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Conceived and designed the experiments: FY IAS CMH JSS RS. Performed the experiments: FY JF XL CWL. Analyzed the data: IAS FY RS. Contributed reagents/materials/analysis tools: FY IAS JF XL RS. Wrote the paper: IAS FY RS. Introduced the idea to optimize drug combinations using a mathematical feedback algorithm: CHM.

Current address: Johnson & Johnson Pharmaceutical Research & Development LLC, San Diego, California, United States of America,

The authors have declared that no competing interests exist.

The ability to control cellular functions can bring about many developments in basic biological research and its applications. The presence of multiple signals, internal as well as externally imposed, introduces several challenges for controlling cellular functions. Additionally the lack of clear understanding of the cellular signaling network limits our ability to infer the responses to a number of signals. This work investigates the control of Kaposi's sarcoma-associated herpesvirus reactivation upon treatment with a combination of multiple signals. We utilize mathematical model-based as well as experiment-based approaches to achieve the desired goals of maximizing virus reactivation. The results show that appropriately selected control signals can induce virus lytic gene expression about ten folds higher than a single drug; these results were validated by comparing the results of the two approaches, and experimentally using multiple assays. Additionally, we have quantitatively analyzed potential interactions between the used combinations of drugs. Some of these interactions were consistent with existing literature, and new interactions emerged and warrant further studies. The work presents a general method that can be used to quantitatively and systematically study multi-signal induced responses. It enables optimization of combinations to achieve desired responses. It also allows identifying critical nodes mediating the multi-signal induced responses. The concept and the approach used in this work will be directly applicable to other diseases such as AIDS and cancer.

There is an increasing interest in utilizing and applying systems biological approaches to study a wide range of problems in biology. In this work, we apply different systems biological approaches to investigate the effects of multiple signals on cellular signaling processes with the goals of understanding and controlling these processes. As a model systems, we use the reactivation of Kaposi's Sarcoma-associated herpesvirus (KSHV) to investigate the effects of several drugs on a quantifiable process, virus reactivation. KSHV, also known as human herpesvirus-8 (HHV-8), is a member of the herpesvirus family, which includes simplex viruses, Epstein-Barr virus (EBV) and cytomegalovirus

Herpesviruses have two distinct phases in their life cycle: latency and lytic replication. Latency is one strategy for viruses to achieve life-long persistent infection. During latency, the viral genome is replicated by cellular DNA polymerase and only a few gene products are expressed at low levels. A reactivation process causes the virus to enter the lytic replication state from latency and upon replication of the viral genome by a viral DNA polymerase, viral progeny are produced, frequently resulting in cell death. Virus reactivation is controlled by a cellular signaling process in which cellular signals are amplified and can be measured with markers such as Green Fluorescent Protein (GFP) or luciferase. In earlier work, we identified RTA (replication and transcription activator) of KSHV, an immediate-early gene, as the switch in the reactivation process

Reactivation, the switch from latency to lytic replication, is an important process for KSHV pathogenesis and a target for the development of therapeutic strategies for the associated tumors. Investigation of the multi-drug regulated reactivation process provides important information for the associated cancer treatment. It should be therapeutically advantageous to intentionally activate the viral lytic cycle in tumor cells in the presence of an anti-herpesviral drug, such as ganciclovir

Maximal induction of virus replication is necessary for an effective therapeutic approach. Several studies have looked at inducing KSHV reactivation with a single drug

Here, we utilize different approaches to study the problem of multi-signal induced KSHV reactivation. First, we utilized mathematical modeling and learning tools to enable systematic and effective selection of combinations of drugs that can result in high reactivation. This approach is based on using input-output data obtained by testing a relatively small number of signal combinations to create a mathematical model that can predict the responses to the complete space of combinations of considered signals and their respective concentrations. The model, in turn, was used for further analysis of the system and to select combinations that can control the cellular responses in a desired manner. Second, we utilized a stochastic search algorithm to drive a set of experimental trials with the goal of identifying combinations of signals that can yield high reactivation. The results of both approaches were compared and further experimental assays were used to validate the results. Third, we used a combination of linear regression models and subset selection algorithms to identify key factors influencing the multi-signal driven responses. We were able to identify multiple drug interactions that play a dominant role in the response. These interactions represent a subset of the possible connections between the signaling targets.

