Exploring excitation energy transfer (EET) in light-harvesting complexes (LHCs) is essential for understanding the natural processes and design of highly-efficient photovoltaic devices. LHCs are open systems, where quantum effects may play a crucial role for almost perfect utilization of solar energy. Simulation of energy transfer with inclusion of quantum effects can be done within the framework of dissipative quantum dynamics (QD), which are computationally expensive. Thus, artificial intelligence (AI) offers itself as a tool for reducing the computational cost. Here we suggest AI-QD approach using AI to directly predict QD as a function of time and other parameters such as temperature, reorganization energy, etc., completely circumventing the need of recursive step-wise dynamics propagation in contrast to the traditional QD and alternative, recursive AI-based QD approaches. Our trajectory-learning AI-QD approach is able to predict the correct asymptotic behavior of QD at infinite time. We demonstrate AI-QD on seven-sites Fenna–Matthews–Olson (FMO) complex. Simulations of energy transfer in light-harvesting complexes are computationally very demanding. Here the authors apply an artificial intelligence quantum dissipative algorithm to study the excited state energy transfer dynamics in a light-harvesting complex. The transfer of solar energy from antenna to RC, which is also known as excitation energy transfer (EET), in the form of excitons is considered to be highly efficient with close to unit efficiency2. Understanding this high efficiency of the natural harvesting systems is very important because this understanding can be potentially applied in designing very efficient organic solar cells and storage devices3. Experiments showed that the long-lasting coherence in the efficient natural light-harvesting complexes (LHCs) is preserved by the surrounding protein environments (scaffold), and this coherence may be responsible for this high efficiency5. The most well-investigated LHC is Fenna–Matthews–Olsen (FMO) complex, which is found in green sulfur bacteria6. The small size and simplicity of the FMO complex also make it a testbed of simulation approaches. The FMO complex is a trimer of identical subunits, where each subunit consists of bacteriochlorophyll (BChl) molecules (system) attached to their protein environments7.From the birth of life, solar energy has been the driving force of life. Via the mechanism of photosynthesis, living organisms capture sunlight with the highly sophisticated pigments in their antenna systems and transfer sunlight energy to the reaction center (RC) in the form of electron-hole pairs (excitons), where it is stored as biochemical energy13. Taking FMO as an example, it is easy to see that the system (BChl molecules) is not isolated from the environment (the protein) and thus, the correct simulation of FMO should treat it as an open system rather than isolated one. In addition, many experiments suggest15, that quantum effects, particularly coherence, might play an important role in the light-harvesting processes and may even be responsible for achieving the high-end efficiency. Temporal and spatial simulation of EET with the inclusion of quantum effects can be done within many frameworks such as classical mapping-based approaches18, perturbative methods21, and dissipative quantum dynamics (QD)27 adopted here.Enormous amount of research work has been done on light-harvesting processes28 and its many improvements and extensions31, the quasiadiabatic propagator path integral (QuAPI)32 and its variant iterative QuAPI (iQuAPI)27, the trajectory-based stochastic equation of motion (SEOM) approach39, the multi-layer multi-configuration time-dependent Hartree (ML-MCTDH)26 and the local thermalising Lindblad master equation (LTLME)22. The development of various quantum dissipative dynamics methods stirs from the fact that each of these methods has some limitations and hence there is no single universal method that works in all cases. For instance, HEOM is numerically exact but comes with a very high computational cost at low temperatures, the SEOM has no explicit dependence on the temperature but has very bad convergence at long-time propagation, in the QuAPI approach all correlation effects are included over a finite time and correlation effects beyond this time are neglected. Most importantly, all these traditional QD approaches require step-wise propagation of trajectories and the next step depends on the previous steps, thus, QD simulation is an iterative, recursive process. Both calculations at each time step and recursive nature of QD makes it rather computationally expensive.QD simulations can be performed using the hierarchical equations of motion (HEOM)46, inspired by advances in application of AI employing machine learning (ML) algorithms in computational chemistry and chemical physics48. AI was also applied to investigate EET in a dimer system44 and the FMO complex40. Saving of computational cost by AI in above studies is impressive, however, one of the studies40 only focused on predicting energy transfer times and transfer efficiencies rather than temporal and spatial evolution, while other related studies46 adopted basically the same recursive nature of QD trajectory propagation.Alleviating the computational cost of QD became a target of a series of studies applying artificial intelligence (AI)The recursive nature of the previous AI-based QD makes it prone to error accumulation. In recursive simulations, previously predicted values are used as an input to predict the next value. Thus, the prediction error at each time-step will accumulate, which results in deterioration of accuracy. In addition, the recursive nature of predictions does not allow us to make a prediction for any arbitrary time without predicting values before that. Finally, a short-time trajectory is needed as the seed to be generated with traditional approaches such as HEOM and then provided as an input to AI model to make prediction for the next time step and ultimately propagate the long-time dynamics. Thus, even when having AI model, we still need to spend valuable computational time to generate the short-time trajectory with the traditional approaches.Here, we suggest an AI-QD approach to directly predict QD with AI as a function of time and other parameters such as temperature, reorganization energy, etc., completely circumventing the need of recursive step-wise dynamics propagation in contrast to the traditional QD and alternative, recursive AI-based QD approaches. Our AI-QD approach is able to predict QD at infinite time with correct asymptotic behavior and can be viewed as trajectory learning, which does not need any short-time trajectory as an input, eradicates the need of traditional approaches to generate the seed, and alleviates the problem of error accumulation. We demonstrate the applicability of AI-QD on seven-sites Fenna–Matthews–Olson (FMO) complex and show how AI-QD can be used for massive, infinite-time QD simulations and provide insights into the desired range of parameters and more efficient paths followed by the transfer of excitation energy.49 to study EET dynamics in the FMO complex:Hs, Henv, Hs-env, and Hreorg denote system (BChl molecules) Hamiltonian, Hamiltonian of protein-environment, system-environment interaction Hamiltonian and the reorganization term, respectively. In Eq. (n is the number of sites (BChl molecules), ϵi is the energy of the ith site and Jij is the inter-site coupling between sites i and j. Pk,i,  Qk,i, and ωk,i are, respectively, momentum, coordinate, and frequency of environment mode k associated with site i. In Hs-env, each site is connected to its own environment. The ck,i is the strength of coupling between site i and mode k of its environment. The reorganization term Hreorg can be seen as a counter term that emerges from the interaction of the sites with the environment50. It is added to stop further renormalization of the site energy ϵi by the environment. In the reorganization term Hreorg, λi is the reorganization energy corresponding to site i51,Ji(ω) is spectral density of the environment corresponding to site i. As shown by Nalbach and Thorwart52, the effects of the discrete molecular modes on the population dynamics are largely irrelevant. As a result, it is acceptable to use continuous environment spectral density such as Drude–Lorentz spectral densityγ and λ denote the characteristic frequency (bath relaxation rate) and the reorganization energy, respectively.We employ the Frenkel exciton Hamiltonianρ is the density matrix. Because of the many-body effects, direct propagation of Eq. , where we adopt Adolphs and Renger’s Hamiltonian for seven sites per subunit54 (see “Methods”). The LTLME is a coherent and complete positive trace-preserving approach, but may not be as accurate as HEOM or SEOM approaches because of approximations used in LTLME derivation55, but here it is not the concern of our proof-of-concept paper.We use the local thermalising Lindblad master equation (LTLME)λ, γ, and T. In addition, time also becomes a part of the input of our AI-QD model. In order to treat infinite time, instead of time, we introduce time-function t → ∞ becomes f(t) = 1. Such normalization, however, can effectively only discern data within rather short time-region, thus, instead of a single time-function, we introduce the set of redundant time-functions ρnn(t) and coherence  terms ρnq, n≠q  .Our training trajectories generated with the reference LTLME-QD approach are chosen by farthest-point sampling from the three-dimensional space of the following parameters: reorganization energy tM we should run reference LTLME-QD trajectories. Based on the prior knowledge that populations plateau in asymptotic limit, for each trajectory we choose a different time-length tM using a vanishing gradient scheme, where tM is chosen such that the gradient of population G is close to zero (see “Methods”). Using the vanishing gradient scheme to find different tM for each trajectory allows us to sample more data from the training trajectories, which are hard-to-learn, while avoiding redundant sampling from trajectories, which are easy-to-learn. This also removes arbitrariness in choosing fixed tM parameter as was done in previous studies using the recursive AI-QD scheme46.We should also decide up to what time-length 6, we thus present results for both cases. For predictions, we just provide the parameters of the test trajectories  as an input and predict the evolution of EET. Figure γ and small values of λ and T) which can be seen as a consequence of the vanishing gradient