

_{OFF}, which is ≈+1 for complex cells and ≈−1 for simple cells. The

*normalized distance*was computed as the distance between the center of

*R*

_{ON}and

*R*

_{OFF}divided by the average of the square roots of the

*R*

_{ON}and

*R*

_{OFF}areas, which is ≈0 for complex cells and »0 for simple cells. The

*overlap index*was computed as ((

*σ*

_{ON}+

*σ*

_{OFF}) − ∣

*m*

_{ON}−

*m*

_{OFF}∣) / ((

*σ*

_{ON}+

*σ*

_{OFF}) + ∣

*m*

_{ON}−

*m*

_{OFF}∣), where

*σ*

_{ON}

*σ*

_{OFF}and

*m*

_{ON}

*m*

_{OFF}are the standard deviations, and means of Gaussian functions fitted to

*P*

_{ON}and

*P*

_{OFF}and

*P*

_{ON}and

*P*

_{OFF}are 1D receptive field slices performed at the centers of

*R*

_{ON}and

*R*

_{OFF}. The overlap index is ≈1 for complex cells and <1 for simple cells (Schiller, Finlay, & Volman, 1976a). The

*relative phase*was computed as ΔΦ = ∣Φ

_{ON}− Φ

_{OFF}∣, where Φ

_{ON}Φ

_{OFF}are the phases of Gabor functions fitted to

*P*

_{ON}and

*P*

_{OFF}, which is ≈0 for complex cells and ≈

*π*for simple cells (Conway & Livingstone, 2003). Measurements of overlap index and relative phase were only performed in neurons that responded robustly to both light and dark stimuli (

*n*= 63).

*Macaca mulatta*) and measured their response linearity, spontaneous firing rate, and receptive field properties. To be consistent with terminology used in previous studies (De Valois et al., 1982; Movshon et al., 1978a, 1978b; Skottun et al., 1991), we call F0 the mean rate under visual stimulation minus the spontaneous activity and we call F0b the mean rate under visual stimulation without any subtraction (the original F0 term plus “baseline”; for details, see Methods). Figure 1 shows representative examples of four cells. The cell in Figure 1a generated linear responses to drifting gratings (F1 > F0b) for all spatial frequencies tested (Figure 1a, left) and had high spontaneous activity (29 spikes/sec; Figure 1a, middle) and a receptive field with a small, round, off-subregion and a weaker, round on-subregion (Figure 1a, right). The cell in Figure 1b was also linear across all spatial frequencies tested (Figure 1b, left) and had low spontaneous activity (3 spikes/sec; Figure 1b, middle), and the receptive field had separate and elongated on- and off-subregions (Figure 1b, right). The cell in Figure 1c was linear when tested at low spatial frequencies but not at high spatial frequencies (Figure 1c, left); the spontaneous activity was low (2 spikes/sec; Figure 1c, middle), it responded only to dark spots and the response was sustained over several tens of milliseconds (Figure 1c, right). Cells that generate linear responses at some spatial frequencies but not others were originally described in the anesthetized primate by De Valois et al. (1982, see below), and a more recent paper (Priebe et al., 2004) in the cat illustrates a cell with remarkably similar tuning to the one illustrated here (Figure 5c in Priebe et al., 2004). Finally, Figure 1d shows a cell that generated nonlinear responses across all spatial frequencies tested (Figure 1d, left) and had low spontaneous firing rate (7 spikes/sec; Figure 1d, middle) and a receptive field that generated on–off sustained responses (Figure 1d, right). If the four Hubel and Wiesel criteria were applied, the cells illustrated in Figures 1a and 1b would be classified as simple and the cells in Figures 1c and 1d as complex cells.

