By combining time-resolved quantitative experimental data generated in primary mouse hepatocytes with interaction graph and ordinary differential equation modeling, we identify and experimentally validate a network structure that represents the experimental data best and indicates specific crosstalk mechanisms.

We combine interaction graph and dynamic modeling with quantitative experimental data to study the hepatocyte growth factor induced signaling network in primary mouse hepatocytes.

Subsequently, by performing a systematic model selection we select the model structure representing the eXperimental data best.

Additionally, the calculated area under the curve of pAkt, pERK and their sum for the model trajectories and the experimental data are in agreement.

They can be used to make predictions on the possible qualitative behavior of a signaling network, and these predictions can be compared with experimental data .

Here, we present a novel hybrid approach (Fig 1), which combines qualitative and quantitative modeling techniques to unravel the HGF induced activation of MAPK and PI3K signaling in primary mouse hepatocytes based on time-resolved experimental data .

We started with an interaction graph master model containing previously reported crosstalk, feedback and feedforward mechanisms and selected then minimal model structures of the interaction graph master model that can explain the observed qualitative characteristics of the experimental data .

To test Which of the identified structures can quantitatively represent the transient and sustained effects observed in the experimental data , we translated each of the 16 compressed selected minimal model structures as well as the core and the complete model into an ODE model.

For each model structure, parameter estimation was performed to determine the model performance in relation to the experimental data .

In order to select all minimal submodels of the interaction graph master model that can explain the observed effects from the experimental data (Fig 3B, left panel) and that contain the core model, we proceeded as follows: starting from the core model, we added one candidate mechanism at a time (that is, all edges making up the mechanism, S3 Table) and derived the model predictions for the resulting interaction graph structure as explained above.

In total, we identified 16 minimal model structures that can equally well explain our experimental data (Fig 3B, right panel and S4 Fig).

Compared to the baseline guinea pig FR model, the optimized cell-specific models showed a significantly improved fit to the experimental data .

Dynamic electrophysiology protocols and optimization improve model fit to in vitro experimental data

For each cell, the GA estimate from the experimental data fit much better than did the FR model (Fig 5 and 87—89 Figs).

We chose a genetic algorithm as it is effective for a range of the number of parameters [50], is computationally simple and readily parallelizable, and has been shown to be successful at optimizing sophisticated ionic models to experimental data [22,23,25].

However, when comparing a generic model such as the out-of-the-box FR model to our experimental data , there are substantial differences, which likely would cause inaccurate predictions if simulating, e.g., effects of pharmacological agents or genetic variations.

demonstrated that it is feasible to estimate conductance parameters for experimental data and showed that the fits improved when using data recorded during multiple periodic pacing frequencies [22].

Further, differences in structure, channel kinetics and IV-relationships between model and experiment are likely to result in less accurate parameter estimations [31] and may underlie the deviations between fit and experimental data during voltage clamp (Fig 5 and 87—89 Figs).

Although we allow a generous range for the conductance parameters (0.01—299% of baseline), some parameters did reach the bounds when fitting the experimental data (Fig 6).

The dissimilarities between the original FR model and the experimental data led to considerable changes in the estimated values for the model parameters for all four cells (Fig 6).

Interestingly, these changes were qualitatively similar between all four myocytes for most of the parameters, indicating conserved differences between our experimental data and the FR model.

In summary, the optimized models show a much closer match to the experimental data as reflected in the individual voltage and current traces as well as in the prediction error.

5, Models 3 and 4) With experimental data (Fig.

These values compare with a mean area of 1.03 for the Experimental Data , which is closest to that of Model 4 (consistent with a visual comparison of Fig.

5 shows individual trajectories from the sample task introduced earlier: while in the serial Models 1 and 2 the initial parts of the trajectories already point towards one of the two buttons, in Models 3 and 4 this is not necessarily the case, as observed empirically in the Experimental Data and in a variety of studies [16, 18, 21, 42].

Experimental data was collected using a MouseTracker apparatus [17] during a visual-lexical decision task to observe the graded effects of competing items attracting the trajectory of the mouse [16].

Here, we considered only those parameter ranges for which neither of the two subpopulations was completely shut down by mutual and/ or recurrent inhibition, because that would be a trivial solution of the network dynamics, which is also not supported by the experimental data [8].

This, however, is a highly simplistic view of the recurrent inhibition within the stria-tum and, as will be described below, is inconsistent with experimental data , especially given the recent findings on the recurrent connectivity in the striatum.

Model predictions and explanation of experimental data

Recent eXperimental data shows higher cortical firing rates in high-conflict situations [38].

In our model, based on the experimental data , FSIs preferentially innervate D1 MSNs [16] in order to maintain the default state of bias as ‘No-Go’ under equal cortical drive, while allowing the cortical activity to switch the balance of D1 and D2 MSNs activity.

Recent experimental data suggest that the activation of ‘Go’ and ‘No-Go’ pathways might not be exclusive in vivo awake behaving animals.

However, recent eXperimental data suggest that such complete shutdown of activity in either one of the two neuron subpopulations may not occur in awake behaving animals [8].

We analyzed the effect of factors, such as the mean firing rate and the recording duration, on the detectability of oscillations and their significance, and tested these theoretical results on experimental data recorded in Parkinsonian nonhuman primates.

We thank Yosef Pinhasi for help With the initial formulation, Moshe Abeles, Dorin Yael and Edward Stein for helpful comments, Anan Moran, Yaara Erez and Hadass Tischler for the experimental data .