Five drugs were selected to be tested in combination (See

(A) Shown are the five drugs that are used in the drug combinations and the mechanisms by which they induce KSHV reactivation. The diagram also illustrates the known crosstalk among these five drugs.

In order to quantify the viral reactivation response, the RTA binding site in the PAN promoter was identified

Measurement of virus reactivation was achieved using flow cytometry where we measured the number of activated cells, i.e., GFP positive, and the total number of cells, i.e., the number of dead and living cells. The reactivation rate (performance) of any given combination was set to be the ratio of GFP positive cells to the total number of cells including dead cells.

Investigation of the combinatorial effect of multiple participating pathways on reactivation can be achieved by treating the latently-infected cells with related chemical agents. Single drug dose curves for each chemical agent were obtained to determine the range of effectiveness of each individual chemical agent (

Drug Name | Conc. No. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Bortezomib | Conc. I (nM) | 0 | 1.25 | 2.5 | 5 | 10 | 20 | 40 | 80 | 160 | 320 |

(C1) | Conc. II (nM) | 0 | 1.25 | 2.5 | 3.75 | 5 | |||||

db-cAMP | Conc. I (mM) | 0 | 0.03 | 0.06 | 0.13 | 0.25 | 0.5 | 1 | 2 | 4 | 8 |

(C2) | Conc. II (mM) | 4 | 5 | 6 | 7 | 8 | |||||

Prostratin | Conc. I (uM) | 0 | 0.31 | 0.63 | 1.25 | 2.5 | 5 | 10 | 20 | 40 | 80 |

(C3) | Conc. II (uM) | 20 | 25 | 30 | 35 | 40 | |||||

Valproate | Conc. I (mM) | 0 | 0.02 | 0.05 | 0.09 | 0.19 | 0.38 | 0.75 | 1.5 | 3 | 6 |

(C4) | Conc. II (mM) | 1.5 | 2 | 2.5 | 3 | 3.5 | |||||

Dexamethasone | Conc. I (nM) | 0 | 1.56 | 3.12 | 6.25 | 12.5 | 25 | 50 | 100 | 200 | 400 |

(C5) | Conc. II (nM) | 0 | 3 | 25 | 100 | 200 |

Using a uniform probability distribution over the set of all combinations of concentrations of five drugs, we randomly selected 600 different combinations to be experimentally tested. Six sets of experiments were conducted. In each set, 100 data points along with a positive control, a single drug (TPA) known to reactivate the virus

The inputs (drug combinations) and their corresponding measured outputs (reactivation rates) were used to generate a mathematical model, KSHV reactivation model. The predictive reactivation model approximates the KSHV reactivation rate as induced by a combination of drugs within the specified range of drug concentrations. The model can be used to simulate and predict reactivation rates in response to all combinations of the five chemical agents. The combinations are not limited to the 600 tested combinations and include all combinations of the lower order mixtures, i.e., two, three, and four-drug combinations. The use of this relatively small number of combinations is facilitated by the assumption that the response function to these five drugs is reasonably smooth. If the response function is not very smooth then it would require testing of additional combinations to improve the accuracy and prediction power of the model.

Several methods can be used to generate a mathematical model. We utilize neural networks, linear regression

We trained a multi-layered perceptron with the data and obtained a representative predictive model (see the

(A) Shown is the correlation between the measured reactivation (x-axis) and the predicted reactivation (trained outputs) (y-axis) using 588 out of 600 total input-output points (see

The predictive model generated provides the ability to determine combinations that can lead to high reactivation rates as predicted by the model. The simulated reactivation rates of all

(A) Distribution of the concentrations of the five drugs in the 50 drug combinations that lead to the highest KSHV reactivation rates simulated by the predictive reactivation model (blue bars). The drug concentration ranges in the optimal drug concentrations generated by the experiment-based cross entropy procedure are shaded in red. The bottom right figure shows a histogram of the reactivation rate of the top performing 50 samples. (B) Representative KSHV reactivation outputs for five-drug combinations. The results of the 1st (top graph) and 12th (middle graph) iterations in the first set of optimization iterations, and the 3rd (bottom graph) iteration in the second set of optimization iterations with smaller concentration ranges are shown. The x-axis represents the different drug combinations used in each iteration; the y-axis shows relative percentage of GFP-positive cells in the total cell population. The highest percentage of GFP-positive cells in individual iterations is set as 1.