Reference | Used F1/F0 ratio to classify cortical cells | Animal | N | Showed distribution of F1/F0 ratios | Showed statistically significant bimodality |
---|---|---|---|---|---|

Schiller et al. (1976b) | Yes | M | 86 | Yes | Not tested |

Movshon et al. (1978a) | Yes | C | 164 | No | Not tested |

Dean (1981) | Yes | C | 43 | No | Not tested |

De Valois et al. (1982) | Yes | M | 343 | Yes | Not tested |

Dean and Tolhurst (1983) | Yes | C | 563 | Yes | Not tested |

Skottun, Bradley, Sclar, Ohzawa, and Freeman (1987) | Yes | C | 48 | No | Not tested |

Lennie, Krauskopf, and Sclar (1990) | Yes | M | 171 | No | Not tested |

Skottun et al. (1991) | Yes | C | 1061* | Yes | Not tested |

Casanova, Nordmann, Ohzawa, and Freeman (1992) | Yes | C | 176 | No | Not tested |

DeAngelis, Freeman, and Ohzawa (1994) | Yes | C | 82 | No | Not tested |

Chino, Smith, Yoshida, Cheng, and Hamamoto (1994) | Yes | C | 89 | No | Not tested |

Hawken, Shapley, and Grosof (1996) | Yes | M | 75 | No | Not tested |

Hawken et al. (1996); Ohzawa, DeAngelis, and Freeman (1996, 1997) | Yes | C | 109 | No | Not tested |

Smith, Chino, Ni, Ridder, and Crawford (1997) | Yes | M | 239 | No | Not tested |

Cumming, Thomas, Parker, and Hawken (1999) | Yes | M | 336 | Yes | Not tested |

Sceniak, Ringach, Hawken, and Shapley (1999) | Yes | M | 85 | No | Not tested |

Ringach, Shapley, et al. (2002) | Yes | M | 308 | Yes | Yes |

Kagan et al. (2002) | Yes | M | 114 | Yes | No |

Priebe et al. (2004) | Yes | C | 102 | Yes | Yes |

Ibbotson, Price, and Crowder (2005) | Yes | W | 123 | Yes | Yes |

Mata and Ringach (2005) | Yes | M | 98 | Yes | No |

*r*

^{2}for two-Gaussians = 0.45;

*r*

^{2}for one Gaussian = 0.23), and was not significantly bimodal (

*p*= 0.93, Hartigan test). The second approach was to make the F1/F0b measurements at the spatial frequency that generated the maximum F1 ( Figure 2b). Again, the difference between one‐ and two‐Gaussian fits was not significant with two different Gaussians than a single Gaussian function, but the difference was not significant (

*r*

^{2}= 0.6 versus

*r*

^{2}= 0.66, difference = 0.06,

*p*= 0.08, Bootstrap and Mann–Whitney test). A Hartigan test for bimodality did not reach significance either (

*p*= 0.21). The third method was the one original described by De Valois et al. (1982). De Valois et al. noticed the existence of cells like the one illustrated in Figure 1c and was aware of the problem that these cells caused when measuring response linearity. To address this problem, De Valois et al. proposed to select the three spatial frequencies that generate the strongest combined F1 and F0 responses and then calculate the F1/F0 ratios as the average F1/average F0 obtained from the three selected spatial frequencies. The distribution obtained with the De Valois et al. method was better fitted with two different Gaussians than a single Gaussian function (

*r*

^{2}= 0.79 versus

*r*

^{2}= 0.47, difference = 0.32,

*p*< 0.0001, Bootstrap and Mann–Whitney test) and also reached significance with a Hartigan test (

*p*= 0.017). The fourth method was to repeat the De Valois et al. method, including the subtraction of the spontaneous activity. The average spontaneous activity in our sample was 12.87 spikes/sec with a median of 6.97 spikes/sec. The subtraction of the spontaneous activity slightly shifted the distribution toward the linear side without altering its general shape. This distribution was also better fitted with two Gaussians than a single Gaussian (

*r*

^{2}= 0.72 versus

*r*

^{2}= 0.46, difference = 0.26;

*p*< 0.0001, Bootstrap and Mann–Whitney test) and also reached significance with a Hartigan test (

*p*= 0.039). As shown in this figure (see also Figure 3), the subtraction of spontaneous activity had a minor effect on the distribution of F1/F0; therefore, in most of the figures of this paper, we use F0b instead.