scheme which may favor these challenging cases due to a larger number of training points sampled from such trajectories. AI-QD approach can even extrapolate to a good degree as its error for the test trajectories propagated with parameters outside the training parameter space is of a similar order of magnitude to the test trajectories propagated with parameters inside the training parameter space (interpolation) as shown in Supplementary Fig. As an application of our approach, we predict EET dynamics in the FMO complex with seven sites per subunit for parameters of the test set trajectories none of which used in training. Site-1 (BChl molecule 1) and site-6 (BChl molecule 6) are most likely to get initially excited as they are close to the photosynthetic antenna complex called chlorosome57 that the transfer of excitation energy in the seven-sites FMO complex follows mainly two paths, i.e., site-1 → site-2 → site-3 ↔ site-4 and site-6 → site-5, site-7, site-4 → site-3, here the ↔ shows that the excitation energy equilibrates between site-3 and site-4 after site-3 is populated  in search of site-35. In Fig. t = 0.5 ps (500 fs) as a function of γ, λ, and T. From Fig. T = 300, the ETT to site-3 or, in other words, to RC complex gets slow as the characteristic frequency γ increases. In contrast, the ETT to site-3 increases with the increase in reorganization energy λ as shown in Fig. T as can be seen in Fig. It was shownγ, λ, T with the search space γ = 25, 30, 35, …, 245, λ = 10, 15, 20, …, 345 and T = 25, 30, 35, …, 345. We report the fastest EET of 0.761 to site-3 for path-2 with γ = 30, λ = 310, T = 25, while for path-1 for the same parameters EET is 0.626. From Figs. −1) is lower than the baseplate, which has been reported to be 12,500 cm−1 60. This allows a quick transfer of the excitation energy to site-1 from the baseplate. However, the energy of site-2  is higher than site-1 and also than site-3 , which on the one hand stops backward transfer from site-3, but on the other hand creates a local minimum on site-1. Despite the local minimum on site-1, the excitation energy is not trapped because of the quantum coherent wave-like motion between site-1 and site-2. Following path-2, the energy of site-6  is higher than the energy of baseplate. To stop backward transfer of excitation energy from site-6 to baseplate, site-6 should quickly transfer excitation energy to other sites such as site-5, site-7, and site-4. This quick transfer from site-6 to site-5, site-7, and site-4 is only possible by the strong coupling of site-6 to site-5 and site-7, which in return are strongly coupled to site-4.In order to find the optimum parameters for the fastest transfer of excitation energy, we have calculated population of site-3 at 0.5 ps for a massive set of ca. 0.57 million possible combinations (site-1 + site-6) of the In this work, we have presented a non-recursive (non-iterative) AI-QD approach for blazingly fast prediction of quantum dynamics, as predictions can be made for any time step up to asymptotic limit completely circumventing the need of recursive trajectory propagation. This can be used, as we demonstrated here, for massive quantum dynamics simulations, for example, in search for the best conditions required for efficient energy transfer in designed photovoltaic devices. Just to put things into perspective, our AI-QD approach can predict the entire 2.5 ps trajectory within ca. 2 min on a single core of Intel(R) Core(TM) i7-10700 CPUs @ 2.90 GHz, independent of the reference method used for generating training trajectories, while the same propagation with the traditional recursive approaches such as HEOM would take hours, and the cost would exponentially increase for low temperatures. The high cost of accurate approaches such as HEOM was also a reason why we used a much faster LTLME for this proof-of-concept study to extensively test our approach (propagation of an entire trajectory takes only 3 min with LTLME on a single CPU of the above computer architecture). It is worth emphasizing that AI-QD is embarrassingly parallel and the calculations can be further significantly sped up by using multiple CPUs or GPUs, because predictions with AI-QD for different time steps are independent of each other and different segments of trajectories can be distributed for independent calculations on many threads.42 has shown that by using Hamiltonian elements as input of an ML model, one can successfully describe scalar properties (energy transfer times and transfer efficiencies) for different Hamiltonians. However, open question remains how successful would be such an approach to learn dynamics and in addition, how to circumvent different dimensionalities of Hamiltonians of different complexes.We demonstrated the feasibility of AI-QD approach on an example of the FMO complex, but this approach is general enough to be used for any other complex after retraining. It remains to be seen how well the AI-QD approach can be extended to describe several LHCs at the same time—a topic of our ongoing research. One could use the LHC Hamiltonian elements as a representation of LHC complexes and an early encouraging study61. Here we adopt Adolphs and Renger’s Hamiltonian for seven sites per subunit54−1. Each site is coupled to its own environment characterized by the Drude–Lorentz spectral density given by Eq.  in the transfer of excitation energy in the FMO complex is negligible.In the seven-sites FMO complex (apo-FMO), where seven BChl molecules (seven sites) exist per subunit, the inter-subunit interaction is very small and each subunit can be considered relatively isolated22 (see Supplementary Methods) implemented in quantum_HEOM package63 with QuTip64 in the back-end with all the possible combinations of the following parameters: λ = {10, 40, 70, 100, 130, 160, 190, 220, 250, 280, 310} cm−1, γ = {25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300} cm−1 and T = {30, 50, 70, 90, 110, 130, 150, 170, 190, 210, 230, 250, 270, 290, 310} K. We consider that all these combinations of parameters make a part of a parameter space tM = 1 ns (106 fs). With the possibility of initial excitation on site-1 and site-6, we generate 1980 trajectories for each excitation case.Trajectories for the reduced density matrix have been generated with the local thermalising Lindblad master equation (LTLME)λ, γ, T (belonging to traj (1980 (site-1) + 1980 (site-6), all these trajectories correspond to their respective combination of parameters in parameter space 65 in the three-dimensional space of λ, γ, and T, we choose 1000 trajectories as our training space TS (500 (site-1) + 500 (site-6), ca. 25% of space tM using a vanishing gradient scheme. In this scheme, we take the gradient G of the population of each site  for 10 consecutive time-steps and if all of them remain less than the threshold value of Gth = 1 × 10−10, we choose our tM. We find tM for all seven sites and then choose the maximum value among them, thus we keep a single value of asymptotic limit (tM) for all seven-sites. By analyzing the gradients, we find the region of the trajectory, where the change in population of the site is very small. By knowing that, we keep the time-length of our trajectory tM up to that region, because beyond tM the change in population is very small, and ML is able to predict it. As the asymptotic limit for each trajectory is different, we have different values of tM for each trajectory. In our training, we have included t → ∞, corresponding to the asymptotic behavior at long-time. Using the strategy of different tM for each trajectory allows us to include more sampling in our training set from hard-to-learn trajectories, while avoiding redundant sampling from easy-to-learn trajectories. For training, sampling is done with different training time-steps Δttrain in different regions of the trajectory. We sample our training points from 0 ps–1 ps, 1 ps–1.5 ps, 1.5 ps–2.5 ps, 2.5 ps–5 ps, 5 ps–25 ps, 25 ps–50 ps, 50 ps–250 ps, 250 ps–tM regions with Δttrain = 5, 10, 25, 50, 100, 200, 500, 1000 fs, respectively. The number of training points depends on the number of trajectories Ntraj chosen for training, training time-step Δttrain and time-length of trajectories tM, which in turn depends on Gth.With all the possible combinations of the parameters 66. Though we have used the CNN model, other neural network architectures such as long short-term memory (LSTM) is also an option. LSTM is considered to be more suitable for extracting long-time temporal dependencies in contrast to convolutional neural networks (CNNs) which are more local. However, CNNs are easy to train and in many studies, they have outperformed LSTM for future forecasting68.We use convolutional neural network (CNN) architecture, because the importance of convolutional layers is much explored for image analysis, where these layers extract important features such as edges, textures, objects, and scenes. When it comes to time-series data, we are using convolutional layers in the hope to extract some important features from the data (such as the time influence). After learning those features, when we provide a test trajectory, the trained ML model will look for those features in that test trajectory69. The optimization was carried out only on 300 training trajectories from the training set TS. After optimization, our training architecture consists of two one-dimensional (1D) hidden convolutional layers, one maximum pooling layer, one flatten layer, three fully connected hidden dense layers and one output dense layer. The convolutional layers extract time-dependent correlations from a moving window, while maximum pooling layer pulls out the important information and decreases the size of the feature map which leads to reducing the computational cost. The flatten layer converts the output from the maximum pooling layer into 1D format as the fully connected dense layers, which are the traditional neural networks, can only work with 1D data. We train our CNN architecture using Keras software package70 with the TensorFlow in the backend71. Activation function, number of filters, kernel size and number of neurons for the respective convolutional and dense layers are given in Table −3 with adoptive mean optimizer and the batch size is 512. Using mean squared error function as a loss, we report 1.86 × 10−7 as the validation loss. The mean absolute error (MAE) and root mean square error (RMSE) averaged over 600 randomly chosen trajectories from the set of test trajectories STP (which were not part of the training process) are given in Table We use 1000 trajectories as our training set TS and 200 trajectories as the validation set VS. After preparation of the input following Fig. λ, γ, and T, respectively. We divide n = {n1, n2, n3, …, n7} = {1, 2, 3, …, 7} (labels corresponding to the seven rows in the reduced density matrix) by 10 to normalize their values, i.e., the input elements corresponding to the rows in the reduced density matrix are {0.1, 0.2, 0.3, …, 0.7}. Labels for sites with possible initial excitation are m = {0, 1}, which, respectively, represent initial excitation on site-1 and site-6. The input time is represented by a set of redundant time-functions f(t) normalizing time. We use a set of 100 logistic functions ck = 5k−1.0 and k ∈ {0, 1, 2, …, 99}, i.e., each logistic function has the same shape and designed to cover the corresponding ≈ 5 ps region and is shifted with respect to the next logistic function by 5 ps, as shown in Supplementary Fig. As we have multiple input elements, we need to normalize them all. In normalized input, we have Supplementary Information