An alternate approach to determine the top performing combinations is to utilize a search algorithm, deterministic or stochastic. Examples include gradient descent algorithms

The cross entropy algorithm was implemented in silico using the KSHV predictive reactivation model (see

An alternate approach to optimizing drug combinations is the use of a search algorithm implemented experimentally rather than on a mathematical model. Recently, several examples of this approach has emerged in biology

The experimental cross entropy implementation proceeded in a sequence of experimental iterations. Our results showed that after 12 to 14 iterations, the drug concentrations converged to the ranges leading to consistently high reactivation rates (

Using two different approaches, we were able to identify a range of concentrations for which high virus reactivation rates are achievable. The results of the two approaches were consistent. To further validate the findings, we conducted sets of experiments to compare the performance of a selected combination from the identified range to the performances of single drugs.

The KSHV early lytic protein K8 is activated by, and expressed after the expression of KSHV RTA (ORF50). It is important for initiating viral DNA replication in the lytic cycle, thus a good marker for viral lytic replication. Western blot analysis of K8 showed that the selected drug combination can cause a much higher induction of K8 than any single drug. The conclusion was consistent 8 hours and 12 hours post treatment (

The figure shows the experimental validation results of the optimal drug combination for KSHV reactivation determined via the cross entropy algorithm. (A) Western blots showing KSHV lytic protein K8 expression 8 hr or 12 hr after drug treatment. The results were quantified as indicated in the

Additionally, we looked at the effect of the selected drug combination on the KSHV lytic transcripts RTA (ORF50) and PAN. RTA plays a central role in regulating the switch from latency to lytic replication in KSHV

The signaling network involves complex connections between various molecules that can be perturbed through a large number of external signals. The signals can cause inhibition of certain molecules/pathways and stimulation of others. The interactions amongst these molecules or pathways are very complex and very hard to predict. Alternately, looking at interactions between the input signals and the measured cellular outputs can shed some light on the induced behaviors at the systems level. Particularly, we can uncover some of the interactions of the signaling that are involved in generating the responses upon stimulation with multiple stimuli.

Based on the predictive reactivation model, we simulated the interactions generated by the five drugs. The data represents a complex multi-dimensional data set. While some mathematical tools can be useful in reducing this complexity, one might be interested in visually examining the behaviors represented by such a large data set. To that end we created an interactive webpage which displays the KSHV reactivation rates for varying concentrations of the considered drugs

Our findings indicate that the dose dependent effect of the individual drugs on reactivation greatly depended on the amounts of the other drugs within the same treatment (

Figure showing plots of the KSHV reactivation rates as a function of drugs db-cAMP and Prostratin, for various concentrations of drug Bortezomib. The colors are solely a function of the reactivation levels in each panel. (A) Drugs Valproate and Dexamethasone are fixed at zero. (B) Drugs Valproate and Dexamethasone are fixed at 6 mM and 210.5 nM.

The addition of low concentrations of Bortezomib to combinations of db-cAMP and Prostratin does not result in a significant increase in performance. Higher concentrations of Bortezomib result in a significant decrease in performance. Examining the effect of only adding Valproate to combinations of Bortezomib, db-cAMP, and Prostratin, we notice an increase in performance, indicating that Valproate interacts positively with the three-drug combinations to improve the reactivation. The sole addition of Dexamethasone to combinations of Bortezomib, db-cAMP, and Prostratin results in a smaller increase in performance. The increase becomes less when high concentrations of Bortezomib are used.

