Discussion | Furthermore, we derived an STDP-like online learning rule by considering an approximation of Bayesian ICA with sequence sampling. |
Introduction | We further found a possible link between stochastic membrane dynamics and sampling process, which is necessary for neural approximation of learning algorithm of Bayesian independent component analysis ( ICA ). |
Neural Bayesian ICA and blind source separation | Neural Bayesian ICA and blind source separation |
Neural Bayesian ICA and blind source separation | To this end, we compared the performance of the model with that of the Bayesian ICA algorithm, in which independence of external sources is treated as a prior [46,47]. |
Neural mechanism of blind source separation | An effective solution for this problem is ICA [76—78], and the neural implementation of the algorithm has been studied by several authors [14,18,79,80]. |
STDP and Bayesian ICA | STDP and Bayesian ICA |
STDP and Bayesian ICA | Our results indicated that STDP in a lateral inhibition circuit mimicked Bayesian ICA [46,47]. |
STDP and Bayesian ICA | By contrast, in the Bayesian ICA framework, the mixing matrix (corresponding to synaptic weight matrix) is treated as a probabilistic variable. |
Suboptimality of STDP | In the Bayesian ICA framework, blind source separation can be formulized as an optimization problem, but, in this case, the problem itself is ill-defined because optimality does not guarantee the true solution. |
pf = 1 — <1 — rsAofi [1 — am: ask/szy] ,qsk = 2; 3 M + 1/2>At12exp[—<k + mam/at]. | We approximated this Bayesian ICA algorithm by a sequential sampling source activity instead of calculating the integral over all possible combinations in the estimation of the log-pos-terior of the response probability matriX Q. |
pf = 1 — <1 — rsAofi [1 — am: ask/szy] ,qsk = 2; 3 M + 1/2>At12exp[—<k + mam/at]. | We further studied the response of the models for the same inputs and 1 found that the logarithm of the average membrane potential ufi = W Z well approxi-,Ll jEQP‘ mates the log-posterior estimated in Bayesian ICA , even in the absence of a stimulus (Fig 7E). |
Results | A third algorithm, ICA , does not require that the constituent components be orthogonal to one another—and instead identifies components by maximizing their independence in a statistical sense. |
Results | ICA has proven useful for deconstructing mixed signals (e.g., audio) into their constituent parts. |
Results | Although our goal in developing PEACS was to apply it in settings where neither the state expression vectors nor cell-state proportions are known, to assess the effectiveness of the algorithms described above (SVD, NMF, ICA ) we needed an idealized context in which cell-state proportions could be experimentally defined. |
Supporting Information | SVD, NMF, and ICA results. |
Supporting Information | The results of first and second dimensions of (D) SVD, (E) NMF, and (F) ICA deconvolution were plotted 82 Fig. |
Extending the protocol: Adding multi-step voltage clamp data | Our 6s long voltage clamp protocol effectively isolates 1K1, ICaL , and 1KS as shown by the disproportionally large contributions of these currents in step -120 mV, +20 mV, and +40 and -30 mV, respectively (Fig 3 B—3F). |
GA optimization using a single action potential | Nine model parameters, describing maximal conductances of ionic currents [the sodium current (INa), the L-type calcium current (ICaL), the T-type calcium current ( ICaT ), the inwardly rectifying potassium (1K1), the rapid and slow delayed rectifier potassium currents (1Kr and IKS), the plateau potassium current (IKp), and the sarcolemmal calcium pump current (IpCa)] and the maximal flux of the sarcoplasmic reticulum Ca2+-ATPase (ISERCA) were estimated using a GA technique. |
Limitations and potential improvements | Our multi-step voltage-clamp protocol effectively isolates IKS, ICaL , and 1K1. |
Limitations and potential improvements | As expected, local sensitivity analysis on simulated calcium traces demonstrates that they are most sensitive to changes in ICaL , IpCa, and ISERCA (SS Fig), which leads to the speculation that the estimation of these parameters could improve. |
Parameter estimation shows changes compared to FR model and variability among individual cells | In contrast, for all four cells, maximal conductance of IKr and 1K1 are increased around 2-fold compared to the FR model, while ICaL is slightly increased. |
Stochastic stimulation protocol improves model fit and predictability over single action potential protocol | Compared to the single action potential, the stochastic stimulation leads to a modest overall improvement of the parameter estimation, but it did notably better in determining the maximal conductances of IKr, ICaL , and 1K3 (Fig 2C). |
Stochastic stimulation protocol improves model fit and predictability over single action potential protocol | However, as shown in Fig 2C, a few parameters remain incorrectly estimated (maximal conductances of ICaL and 1K5), and some are estimated with a large spread (maximal conductance values of IKP, IpCa, ICaT , and IKr). |
Supporting Information | Blue symbols indicate parameters with a statistically significant effect on the model output While the red symbols indicate the parameters with a nonsignificant effect on the model output ( ICaT , 11(1), and IpCa). |
The combined stochastic current and multi-step voltage clamp protocol improves parameter estimation | The estimation of the ICaL conductance is very close to 1, but is slightly overestimated in all runs. |
The combined stochastic current and multi-step voltage clamp protocol improves parameter estimation | However, a few conductances were estimated poorly (in particular ISERCA and ICaT ) and models optimized based on voltage clamp data alone were, not surprisingly, inferior at predicting complex action potential dynamics during stochastic pacing (Fig 4C). |
AMSN | At low cortical rates, | Dlefl| is larger than | DZeficl due to the scaled cortical excitation for D1 ( ICl > ICZ) and hence, the D1 type neurons dominate. |
AMSN | In all subsequent analyses, we used the scenario II, keeping ICl > [CZ and maintaining identical input rate XCTX to both D1 and D2 MSNs. |
Effect of Dopamine on the DTT | Therefore, in our model we simulated the effect of dopamine depletion by decreasing ICI and increasing ICZ, whereas higher than normal dopamine was simulated by increasing I01 and decreasing I02. |
Effect of cortical spiking activity correlations on the DTT | For weak input correlations, as D1 MSNs form stronger synapses with cortical afferents, ( ICl > ICZ; scenario II), D1 MSNs spike at higher rate than D2 MSNs (Fig 5B). |