Introduction: Severe COVID-19 pneumonia has two phases that are not mutually exclusive. Repurposed drugs target only one phase and the association of combination therapy to survival is unknown.Objective: To determine the association of hydroxychloroquine, azithromycin, and methylprednisolone versus methylprednisolone only to in hospital survival.Methods: This is a secondary analysis of a retrospective cohort of patients admitted for severe covid-19 in 13 hospitals in New Jersey, United States from March–June 2020. Propensity score match with 11 variables was constructed between those who received no methylprednisolone and methylprednisolone. Multivariate Cox regression was used for risk of in hospital mortality.Measurements and main results: There were 759 patients, 380 in no methylprednisolone and 379 with methylprednisolone. Multivariate Cox regression shows that methylprednisolone, hydroxychloroquine, and azithromycin had prolonged survival compared to methylprednisolone alone [HR 0.45 ]. In patients who received hydroxychloroquine and azithromycin, those who also received high dose methylprednisolone were associated with worse survival compared to those who received low dose methylprednisolone . Nursing home residents [HR 2.77 ], coronary artery disease  were independently associated with worse survival.Conclusion: Combination therapy was associated with improved survival compared to monotherapy. However, nursing home residents, coronary artery disease, and mechanical ventilation were independently associated with mortality. Larger randomized controlled studies are needed to confirm conclusions. Hydroxychloroquine has in vitro activity against SARS-CoV-2 through impairment of terminal glycosylation of angiotensin converting enzyme receptor 2 (ACE2) and increase pH of endosomes that virus use for entry.  pandemic surge in June 2021, there were 170,812,850 cases, 3,557,586 deaths, and mortality rate of 2% . In Marcr entry. . Azithrofibrosis . The eff studies .In the beginning of the pandemic, there were reservations on the use of corticosteroids due concerns for prolonging viral shedding, which was seen in other viral diseases such as influenza. Since then, a European study on dexamethasone showed improved survival in patients requiring oxygen support . MethylpIn our institution, azithromycin 500 mg IV for 5 days and hydroxychloroquine 800 mg on day 1 followed by 400 mg once a day for day 2–5 were also given to hospitalized patients. Methylprednisolone, with dose and duration at the discretion of the provider, were given to patients who were sick or at a higher risk of dying.Corticosteroids have become standard of care for COVID-19. We would like to determine if the addition of hydroxychloroquine and azithromycin to methylprednisolone is associated with improved survival compared to methylprednisolone alone.Real world data was collected from Hackensack Meridian Health (HMH), a NJ health network comprising of thirteen hospitals on patients ≥18 years of age, and hospitalized for at least 2 days between 1 March 2020 and 15 June 2020 with severe COVID -19 Pneumonia.Patient and public were not involved in the design, conduction and dissemination of this study.Demographic data such as age, gender, race, ethnicity, comorbidities, and sex were self-reported. Weight and height were measured. SARS-CoV-2 was detected in nasal swabs by RT-PCR. Routine blood tests included complete blood count (CBC), coagulation profile, complete metabolic profile (CMP), inflammatory markers , and arterial blood gas (ABG). Data was entered into Redcap and abstracted from June to December 2020.The primary outcomes are the associations of combinations of hydroxychloroquine, azithromycin, and methylprednisolone to in hospital survival. In the patients who received hydroxychloroquine, azithromycin, and methylprednisolone, we then wanted to compare the association of methylprednisolone dose to in hospital survival. The secondary outcome is a descriptive analysis of inflammatory markers in survivors versus non-survivors in those who received hydroxychloroquine, azithromycin, and methylprednisolone.2 vs. <30.0 kg/m2), sex , diabetes (Yes/No), hypertension (Yes/No), cancer (Yes/No), respiratory rate (RR)[ >22 breaths per minute (bpm) vs. ≤22 bpm], chronic kidney disease (Yes/No), low oxygen (oxygenation >94% vs. oxygenation≥94%), CRP (>20 mg/dl vs. ≤ 20 mg/dl), and quick sequential organ failure assessment (qSOFA) . , body mass index (BMI) . .A nearest-neighbor method was employed using a caliper of 0.20 to obtain the propensity matched sample. A post-match assessment of the distribution of propensity scores (or logit of propensity scores) and balance in the adjusted variables between the no methylprednisolone (NMP) and methylprednisolone using standardized difference and variance ratio were performed. This analysis and graphical displays were obtained by the ASSESS statement of PROC MATCH in SAS 9.4 .t-test or Wilcoxon signed-rank test, as appropriate. Comparison of paired categorical variables was performed using McNemar’s test or Bowker test of symmetry, as appropriate  were included in an initial full model fit and backward elimination selection procedure was performed until significant variables (at 5% levels) were retained (p < 0.10) were included in an initial full model fit and backward elimination selection procedure was performed until significant variables (at 5% levels) were retained  were obtained using Kaplan-Meier method which reported median (95% CI), 60-days rates (95% CI), and the intervals were calculated using the arcsine square root transformation method . To examretained . To thisretained . To thisretained .p < 0.0001). Data on P/F ratio was lacking; and FiO2 was used since 95% of patients had this data. The supremum test also indicated that non-proportionality was observed in other variables such as nursing home, lack of taste or smell, white blood cells<11,000 cells/ml, creatinine>1.5 ng/ml, respiratory rate >22 breaths per minute (BPM), hydroxychloroquine, methylprednisolone, calcium, and initial diastolic blood pressure. All variables with non-proportional hazard were adjusted using FiO2, as indicated above (Supplementary Table S1–S3) .Between March 4 and 15 June 2020, 2041 patients were flagged in the electronic health record with a diagnosis of COVID-19 and pneumonia. A total of 539 patients were excluded based on ineligibility criteria  A propensity score matched sample was constructed out of 759 patients [380 in no methylprednisolone and 379 in methylprednisolone]. After an examination of the proportional hazards assumption, methylprednisolone, and fractionated inspired oxygen (FiO2) significantly violated it (both with p < 0.047) and required more patients higher oxygen support compared to no methylprednisolone (129 vs. 35 p < 0.0001). At that time, the use of non-invasive mechanical ventilation (BPAP or CPAP) was rare due to concerns of aerosolization of the virus.In both methylprednisolone and no methylprednisolone, the patients were admitted 5 days from the onset of symptoms. The methylprednisolone group had higher levels of CRP (12.64 mg/dl vs. 9.88 mg/dl p < 0.03)] (p < 0.0001)], coronary artery disease (CAD)  were associated with worse survival.Multivariate Cox regression shows that methylprednisolone, hydroxychloroquine, and azithromycin had prolonged survival compared to methylprednisolone alone [HR 0.45 ] . Nursingp = 0.015). For those who received methylprednisolone and hydroxychloroquine, multivariate Cox regression showed improved survival compared to azithromycin . For those who received methylprednisolone, hydroxychloroquine, and azithromycin, they are associated with prolonged survival compared to methylprednisolone and hydroxychloroquine . Methylprednisolone, hydroxychloroquine, and azithromycin was associated with prolonged survival compared to hydroxychloroquine and azithromycin .Other combinations were also explored. For those patients who received methylprednisolone and azithromycin, multivariate Cox regression showed improved survival compared to hydroxychloroquine  (p = 0.3090), hence the Cox proportional hazard model was appropriate to analyze the comparison of High dose vs. Low Dose). Multivariate Cox regression showed that patients treated with high dose methylprednisolone, hydroxychloroquine, and azithromycin were associated 64% higher risk of in-hospital mortality compared to low dose methylprednisolone, hydroxychloroquine, and azithromycin .We further wanted to see the effect of methylprednisolone dose combined with hydroxychloroquine and azithromycin. The Youden index method determined dose cutoff as 1.36 mg/kg/d . Low-dos 0.0250) . The Supp = 0.12), CRP (median 12.19 mg/ml versus 13.25 mg/mL p = 0.17), and ferritin (median 799.60 ug/L versus 867 ug/L p = 0.21) were not significant. The difference between survivors versus non-survivors for d-dimer (median 1.12 mcg/mL versus 1.91 mcg/mL p = 0.0007) was significant . .Hydroxychloroquine, azithromycin, and methylprednisolone were associated with improved survival compared to methylprednisolone alone in hospitalized severe COVID-19 pneumonia. However, nursing home residents, CAD, and invasive mechanical ventilation were independently associated with mortality. Future implications of this study may warrant prospective studies evaluating the association of survival if hydroxychloroquine, azithromycin, and corticosteroids are given before the onset of ARDS, a symptom-based or phase-based approach to the administration of corticosteroids to hydroxychloroquine and azithromycin, or the use escalating d-dimer as biomarker for non-responsiveness to this combination.