*r*= −0.98,

*p*< 0.0001) and an exponential function (

*r*

^{2}= 0.99,

*Y*= 16.1 + 103.9e

^{−1.6X}).

*r*= −0.5,

*p*< 0.0001) than that described by a single exponential function. The two main reasons for the weak correlation were the diversity of PSTH shapes and the wide range of firing rates, particularly for cells with F1/F0 < 1. For example, the two cells with F1/F0 < 1 illustrated in Figure 1 had mean firing rates of ∼200 spikes/sec (e.g., Figure 1d) and <50 spikes/sec ( Figure 1c). Moreover, there were some color-selective cells with F1/F0 < 1 that responded poorly to luminance gratings. The weak correlation between F0 and F1/F0 could result from a combination of multiple power laws with different exponents. The different exponents may reflect the diversity of nonlinear relations between membrane potential and spiking output across cells in visual cortex (Priebe et al., 2004).

*r*= −0.14,

*p*= 0.06; Figure 3d), as would be expected from the relatively similar spike thresholds and mean membrane potentials of linear and nonlinear cells measured in cat visual cortex (Priebe et al., 2004). Stronger correlations could be demonstrated between the spontaneous firing rate and other response properties. Figure 4 shows multiple correlations between spontaneous firing rate and several response properties including selectivity to orientation, spatial frequency, and direction of movement, measured individually or combined. It also shows correlations with contrast sensitivity, response amplitude (F1 or F0b), and receptive field structure. The receptive field structure was measured using five different methods that quantify the overlap/distance between on and off receptive field subregions, as in Mata and Ringach (2005).

*r*= 0.4,

*p*< 0.0001), the orientation tuning (

*r*= 0.36,

*p*< 0.0001), and the response latency of the cell (

*r*= −0.35,

*p*< 0.0001). The negative correlation between the spontaneous firing rate and the response latency is particularly interesting because it replicates, at the level of V1, a trend that is observed in the early visual pathway: a reduction in spontaneous activity as information progresses from retina to thalamus and from thalamus to visual cortex. The relation between spontaneous firing rate and response selectivity is also important because it provides support to models that associate high cortical amplification to a loss of response selectivity (Chance et al., 1999; Mata & Ringach, 2005; Priebe et al., 2004).

*r*= 0.36,

*p*< 0.0001) but it is clearly best described by a triangular space than by a straight line. The scatter plot in Figure 4b shows a triangular distribution so that the cells with the highest spontaneous activity (>30 Hz) had all poor orientation selectivity and cells with the sharpest orientation tuning (circular variance <0.3) had all very low spontaneous activity. This relation can still be demonstrated after subtracting the spontaneous firing rate in the calculation of circular variance (not shown,

*r*= 0.28,

*p*< 0.0001).

*r*= −0.41 awake,

*r*= −0.41 anesthetized), relative phase versus overlap index (

*r*= −0.74 awake,

*r*= −0.72 anesthetized), and relative phase versus normalized distance (

*r*= 0.40 awake,

*r*= 0.43 anesthetized). The most different correlations measured are the relative phase versus correlation coefficient (

*r*= −0.43 awake,

*r*= −0.79 anesthetized), the overlap index versus the correlation coefficient (

*r*= 0.58 awake,

*r*= 0.93 anesthetized), and the relative phase versus the discreteness (

*r*= 0.45 awake,

*r*= 0.73 anesthetized).

*r*= −0.35,

*p*< 0.0001; SF bandwidth versus circular variance,

*r*= 0.4,

*p*< 0.0001). Interestingly, the contrast that generated half-maximum response was not correlated to any response property except response linearity. However, the correlation with response linearity was quite strong (

*r*= 0.46,

*p*< 0.0001), which reveals a tendency for neurons that generate linear responses to be poorly sensitive to contrast.