The above results reflect visual analysis of the responses, in the sequel, we seek to quantitatively analyze these interactions to determine the most significant ones. Such can be achieved using mathematical modeling similar to what is used for optimization. While a drawback of neural networks models is that they are black-box models and do not shed light onto how the different inputs are processed to produce the outputs, other modeling techniques can help in this regard. We fitted a linear regression model to represent the relationship between the drugs and the reactivation (see

The correlation coefficient between the experimental data and predicted data based on the linear model was 85%, the correlation coefficient for the additional 48 points was 83%. The model provides an insight into which factors play the biggest role in the response (

(A) Plot of the regression coefficients of the different regressors used in linear regression. (B) Plot of the percentage of variance explained as a function of the number of Partial Least Squares components used in Partial Least Squares Regression. (C) Plot of the lowest residual sum of squares for models of

The residual sum of squares of the best models shows that there is no significant reduction in the residual sum of squares for models with more than 10 variables (95% reduction in the residual sum of squares). This indicates that 10 variables are sufficient to generate a model with comparable prediction and error to the 31-variable model (

Testing a system with five drugs provides advantages over studying mixtures of a smaller set of drugs. A system level study of combinations of multiple drugs enables fast and effective selection of a smaller subset of drugs that is most potent. Although a set of five drugs was used in this study, it is sometimes desirable to use a smaller number of drugs that can interact in a desirable way. We computed the maximum predicted reactivation rate for all possible mixtures of two, three, four, and five drugs, as well as for single drugs (

(A) Plot of the maximum achievable reactivation rates using combinations of two, three, four, and five drugs as predicted by the mathematical KSHV reactivation model. (B) A summary of the predicted interactions between the applied drugs and their effects of these interactions on KSHV reactivation.

For two-drug mixtures, there is over a six-fold difference between best and worst two-drug combinations. A mixture of Bortezomib and Dexamethasone or Valproate and Dexamethasone perform poorly even compared to a single drug. In contrast, a combination of db-cAMP and Prostratin have a reactivation rate higher than the sum of the individual reactivation rates. Prostratin and Valproate exhibit a similar behavior. This is consistent with our findings of strong positive interaction between Prostratin and Valproate. A mixture of Bortezomib and Prostratin does not improve on the best reactivation rate of Prostratin, suggesting negative or no interaction between the two drugs. This is also consistent with the findings presented above.

For three-drug combinations, the best combination is more than twice as effective as the worst mixtures. Furthermore, the best three-drug mixture is about 130% more effective than the best two-drug mixture. Four and five-drug mixture are slightly more effective than the best three-drug mixture. The four-drug mixtures generally perform better than than the three-drug mixtures.

Without a study of the combinations of five drugs, evaluating the reactivation rates for combinations of two drugs requires conducting 10 experiments individually to determine the maximum reactivation rate of the 10 possible two-drug combinations out of a set of possible five drugs. Selection of three or four-drug combinations requires similar experiments. Therefore, the combinations of the systems approach, computational tools, and experimental design enabled efficient multi-signal control of cellular/viral processes.

Our results indicate that the use of combinations of drugs can have a substantial effect on virus reactivation. In particular, multiple drugs can interact and induce higher levels of virus reactivation. However, the combination needs to be judiciously selected out of a large number of drug concentration combinations. The use of an improperly selected combination can have a drastic effect on the cellular response and on virus reactivation. The low reactivation rates of combinations imply either the ineffectiveness of these combinations in reactivating the virus or the high toxicity of these combinations. The biological relevance of our results was supported by multiple experimental assays that directly measured viral lytic replication products, and demonstrated a synergistic reactivation by a proper drug combination, much higher than by any individual drug, a pattern very consistent with what was obtained in the fluorescent reporter system. The measurement of virion production 48 hours post treatment also confirms our findings and provides additional proof of the validity of our approach. The work presented here, builds upon our recent work in which the approaches used here were introduced to address another problem of multiple signal response quantification and analysis and were applied to study the differential response of cancer and normal cells

With the development of genomics and proteomics, more and more cellular components and their physical interactions are identified. However, their dynamic functional interactions have not been studied extensively or quantitatively. Systems biological approaches are emerging with the aim of understanding these functional interactions. In retrospect, a mathematical model-based approach provides means for understanding system level behaviors exhibited by the interacting cellular components in response to one or multiple stimuli.