Recent imaging studies with the stop-signal task in healthy individuals indicate that the subthalamic nucleus, the pre-supplementary motor area and the inferior frontal gyrus are key components of the right hemisphere “inhibitory network”. Limited information is available regarding neural substrates of inhibitory processing in patients with asymmetric Parkinson’s disease. The aim of the current fMRI study was to identify the neural changes underlying deficient inhibitory processing on the stop-signal task in patients with predominantly left-sided Parkinson’s disease. Fourteen patients and 23 healthy controls performed a stop-signal task with the left and right hands. Behaviorally, patients showed delayed response inhibition with either hand compared to controls. We found small imaging differences for the right hand, however for the more affected left hand when behavior was successfully inhibited we found reduced activation of the inferior frontal gyrus bilaterally and the insula. Using the stop-signal delay as regressor, contralateral underactivation in the right dorsolateral prefrontal cortex, inferior frontal and anterior putamen were found in patients. This finding indicates dysfunction of the right inhibitory network in left-sided Parkinson’s disease. Functional connectivity analysis of the left subthalamic nucleus showed a significant increase of connectivity with bilateral insula. In contrast, the right subthalamic nucleus showed increased connectivity with visuomotor and sensorimotor regions of the cerebellum. We conclude that altered inhibitory control in left-sided Parkinson’s disease is associated with reduced activation in regions dedicated to inhibition in healthy controls, which requires engagement of additional regions, not observed in controls, to successfully stop ongoing actions.The online version contains supplementary material available at 10.1007/s11682-021-00587-5. Patients with Parkinson’s disease (PD) have delayed motor inhibition relative to age-matched controls on the standard , independent of hand of performance.Correct inhibition was achieved at 61% (LPD patients) and 68% (controls) probabilities without statistical differences between groups  = 8.15, p = 0.007] indicating that patients were significantly slower than controls  independent of hand. No significant Hand x Group interaction was found  and the main effect of Hand was not significant either . For Stop-Respond trials, a 2-way ANOVA with Hand (right vs. left) and Group (patients vs. Controls) on Stop-Respond RTs showed a significant Hand x Group interaction  and main effect of Hand  without a significant Group effect . This was due to significantly longer Stop-Respond RTs for patients compared to controls with the left  and right hands , while faster compared to Go RT across groups and hands . The differences between groups in errors was not significant . Thus, the overall response speed was slower in the patient group but there were no significant group difference in accuracy.A 2-way ANOVA with Hand (right vs. left) and Group (patients vs. Controls) on Go RTs showed a significant Group effect  or main effect of Hand  was found. As expected, there was a significant Group effect  with significantly longer iSSRTs in LPD patients, indicating worse/delayed motor inhibition than controls . In summary, patients and controls showed significant differences on the Go RTs, SSD, iSSRT and Stop-Respond RTs but without significant main or interaction effects of Hand across most measures (Table A 2-way ANOVA with Hand (right vs. left) and Group (LPD vs. controls) on SSRT was performed. No significant Hand x Group interaction [For the Stop-Inhibit trials (successful inhibition) we found significant main effects in our sample  and pre-SMA as shown in Fig. To further identify the brain areas specifically activated in relation to motor inhibition subtracting the motor component, we examined the Stop-Inhibit-Go contrast controlling for response initiation involved on Go trials. Compared to controls, while using their more affected left hand, LPD patients showed a similar pattern to the Stop-Inhibit contrast, with significant underactivation in the left IFG BA48  that extends into the insula . When performing the task with the right hand, relative to controls, the LPD patients showed underactivation in brain regions including the bilateral thalamus extending to the left STN , as described in the Fig. FDR < 0.005).The rationale for performing the PPI analysis with the right and left STN as seeds was to examine the functional connectivity of these key subcortical nodes of the inhibitory network, which are hyperactive in PD [Bergman et al., To ascertain the right hemispheric inhibitory network dominance in response inhibition, we examined motor inhibition on a stop-signal task in a selected group of PD patients with predominant LPD motor features. Behaviorally, LPD patients had significantly longer SSRTs compared to age-matched healthy controls, irrespective of whether they were using the right or left hand, indicative of delayed motor inhibition. As impulsivity is one of the prevalent non-motor characteristics in PD  on difficult Stop trials when using the most affected hand. Moreover, we did not find connectivity changes of either the STN when stopping with the right hand (left hemisphere), compared to controls. Thus, the more affected right-hemisphere in left predominant PD would produce physiological changes in the well-known right-hemisphere inhibitory network.Differences in the inhibitory while using the more and less affected hands in left-sided PD are suggested by other aspects of the results. The difficulty of motor inhibition as indexed by the SSD regressor for the right hand was associated with under activation in the inhibitory network of the left STN and thalamus relative to controls. In line with the findings of some thalamic nuclei role in adjusting inhibitory control for more difficult timings [Li et al., go no-go tasks engages a right hemisphere ‘inhibitory network’ including the IFG, ACC and pre-SMA but also the STN, caudate, and thalamus [Aron et al., go no-go or motor inhibition on the stop-signal tasks. While patients with predominance of right or left-sided parkinsonism are normally included within the same cohort, it is possible that laterality of motor signs had an effect on motor inhibition. Our study is the first to examine the impact of lateralized parkinsonism on the neural networks engaged by motor inhibition.In healthy participants, successful motor inhibition on the stop-signal or Go no-go task [Vriend et al., The STN as part of the subcortical inhibitory network [Aron et al., There is considerable evidence from a variety of sources for involvement of the cortico-striato-subthalamic-pallidal-thalamic-cortical circuits in reactive, proactive, selective, goal-directed and habitual inhibition [for reviews see Aron, We show, for the first time, the neural correlates of delayed motor inhibition with the right and left hands in patients with left predominant PD. There were important differences in the patterns of brain activation during motor inhibition between hands. For the less affected right hand we found slight under activation of the right inhibitory network, however for the more affected left hand the delayed inhibition was associated with significant under activation of the right inhibitory network and altered functional connectivity of both STNs, requiring engagement of additional regions through strengthening connectivity with cerebellar and other brain structures, as compensatory mechanism for the execution of the task. The results promote further understanding of the neural substrates of delayed motor inhibition in PD.Supplementary file1 (DOCX 3780 KB)Below is the link to the electronic supplementary material.