The modulation index is validated on the same experimental data demonstrating the unbiased detection of beta oscillation in the globus pallidus during Parkinsonism.

We showed that in both simulated and experimental data , the estimated magnitude of the oscillation depends highly on the mean firing rate of the spike train.

The application of this measure to experimental data recorded from GPi neurons in the Parkinsonian NHP revealed that the modulation index is independent of the firing rate.

Finally, we derive a solution for the evaluation of the actual recording duration required for the detection of spike train oscillations in experimental data .

This implies that in real experimental data , nai've usage of the power spectrum results in a biased detection of oscillatory activity that can easily lead to misinterpretation of the experimental dataset.

Theorems were proven to illustrate the properties and boundaries of the COOP, which was then applied to both synthetic and experimental data .

We have extensively characterized this co-orientational order parameter analytically, validated it using synthetic data, and demonstrated its use with experimental data of Z-lines and actin fibrils architectures in engineered cardiac tissues.

To compare the COOP, COOPC, and COOPu in the analysis of the experimental data , the one way ANOVA with the Student-New-man-Keuls test was used.

The errors and sample sizes were confirmed to be experimentally realistic, thus we next moved to testing the parameter with synthetic and experimental data .

Flow chart sketching the implementation of the neW method for experimental data .

Experimental data (green dots) is taken from [40].

We find that we need to take into account the intriguing, and to our knowledge unexplained, fact that mCLBZ is localised to the growing bud of yeast cells to fully eXplain experimental data [35].

Both model versions were fitted independently to eXperimental data from Aldea and colleagues who analysed asynchronously growing daughter cells using time-lapse microscopy [15].

It is important to stress at this point that the experimental data was generated analysing only daughter cells [15].

Experimental data clearly show that S-GZ-M duration is not constant between different media [13—15].

Since both models reproduce the experimental data for glucose, galactose, raffinose and ethanol (Fig 3A), we conclude that, regardless of compartmentalization, translation of mCLB is a good candidate.

In this study, we use a mathematical model of Dorsal dynamics, fit to experimental data , to determine the ability of the Dorsal gradient to regulate gene expression across the entire dor-sal-ventral axis.

We found that two assumptions are required for the model to match experimental data in both Dorsal distribution and gene expression patterns.

In comparing our modeling results against the experimental data , we found that only when our model includes nuclear Cact and nuclear dl/Cact complex can it account for experimental observations such as the declining basal levels of dl-Venus fluorescence (Fig.

Further experimental data is needed to verify the predictions made by our model; however, the modeling work presented here suggests that, in some cases, an accurate mathematical framework may be necessary to properly interpret fluorescence-based data.

This comports With the experimental data , Which are the average of 10+ embryos.

To this end, experimental data from Xu et al.

In order to improve the fitting to this condition, we can perform a rejection step during the sampling so that every accepted parameter set agrees with the experimental data under this condition.

7B, the inclusion of additional experimental data further constraints the plausible kinetic space.

In this manner, estimated macroscopic constants can readily be compared With available eXperimental data .

This property results from the timescale separation between cytokine diffusion and cytokine uptake (see Fig 1E and SI Text), and explains recent experimental data [7].

Thus, the synaptic cytokine secretion results in locally much higher concentrations than homogeneous secretion (see Fig 1C), in line with experimental data [12].

In accordance with experimental data , already activated IL-2 secreting cells have high IL-2R expression which, for simplicity, we take as constant [37].

Consistent with experimental data [39], AFC themselves do not express IL-2R but constitute simply ‘excluded volumes’ with respect to the IL-2 dynamics.

These findings were supported by experimental data from primary T cells cultured ex vivo [4].

This experimental data (Fig 6B) can be reproduced fairly well by a 9-state cycle model with realistic kinetic parameters (Fig 6A).

Adjustment of the protein concentrations and the consideration of two promoter states (PR2 and PR3), which can each be tran-scriptionally permissive, allows for qualitative correspondence of the model simulations and experimental data .

The experimental data (Fig 6F) can be reproduced by our model (Fig 6E) if the looping event between the distant RE and T88 in the model occurs during the chromatin state corresponding to RNA polymerase II binding.

Using a variety of experimental data and observations, we here compare a number of transcription activation mechanisms in terms of their ability to be both fast enough and responsive to multiple factors.

The protein concentrations were adjusted to fit experimental data .

We establish a relative measure based on apparent simulated melting temperatures that is independent of simulation length and, under certain assumptions, proportional to equilibrium stability, and we justify this theoretical development with extensive simulations and experimental data .

These predictions are in good agreement with statistical analysis of published experimental data and FoldX predictions [8,12].

Conversion of simulation temperature to physical temperature would require use of experimental data (e.g., WT unfolding temperature and deviation of temperatures over all mutants) and therefore would not provide a completely simulation or theo-ry-based prediction.

The simulations are critically assessed by quantitative comparisons with several types of experimental data that provide structural information on both secondary and tertiary levels.

The quality of the simulated ensembles has been assessed by comparing to existing experimental data that provide structural information on both the secondary and tertiary levels [37—40,43].

Theoretical residual dipolar coupling (RDC) values were computed from the simulated ensembles using the PALES software [95], and the final ensemble-averaged RDC profiles were uniformly scaled to best reproduce the experimental data [39].