Moreover, the emerging interest and need to develop combination therapies and individualized medicine calls for additional efforts in analyzing multi-signal induced cellular responses. Studies should also involve examining multiple cellular outputs or network signaling intermediates in response to multiple cellular inputs. The approach used in this work is capable of addressing such problems. Additionally, examining the kinetics of cellular responses will allow for more dynamic control.

This study using KSHV reactivation as a model system to study multi-signal response quantification, a general issue in cell biology. The concept and the approach used in this work will be directly applicable to other problems such as Epstein-Barr Virus (EBV)-associated malignancies. Moreover, many cancers and HIV associated malignancies can benefit from systematic approaches to studying multi-signal induced responses.

The selection of suitable drug combinations was achieved using two different approaches. The experiment-based cross entropy implementation involved iterative testing of combinations in order to search for best performing combinations. The algorithm showed reasonable convergence. The advantages of experiment-based optimization are apparent when the objective function is clearly defined and we are interested in achieving that goal in a reasonably smaller number of tests. Furthermore, when there is no interest in deducing more information regarding the relationship between input signals and output responses, an experiment-based optimization approach can yield satisfactory results without added experimental overhead.

On the other hand, a model-based approach was also quite effective in achieving the desired goals. The results were consistent between the two different approaches emphasizing the power of using various mathematical tools to study biological problems. Generating a predictive model required testing a relatively small number of drug combinations. As the combinations are tested over a shorter period of time, the sensitivity of this approach to variations in cell conditions is less prevalent than the experiment-based approach. Another advantage of a model-based approach is that it enables optimizing combinations based on a different number of performance functions with varying sets of parameters without additional experimental measurement. This allows efficient analysis of multiple optimization questions and enables customization of combinations to specific needs, e.g., personalization of treatment based on an individual's characteristics. The model also can be used to study problems beyond the optimization and control of cellular responses such as analyzing the relationships between the various signals in view of the effects of these signals on some measured the cellular outputs.

The selected drugs target distinct parts within the signaling network. Yet, there are significant interactions between the targets of these drugs through other molecules within the signaling network. To illustrate this, we have summarized the interactions as predicted by the neural network model and through the regression analysis (

The negative interaction between Bortezomib and Prostratin is consistent with the observation based on the neural network model. The positive interactions between db-cAMP and prostratin, and valproate and Prostratin are also consistent with the observations based on the neural network model. The reported interactions indicate that PKC activates NF-kB in T and B lymphocytes. It has been reported that NF-kB inhibits reactivation both

The comparison between known knowledge of the cellular pathways targeted by the drugs and the potential interactions we have obtained from the drug combination study can shed light on the molecular mechanisms of reactivation regulation by cellular factors. For example, some of our observations of the drug interactions here are consistent with our knowledge about the signaling pathways these drugs target. In view of the positive interaction between db-cAMP and Dexamethasone, it is suggested that Dexamethasone could potentiate PKA signaling and thereby facilitate PKC signaling, possibly through the synergistic effect on CRE-mediated gene expression, and CREB may be playing an important role in the mediation of CRE-dependent transcription

On the other hand, the data provides several questions that can be the basis for new studies. The results suggest that a strong positive interaction exists between Valproate and Prostratin. The underlying mechanisms of this interaction are not clear and require further investigation. Moreover, it is of importance to investigate further the causes of positive or negative interactions of the signals inducing reactivation. The utilization of the proper interactions, by judicious selection of drug doses, led to a significant increase in virus reactivation. Furthermore, there are indications of accelerated response with a combination of signals as opposed to a single signal. This potential acceleration in the response suggests the nonlinearity of the cellular responses. It provides multiple opportunities to verify, analyze, and quantify this change, particularly for providing a mathematical framework for this change, as well as for studying some of its mechanistic causes.

In our previous work, a genome-wide cDNA screen was performed to systematically identify cellular signals that regulate viral reactivation

Bortezomib is a proteasome inhibitor that at least in part reactivates KSHV by inhibiting NF-kB activity

With the utilization of the five drugs that function in different yet potentially connected signaling processes (

The BC-3-G cell line was established as previously described

In our setup, the cells were plated in 24-well plates (5

The western blots were performed using a rabbit polyclonal antibody against KSHV early lytic protein K8, and the quantification of the western blot bands was done using the Image-Quant image analysis software (Molecular Dynamics).