During perceptual decision-making, the firing rates of cortical neurons reflect upcoming choices. Recent work showed that excitatory and inhibitory neurons are equally selective for choice. However, the functional consequences of inhibitory choice selectivity in decision-making circuits are unknown. We developed a circuit model of decision-making which accounts for the specificity of inputs to and outputs from inhibitory neurons. We found that selective inhibition expands the space of circuits supporting decision-making, allowing for weaker or stronger recurrent excitation when connected in a competitive or feedback motif. The specificity of inhibitory outputs sets the trade-off between speed and accuracy of decisions by either stabilizing or destabilizing the saddle-point dynamics underlying decisions in the circuit. Recurrent neural networks trained to make decisions display the same dependence on inhibitory specificity and the strength of recurrent excitation. Our results reveal two concurrent roles for selective inhibition in decision-making circuits: stabilizing strongly connected excitatory populations and maximizing competition between oppositely selective populations. In decision circuits, inhibitory neurons signal animal choices. Here, the authors show that choice-selective inhibition can stabilize the circuit dynamics or promote competition depending on inhibitory output connections, affecting choice behavior. The functional properties of decision-making neural circuits have been extensively studied and modeled9. Central to the function of these circuit models are attractors in the activity space which characterize the population’s encoding of a given choice. The attractor mechanism driving the decision-making activity in these models relies on structured recurrent connections between populations of excitatory neurons that are each selective for a different choice11. Inhibitory neurons, in this view, are merely supporting actors facilitating competition and providing balance to the excitatory neurons.Perceptual decision-making requires neural circuits to integrate evidence and classify a stimulus to trigger the correct behavioral response. Neurons in a range of cortical areas modulate their firing rate to signal animal’s choice12. In primary sensory areas, inhibitory neurons are generally more broadly tuned13 and more densely connected to neighboring excitatory neurons15. These inhibitory neurons reliably modulate spike output to reflect stimulus features and have highly specific connectivity to surrounding excitatory neurons17. The stimulus selectivity of inhibitory neurons is enhanced by learning and attention18 suggesting that task dependent modulation of inhibitory activity is necessary for cognition. Beyond the primary sensory cortex, stimulus information and animal choice can be decoded from the activity of inhibitory neurons in secondary sensory and association areas indicating a role for selective inhibition in higher cognitive functions, such as decision making21. While there is growing evidence that the activity and connectivity of inhibitory neurons is as complex as excitatory neurons, how the selectivity of inhibitory activity and the diversity of their connections affect the decision-making function of cortical circuits is still unknown.Since the canonical models of decision-making circuits were built, the diversity and complexity of inhibitory neurons within the cortex have been characterized in increasing detail4 to account for the presence of inhibitory choice selectivity. Our model allows us to parametrically alter the specificity of connections between two choice-selective excitatory and two choice-selective inhibitory populations. Through analysis of this model, we found that while inhibition must drive competition between choice-selective excitatory populations it must also stabilize activity driven by recurrent excitation at the same time. These two concurrent roles are mediated by inhibitory connections to the excitatory populations and either role can be enhanced by structured inhibitory connectivity. We found that inhibitory selectivity expands the space of possible circuits which support decision-making by enhancing either a competitive or stabilizing role for inhibition. In addition, the connectivity motif between choice selective populations alters the underlying attractor dynamics and modulates the decision-making performance to prioritize speed or accuracy. We generalized these results by training recurrent neural networks (RNNs) to perform the same decision-making task. After training, RNNs had both excitatory and inhibitory units significantly selective for choice and displayed a similar dependence between the specificity of excitatory and inhibitory connections found in the mean-field model. Finally, we perturbed inhibitory neuron activity in these models to probe the dynamical regime in which the circuit operates. We found two regimes in which circuits respond differently to perturbations of inhibitory neurons: one in which the competitive role dominates and the other in which the stabilizing role dominates. Our work demonstrates that choice selective inhibition impacts decision-making behavior by enhancing either the competitive or the stabilizing role for inhibition in the circuit. These results generate testable predictions for perturbation experiments.To reveal the role of choice selective inhibitory neurons in decision-making computations we extended a well established mean-field model of decision-making circuits1 and E2) populations are the dynamic variables4. The average strength of connections between the four choice selective populations is controlled by a specificity parameter γ. For each of three connection classes  is the strength of feedback connections within excitatory populations selective for the same choice, and (1 − γEE) is the strength of connections between excitatory populations selective for the opposite choice. We keep γEE positive due to the importance of recurrent feedback excitation in the function of these circuits4. When γEE = 1, each of E1 and E2 have a strong self-excitatatory feedback and are not connected to each other. When γEE = 0, the strengths of excitatory connections between and within E1 and E2 are all equal. Inhibitory choice selectivity is controlled by γEI defined in the same way, which is also positive because inhibitory neurons inherit choice and stimulus information from the excitatory neurons. When γEI = 1, inhibitory population I1 receives excitatory inputs from E1 but not E2 and vice versa. When γEI = 0, each I1 and I2 receive equal excitatory inputs from E1 and E2. Thus, inhibitory activity is not choice selective when γEI = 0 because inhibitory neurons receive equal input from both excitatory populations. Inhibitory choice selectivity emerges as γEI increases  populations integrate dedicated streams of sensory evidence to produce a categorical choice Fig. a. In conγIE ≠ 0; Fig. γIE can range between  with negative values favoring connections between E and I populations with opposite choice preference and positive values favoring connections between E and I populations with the same choice preference. When γIE = 1, I1 sends inhibitory output to E1 but not E2. When γIE = −1, I1 sends inhibitory output to E2 but not E1. Thus, the specificity of inhibitory output connectivity defines three circuit motifs: contraspecific for γIE < 0, ipsispecific for γIE > 0, and nonspecific for γIE = 0.For inhibitory choice selectivity to have any effect on circuit function, the outputs of inhibitory populations must be structured  or nonspecific (γIE = 0), the strength of recurrent excitation (γEE) is highly constrained and deviations from a narrow range leads to the loss of one of the essential fixed points  governing decision-making behavior. We sampled the specificity parameter space to identify circuits which support these eight fixed points Fig. a. We fouing Fig. b. When ints Fig. c. For ciγEE Fig. b.Fig. 2CγEE is low, nonspecific and ipsispecific circuits lack the fixed points representing choice both in the presence and absence of stimulation as well as the saddle point during the stimulus . This four-variable model produces the firing-rate dynamics and attractors similar to the original two-variable mean-field model , ipsipecific circuits are more accurate at classifying difficult stimuli but more often fail to separate the outputs sufficiently producing invalid trials  to perform a decision-making task21 (Methods). We constructed ROC curves by decoding network choice from a unit’s activity on the time-step following stimulus offset. To identify which units significantly modulated their firing rate to reflect choice, we compared the area under the ROC curve (AUCROC) to a shuffle distribution generated from randomized trial labels . Units that were identified as choice selective increased activation following the onset of a stimulus corresponding to their preferred choice . Also, the proportion of significantly selective units was higher for inhibitory than excitatory units . Thus, inhibitory unit activity contained overall more choice information than excitatory unit activity despite the fact that only excitatory units received stimulus input. In this respect RNNs differ from experimental data in which excitatory and inhibitory neurons contained similar choice information21.We determined whether inhibitory neurons in these RNNs were choice selective. We classified recurrent units as choice selective using receiver operator characteristic (ROC) analysisγ from the weights of trained RNNs defined in the same way as for the mean-field model (Methods). Trained networks consistently had strong excitatory-excitatory (γEE = 0.59 ± 0.07) and excitatory-inhibitory (γEI = 0.39 ± 0.06) specificity  but their distribution showed both ipsispecific and contraspecific motifs. Inhibitory-inhibitory connections were nonspecific on average with higher variation than inhibitory-excitatory connections (γII = −5.0 × 10−3 ± 0.06). Confirming the trend predicted by the mean-field model, excitatory specificity γEE was correlated with the inhibitory specificity index γEIγIE, where networks with stronger recurrent excitation were ipsispecific and networks with weaker recurrent excitation were contraspecific  excitatory gain can be compensated by either an increase (decrease) in excitatory connection specificity or by strengthening of the contraspecific (ipsispecific) motif. Accordingly, we expect that changing the activation function slope of the excitatory units in RNNs should either shift the excitatory-excitatory specificity against the direction of the gain change or shift the inhibitory specificity towards contraselective (for lower slope) or ipsielective motif (for higher slope). We trained two additional sets of networks with hypoexcitable (slope 0.5) or hyperexcitable (slope 1.5) excitatory units. Changing the excitability of excitatory units led to large shifts in ν0,I  leads to a decrease in τslow, i.e. faster dynamics. Around a high baseline value of inhibitory activity  a low-inhibition regime where the competitive role dominates, and (ii) a high-inhibition regime where stabilizing role dominates. In trained RNNs, perturbations of all inhibitory neurons indicate that these networks operate in the stabilizing inhibition regime.γEE) and inhibitory connections (γEIγIE) reveals how the contra- and ipsispecific motifs enhance one of two roles for inhibition: facilitate competition between populations coding for opposite choices or stabilize amplification driven by strongly recurrent excitation. When γEE is low and excitatory populations alone cannot drive selective activation, contraspecific inhibitory motifs support decision-making by maximizing competition. Conversely, when γEE is high and excitatory self-amplification becomes unstable, ipsispecific inhibitory motifs stabilize firing rates.Decision-making circuits with non-selective inhibition exist only within a narrow range of excitatory-excitatory connection specificity. When inhibitory neurons inherit choice-selectivity from excitatory neurons and also project to excitatory neurons via specific connections, a broad range of circuit configurations can support decision-making. In circuits capable of decision-making, the correlation between the specificity of excitatory . Studies of E-I RNNs which focus on the impact of inhibitory connections show that specificity of inhibitory-inhibitory connections can be critical to circuit function23. The apparent difference in the importance of inhibitory-inhibitory selectivity between our networks and previous work could result from differences in the training procedures35. We observed a large impact of RNN training hyperparameters on the emerging circuit structure. Future work is needed to understand how details of training influence the emerging circuit structure and computations performed by RNNs.We found a similar relationship between excitatory and inhibitory connection specificity in RNNs suggesting the balance between competitive and stabilizing inhibition is a general principle in E-I networks. While specific connections between excitatory and inhibitory units were clearly important for the decision-making function in our networks, connections between inhibitory units appeared unconstrained, indicating this connection class has limited effect on circuit function like in the mean-field model. RNNs are increasingly often used to develop theories of how neural circuits perform computations3. While these models reproduce the dynamics of decision-making circuits they do not fully account for the diversity of interneurons within the cortex. Cortical inhibitory neurons show selective activation in many modalities including primary sensory37 and association areas21. Moreover, choice-selectivity of parietal inhibitory neurons is equal to that of excitatory neurons during an audio-visual discrimination task21.Our results show that selective inhibition can have a marked effect on the function of neural circuits. Many models of categorical decision-making rely on a nonspecific pool of inhibitory neurons to enforce winner-take-all competition between excitatory neuronsγEI in our model). While it is possible that choice selectivity could arise from external inputs to interneurons38 or even from random connections between excitatory and inhibitory neurons39, most circuit models assume stimulus information is exclusively provided by inputs to excitatory neurons. Inhibitory choice-selectivity also emerged in our RNNs trained to perform 2AFC task28. In our RNNs, inhibitory units can only inherit stimulus or choice information through specific connections from excitatory populations, unlike in other trained RNNs23. For both excitatory and inhibitory units in trained RNNs, we found that the fraction of selective units was higher than is commonly used in circuit models4 and found in experiments21. This difference could be due to the simplicity of RNNs compared to in vivo circuits, and also a training process which aims to minimize total activity through regularization. In addition, decisions in the RNN are fully determined by the local circuit, whereas an animal’s behavioral output arises from a broadly distributed circuitry. Although higher choice selectivity for inhibitory units was robust to doubling the network size .In attractor networks, modulation of 16. A shift in output specificity could be mediated through top-down activation of inhibitory subnetworks or through neuromodulation of distinct inhibitory subtypes such as PV+, SOM+, or VIP+. Acetylcholine has layer-dependent effects on the responsiveness of both regular spiking and fast spiking neurons in the visual cortex, which could differentially activate distinct inhibitory motifs on behaviorally relevant timescales42. Additionally, acetylcholine can reduce the release of inhibitory neurotransmitters in cortical neurons43, thus directly affecting inhibitory connectivity.Selective neuromodulatory control of genetically identifiable inhibitory subtypes may provide for control of inhibitory motifs. Inhibitory subtypes have distinct connectivity patterns to neighboring excitatory neurons: fast-spiking cells have far more reciprocal connections to excitatory neurons than adapting interneurons4. This assumption is based on the timescale separation between decay time constants of slow NMDA (~100 ms) and fast GABA (~5 ms) conductance. The slow NMDA dynamics dominate the time evolution of network activity, and one can assume that all other variables reach their steady-state nearly instantly4. Despite being fast, the dynamics of GABA synapses can also affect decision-making behavior44. A study44 considered a set of circuits with parameters chosen so that when the steady-state assumption is applied, all models reduce to the two-variable model with the exact same parameter set. Thus, all differences in dynamics of these circuits were driven by GABA dynamics. In these circuits, the GABA dynamics mediated a speed-accuracy trade-off and, moreover, this tradeoff was more efficient in circuits with selective inhibition44. While this study considered only ipsispecific inhibitory connectivity and a narrow space of circuits that all map onto a single parameter set of a two-variable model, our work explores a wide range of circuit configurations ranging from contraspecific to ipsispecific inhibitory motifs. Our findings are robust to the steady-state approximation of GABA dynamics as we show using a four-variable mean-field model  fail to reach the imposed decision threshold on a fraction of trials with low stimulus strength, which we call invalid trials. This behavior is common across spiking45. The stabilizing and competitive regimes can be differentiated by the behavioral response to perturbations of inhibitory activity. Perturbations during reaction time tasks should reveal which inhibitory role is dominant in vivo. The balance of these two roles is critical for circuits to perform decision tasks, and shifts in this balance could align dynamics with changing task requirements. More experimental work is needed to uncover how inhibitory subnetworks strike this balance in the cortex. Specifically, whether functional selectivity is constrained to certain inhibitory subtypes and whether inhibitory neurons are recruited to perform a task in a state dependent manner are important questions for future work.We show that choice selective inhibition can enhance one of two roles for inhibition in decision-making circuits: facilitating competition or stabilizing excitatory feedback. Both these roles are simultaneously fulfilled by inhibition in any decision making circuit. Enhancing activity of all inhibitory neurons can shift the circuit from a regime where the competitive role dominates to a regime where the stabilizing role dominates regardless of which inhibitory motif is present. This effect echos results which find shifts in E/I balance can induce leaky or unstable integration4 and reflects the experimental observation that only a fraction of all recorded neurons shows choice selectivity21. Each selective population contains the fraction f of the total number NE (NI) of excitatory (inhibitory) neurons, so that 1 − 2f is the proportion of nonselective neurons. We reduce the dynamics of the full network with 6 excitatory and inhibitory populations to a dynamical system with two variables representing the activations of N-methyl-D-aspartate (NMDA) conductances (in terms of fraction of channels open) for synapses originating from two choice-selective excitatory populations4. The model reduction to two dimensions leverages the timescale separation between decay time constants of the slow NMDA (~100 ms) and fast γ-aminobutyric acid  and α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid  receptors. The slow NMDA dynamics dominate the time evolution of the system, and one can assume that all other variables reach their steady-state nearly instantly4. The dynamics of the NMDA activation variable for population i  are governed by:τNMDA = 0.1 s and γ = 0.641. The non-linear function Φ transforms input current xi [nA] into firing rate:a = 270 nC−1, b = 108 Hz, and d = 0.154 s. The input to population i is:j refers to the other excitatory population. The complexity of the circuit structure, including interactions between all selective and nonselective excitatory and inhibitory neurons, is collapsed into two-dimensional model through the variables α1, α2, and Ii0, as described in the section Circuit Structure below.Our mean-field model accounts for interactions among 6 populations: 3 excitatory (2 choice selective and 1 nonselective) and 3 inhibitory (2 choice selective and 1 nonselective). Including nonselective neurons in the model is consistent with previous workμ. We define the strength of evidence for one versus the other choice as stimulus coherence c, which can range between −100% and 100%. For population i the stimulus is then defined as:The stimulus μ to 40 Hz. Noise is introduced through the inputs Iη,i to the two excitatory populations filtered through fast synaptic activation of AMPA receptors:τAMPA is 0.002 s and η(t) is a white Gaussian noise with zero mean and standard deviation 0.02 nA. We performed numerical simulations using the Euler method with a 2 ms time step.For all cases, we set α1, α2 between the two excitatory populations, and the background currents Ii0,. This reduced model is based on approximating the firing rates of all three inhibitory populations (two choice-selective and one nonselective) and of the nonselective excitatory population as linear functions of their inputs. Thus, the firing rates of these populations change linearly in response to changes in the firing rates of the two explicitly modeled excitatory populations E1 and E24. We define α1 as a term which describes how activity S1(2) from the excitatory population E1(2) filters through the circuit (i.e. via E2(1), E0, I0, I1, I2, and feeding back onto itself) to impact its own firing rate. Similarly, α2 describes how the activity S1(2) filters through the circuit to impact the firing rate of the opposite excitatory population. Ii0, describes the net input from the population activity that does not depend on the activity of E1 or E2. Thus, this model accounts for interactions between all six populations with only two dynamical system equations Eq. :The effective interaction strengths α1 account for the effect of an excitatory population’s activity on its own activity filtered via (a) direct self-coupling, (b) the activity of the inhibitory population with the same choice selectivity, (c) the activity of the inhibitory population with the opposite choice selectivity, and (d) the activity of nonselective inhibitory neurons. Similarly, α2 describes the influence of one excitatory population’s activity onto the other fed through all other populations in the circuit and also consists of four components α2 = λ2(αa2 + αb2 + αc2 + αd2):These components of α2 account for the effect on an excitatory population’s activity from the oppositely selective excitatory population’s activity filtered via (a) direct coupling, (b) the activity of the inhibitory population with the same selectivity, (c) the activity of the inhibitory population with the opposite selectivity, and (d) the activity of nonselective inhibitory neurons. The effects of nonselective neurons and external background inputs are described by Ii0, = λI:The components of i from the nonselective excitatory population filtered via (a) direct coupling, (b) the nonselective inhibitory population, (c) the inhibitory population with the same choice selectivity, (d) the inhibitory population with the opposite selectivity. The term ψ accounts for the NMDA activation of nonselective excitatory neurons. We calculated the firing rate of inhibitory populations as ΦI,1(2) = α1,IS1(2) + α2,IS2(1) + I0,II, where:These terms account for the input to the excitatory population EAll parameter values are provided in Table 32, whereas many other studies assign a choice at random on trials when the network does not reach the decision threshold45. The random assignment of choices on invalid trials can conceal differences in network dynamics, making distinct dynamical regimes indistinguishable in psychometric functions45.We considered a trial to be valid if the following criteria were met: (i) the firing rate difference between the two choice selective excitatory populations was less than 5 Hz for the entire period prior to stimulus onset, (ii) the firing rate difference was above the decision threshold of 15 Hz for at least one time step during the stimulus period and the time point following stimulus offset. Fraction completed trials for each stimulus level was defined as the number of valid trials out of all trials presented. Only valid trials were considered for computing chronometric and psychometric functions. Our treatment of invalid trials is more conservative than in many other studies, as we report invalid trials as a separate behavioral outcome different from correct or incorrect decision−6. To identify the stability of the fixed points, we computed the Jacobian matrix analytically and found its eigenvalues numerically using the eig function in MatLab. For the saddle points, τslow is the inverse of the positive eigenvalue of the Jacobian matrix.We analyzed the mean-field model to find null-clines and fixed points using MatLab’s fsolve function with the Levenberg-Marquant algorithm and a tolerance of 1 × 10Recurrent neural networks (RNNs) were composed of 100 excitatory and 25 inhibitory units. We obtained the same results with networks twice as large  nonlinearity sE(I)+, where sE(I) sets the excitability of the excitatory or inhibitory units. xin is the input activation and u(t) is the instantaneous input. The time constants of recurrent units and inputs are set by αr and αin. Weights within and between units are housed in the matricies WEE, WEI, WIE, WII. Only the excitatory units receive projections from the input and project to the output through Win and Wout, respectively.Here u(t) =  representing sensory evidence:RNNs received two input streams μ = 3.2 was fixed and stimulus difficulty was set by c which ranged between − 20 and 20.The stimulus period was 21 time steps and σin(t) that are sampled from a Gaussian distribution. We ensure that each element has a standard deviation σ0,r and σ0,in via scaling:The recurrent and input noise are modeled by the elements of z  and targets T . We set the entries in T to the baseline value of 0.2 and, following a stimulus onset, raise the entries to 1 for the output corresponding to the correct choice. This target is designed to train the network to remain in a low activity state until stimulated and elevate the correct output in response to a stimulus. Half of training trials were catch trials, on which no stimulus was presented and target values remained at 0.2 throughout the trial. The training batch consisted of Ntrial = 200 trials which were randomly generated every training epoch. Within the training batch, noncatch trials were equally divided between possible choices and the difficulty was randomly sampled.The goal of RNN training is to minimize the difference between the output wμ = 0.0375 and scale wσ = 0.5 for excitatory weights WEE, WEI, and θwμ and scale wσ for inhibitory weights WIE, WII. The scaling factor θ = NEsE/NIsI adjusts the strength of inhibitory connections to offset for differences in the number and excitability between excitatory and inhibitory units. Input and output weights Win, Wout were randomly initialized from a uniform distribution and then values were normalized so the weights associated with each input and output summed to 1 across units. All weights were trained via back-propagation through time to minimize the loss function:Recurrent network weights were randomly initialized from a Gamma distribution with a shape x is a concatenation of xE and xI of the size Ntrial × Ntime × (NE + NI), and W is a concatenation of WEE, WEI, WIE, and WII of the size (NE + NI) × (NE + NI). To encourage the network to integrate the stimulus for extended time, we used a mask M , where entries were zero during the stimulus period so that time points during the stimulus were not considered when calculating the error term of the loss function. On catch trials, all entries of M were set to 1. The hyperparameter λx = 0.1 controls the amount of L2 regularization intended to minimize the activation of each unit. The hyperparameter λw = 1.0 controls the amount of L1 regularization applied to weights. We updated the weights by stochastic gradient descent using the ADAM optimizer in PyTorch and Python 3.7 with a learning rate 0.01. During training, the norm of the gradient was clipped at 1.Here WEE, WEI, WIE, WII, Win, and Wout were set to 0 after every training step. We prevent self-connections by elementwise multiplying WEE and WII by (1 − I), where I is the identity matrix and 1 is a matrix of 1s, after every training step.To maintain the identity of excitatory and inhibitory units and to keep the input and output weights positive, all negative elements of We terminated RNN training based on its task performance. We tested RNN performance on a validation batch of trials after every training epoch. Each validation batch consisted of 100 trials with stimulus strength ranging between −20 and 20 in steps of 2. The network registered a decision when the difference between the output variables was above a threshold of 0.25. Trials were considered valid if at least 75% of the prestimulus period was below the decision threshold and at least 50% of the post stimulus period was above the decision threshold. Overall performance was measured as the fraction of correct choices out of all trials except for the ambiguous case where stimulus was equal to 0. We compute the accuracy and the psychometric function only using valid trials. We terminated training when a network’s overall performance reached 85%. RNN parameter values are shown in Table 21. For each unit, we computed the receiver operating characteristic (ROC) using the roc function and the area under the ROC curve (AUCROC) using the trapz function in Matlab. A unit with the same activity for either choice will have an AUCROC equal to 0.5, thus our choice selectivity measure was defined by AUCROC − 0.5. To identify significantly selective units, we compared AUCROC to a shuffled distribution generated from that unit’s activity by shuffling the choice outcomes 150 times. We considered units to be choice selective if their AUCROC fell within the lowest or highest 2.5% percentiles of the shuffled AUCROC distribution.After training, we analyzed the activity of excitatory and inhibitory RNN units to quantify their choice selectivity. Our metric is based on the ability to decode the choice registered by the network based on the activity of the unit at the time point immediately following stimulus offsetγ as:We measured the specificity of connections between choice selective units in RNNs. For each connection class , we computed γ used in the mean-field model. To assess significance of correlations between γ for the 4 connection classes, we computed a shuffled distribution constructed by shuffling the network labels 5000 times.This expression is identical to the specificity νI0, by a small amount within the range  around a baseline. We used two baseline values of νI0,: 11.5 for low-inhibitory regime and 14 for high-inhibitory regime. In RNNs, we delivered perturbations in a similar manner, where we delivered a constant input within the range   during the stimulus period.We perturbed activity of inhibitory neurons by delivering the same constant input to all inhibitory neurons during the stimulus period. In the mean-field model, we modified the parameter 1 and E2  are governed by:1 and I2  are governed by:To model the effects of inhibitory-inhibitory specificity and dynamics of inhibitory synapses, we developed a simplified version of our model which explicitly modeled the activity of selective inhibitory populations. In this model, the dynamics of NMDA synapses for excitatory populations Ex) is of the form Eq.  receive stimulus information through Iν,i which is implemented as in the two-variable model (Eq. (ν(t) set to 0.2 nA.Only excitatory populations (l to Eq. . Noise idel (Eq. ) with thγII which can range between . The synaptic parameters JNMDA,E, JNMDA,I, JGABA,E, JGABA,I, and the background input currents I0,E(I) were chosen so that the firing rate dynamics of E1 and E2 matched that of the two-variable model on a noiseless trial with a stimulus strength of 0.05 using PyABC parameter inference51. The values of these parameters are defined in Table The weight parameters Further information on research design is available in the Supplementary InformationPeer Review FileReporting Summary


CILK1 mutations show longer cilia and abnormal Hedgehog signaling. Our study aimed to identify small molecular inhibitors of CILK1 that would enable pharmacological modulation of primary cilia. A previous screen of a chemical library for interactions with protein kinases revealed that Alvocidib has a picomolar binding affinity for CILK1. In this study, we show that Alvocidib potently inhibits CILK1 (IC50 = 20 nM), exhibits selectivity for inhibition of CILK1 over cyclin-dependent kinases 2/4/6 at low nanomolar concentrations, and induces CILK1-dependent cilia elongation. Our results support the use of Alvocidib to potently and selectively inhibit CILK1 to modulate primary cilia.The primary cilium provides cell sensory and signaling functions. Cilia structure and function are regulated by ciliogenesis-associated kinase 1 (CILK1). Ciliopathies caused by  Cilia and flagella are microscopic structures protruding from the cell surface that provide sensory functions and motility. Acting as cellular antenna, the primary cilium in animal cells senses environmental cues and transduces and integrates extracellular signals ,2. StrucCILK1 mutations that compromise the kinase activity are associated with ciliopathies that manifest in longer cilia and abnormal ciliary signaling [CILK1 variants were recently linked to epilepsy [One approach to target the primary cilium is by the inhibition of ciliogenesis associated kinase 1 (CILK1). This kinase was formerly named intestinal cell kinase (ICK) after the tissue it was cloned from . CILK1 iignaling ,16,17. Cepilepsy . These eepilepsy . HoweverIn this study, we identified Alvocidib (flavopiridol), a semi-synthetic flavone related to a natural product extracted from Indian plants, as a potent and relatively selective inhibitor for CILK1 in cells. Although Alvocidib had been widely used as a pan-CDK (cyclin-dependent protein kinase) inhibitor , we demohttp://www.kinasenet.ca/, accessed on 26 April 2021). The results revealed that CILK1 has the highest binding affinity for Alvocidib (Kd = 690 pM), followed by R547 (Kd = 2.2 nM) and AT7519 (Kd = 8.3 nM). All three compounds are known as ATP-competitive inhibitors of CDKs, which share significant sequence alignment with CILK1 and structural similarities in the catalytic domain. We tested for the inhibition of CILK1 activity in cells by Alvocidib and AT7519. We co-expressed either GST-CILK1 or Flag-CILK1 with HA-KIF3A as a preferred CILK1 substrate in HEK293T cells. We treated cells with increasing concentrations of Alvocidib and assessed the phosphorylation of KIF3A-Thr672 by immunoblotting for total KIF3A and phosphosite pT672 in both cell lysates and anti-HA immunoprecipitates. As shown in Alvocidib was identified as a ligand for CILK1 by screening of a chemical library for binding to kinases  essentially eliminated KIF3A-Thr672 phosphorylation by either GST-CILK1 or Flag-CILK1 after 15 min treatment, and this inhibition remained complete for at least 2 h post treatment D. Our daNext, we co-transfected HEK293T cells with GST-CILK1 and HA-KIF3A and then treated cells with Alvocidib at a range of concentrations in the low nanomolar range, based on data in In addition to inhibition by competing for ATP binding, one way to reduce CILK1 activity in cells would be to interfere with its activation by phosphorylation of the TDY motif. Phosphorylation of the TDY motif in the CILK1 activation loop is essential for kinase activation . We extr50 values in the 20–100 nM range in biochemical assays [Alvocidib inhibits CDK1, CDK2, CDK4, CDK6, and CDK9 with ICl assays ,23,24. TAlvocidib can arrest the cell cycle by causing not only inhibition of CDKs but also downregulation of cyclin D1 and D3 . However90) or DMSO (solvent control) for 4 h and then fixed and immunostained cells with cilia marker Arl13B and basal body marker γ-tubulin  cell lines that express either wild type (WT) CILK1 or the R272Q mutant form. Our prior work has shown that the R272Q mutation in CILK1 eliminates kinase activity and there is cilia elongation in MEFs expressing this CILK1 inactive mutant . We trea-tubulin A. We mea-tubulin B. In WT -tubulin B. Howeve-tubulin B. We thuCilk1 in mice caused abnormal extension of the cilium [rosv-cross-hybridizing kinase) branch of the protein kinome, CILK1 is clustered with MAK  and MOK (MAPK/MAK/MRK-overlapping kinase) [In this study, we show that Alvocidib offers a new pharmacological tool to modulate primary cilia by the inhibition of CILK1. Cilium elongation as a result of Alvocidib inhibition of CILK1 is consistent with prior observations that genetic deletion or inactivation of e cilium ,16 and oe cilium ,19,26. I kinase) . These R kinase) ,29,30,31http://www.kinasenet.ca/, accessed on 26 April 2021). However, Alvocidib reportedly has a 40-fold higher binding affinity for CILK1 (Kd = 0.69 nM) than for MAK (Kd = 28 nM), suggesting that Alvocidib has a strong preference for CILK1 over MAK. Therefore, we postulated that Alvocidib at the low nanomolar range can selectively inhibit CILK1 but not MAK in cells, which remains to be determined. It is worth pointing out that an insignificant elongation of primary cilium by 100 nM Alvocidib in Cilk1 mutant cells suggests that MAK is likely not a primary target by Alvocidib at low nanomolar concentrations in cells.Since MAK is mostly related to CILK1 in sequence and both are negative regulators of cilia length, is it possible that Alvocidib inhibition of MAK also contributed to cilia elongation. CILK1 and MAK are 88% identical in the catalytic domain. It is therefore unsurprising that they share the top three drugs  in the ranking of drug-target binding affinity  and AT7519 (S1524) were from Selleckchem . Glutathione Sepharose 4B (17-0756-01) and Gammabind Plus Sepharose beads (17-0886-01) were from GE Healthcare . Anti-FLAG tag affinity beads (ab270704) were from Abcam . pEBG-GST-CILK1/ICK encoding GST-CILK1/ICK was described in ,21. pCMVKIF3A phospho-Thr672 rabbit polyclonal antibody was generated at GenScript  and described in . GST-tag2 in Dulbecco’s modified Eagle’s medium (DMEM) supplemented with 4.5 g/L glucose, 10% fetal bovine serum, and penicillin-streptomycin. HEK293T cells were transfected using a calcium phosphate protocol as described in [Mouse embryonic fibroblast (MEF) cells were isolated from Cilk1 wild type and R272Q mutant embryos (E14.5-E15.5) . HEK293Tribed in .Forty-eight hours after transfection, cells were lysed in lysis buffer , 10 mM sodium orthovanadate, 5 mM sodium fluoride, 10 mM sodium pyrophosphate, 10 mM β–glycerophosphate, and 1 µM microcystin LR). Cell lysate was cleared by centrifugation. GST-CILK1 proteins were pulled down from cell lysate using Glutathione Sepharose 4B beads  following the manufacturer’s instructions. HA-KIF3A proteins were immunoprecipitated from cell lysate using HA antibody and captured on GammaBind Sepharose beads .Cell extracts or Sepharose beads were boiled for 5 min in an equal volume of 2X Laemmli sample buffer  and loaded on an SDS-gel. Samples were transferred to a PVDF membrane and blocked for one hour in 5% dry milk before primary antibody incubation in TBS containing 0.1% Tween-20 and 5% bovine serum albumin (BSA) for 90 min at RT or overnight at 4°C. This was followed by extensive rinses and one-hour incubation with horseradish peroxidase (HRP)-conjugated secondary antibody. Chemiluminescence signals were developed using Millipore Immobilon ECL reagents from EMD Millipore .MEF cells grown on gelatin-coated coverslips were fixed by 4% paraformaldehyde (PFA) in PBS, rinsed in PBS, and then permeabilized by 0.2% Triton X-100 in PBS. After one hour in blocking buffer , MEF cells on cover slips were incubated with primary antibodies at 4 °C overnight followed by rinses in PBS and one hour incubation with Alexa Fluor-conjugated secondary antibodies. After extensive rinses, slides were mounted in antifade reagent containing DAPI  for imaging via a confocal Laser Scanning Microscopy 700 from ZEISS .The Zen 2009 program was used with a confocal Laser Scanning Microscope 700 from ZEISS  to collect z stacks at 0.5 μm intervals to incorporate the full axoneme based on cilia marker Arl13b staining. All cilia were then measured in Fiji/ImageJ (version 1.52t)  via a standardized method based on the Pythagorean Theorem in which cilia length was based on the equation L2 = z2 + c2, in which “c” is the longest flat length measured of the z slices and “z” is the number of z slices in which the measured cilia were present multiplied by the z stack interval (0.5 μm).t-test. Data were reported as mean ± standard deviation (SD). p-values less than 0.05 were considered as significant.Quantified experimental data were analyzed by the Student’s We have demonstrated here that Alvocidib at low doses can modulate primary cilia via potent and selective inhibition of CILK1. We believe that Alvocidib offers a useful new tool compound to study the role of the primary cilium in cell signaling related to neural circuit function and cancer chemoresistance.