The RT-Q-PCR was performed in an Opticon2MJ thermocycler (MJ Research). The primers used for RT-Q-PCR were: ORF50-F (

Supernatants from cells treated with chemicals were collected and cleared by centrifugation first at

A multi-layered perceptron with two hidden layers was used to fit the model. The hidden layers consisted of 40 and 20 neurons respectively. The transfer function (activation function) of each neuron is a sigmoidal function. The selection of this neural network structure was a result of trying different structures with a varying number of neurons. The input and output data was pre-processed prior to training by mapping them into the [−1, 1] range. Outputs of the network were post-processed to map them back to the original range. Preprocessing of data allows for better training of the network. A back-propagation Levenberg-Marquardt algorithm was used to train the neural network. The neural network fitting algorithm divides the data into three sets, training (98%), validation (1%), and testing (1%). The training and validation sets are used to train the model and prevent overfitting of data. The testing data is used for post analysis to assess the models predictive capabilities. However, this set is small and no meaningful conclusions can be drawn from it. Instead, we tested an additional set of 48 combinations and used that to test the generalizability of the model (see main text). The low percentages of validation and training set sizes were chosen to maximize the number of points used to fit the model. Training of the model was done using the neural network toolbox of Matlab.

We applied the cross entropy combinatorial optimization algorithm both to the predictive reactivation model and experimentally to optimize multi-drug combinations for high KSHV reactivation. The search process evolves in iterations in which the performances of selected points are evaluated. The selected points are randomly chosen using joint Gaussian probability density function over the set of all combinations. The assumption of independence between the different input variables results in a joint density function which is the product of Gaussian distributions, each associated with an input variable. Each Gaussian distribution has a mean and a standard deviation which are continuously updated through the iterations of the algorithm. The means and standard deviations of the distributions reflect the current belief of the values of the maximizing inputs as well as the confidence level. The evolution of the means and standard deviations is based on the convex combination of the current means and standard deviations, and the means and standard deviations of a top performing percentage of model-predicted (or experimentally-measured) performances. The algorithm terminates when the change in the means becomes small and the standard deviations approach zero.

In the experimental CE implementation, and similar to the simulated CE implementation, 45 drug combinations were selected in our setup to enable the collection of as many stimuli- response data as enabled by manual measurements. In each iteration, the performances of 45 randomly chosen sample combinations were experimentally evaluated. The top performing 16% of combinations were used to update the means and standard deviations. The choice of 45 combinations was based on a feasible number of combinations to be tested manually in duplicates and based on the previous section. The iterations proceeded for months.

The response of the virus is experimentally measured and is denoted by the function

Notice that since the smallest value for the concentrations is zero, taking the log is not possible. Instead, we replace the zero elements in the concentrations with a pseudo element equal to one half of the lowest concentration greater than zero. Whenever the random outcome of a sample element is the pseudo element, it is replaced with zero in the testing stage.

Therefore, the elements of the samples, i.e.,

To make sure that all data points lie within the allowable input range, any point lying outside the allowable input range was dropped and a new point was generated using the same probability density function. Furthermore, the random outcomes are rounded off or discretized to the nearest possible concentration value in the following manner. First, let

The discretized

It is important to note that implementation of the CE method to the mathematical model is not necessary unless the number of drugs and concentration is very large, in which case the CE method provides a computational faster approach for searching for the optimal. For systems with 5 drugs a simple sorting algorithm that ranks combinations based on their performance suffices and is reasonably fast.

We used a regression model that is linear in the log of the concentrations. The model is of the form

Examining the eigenvalues of the correlation matrix

To evaluate the convergence of the cross entropy method, we ran several simulations. First, one thousand different runs of cross entropy were executed, each using 45 samples per iteration. The same initial means and standard deviations were used for all one thousand runs. The results showed that the algorithm converged to combinations whose performance is within 16% of the maximum performance. Out of the one thousand runs, 556 converged within 5% of the maximum performance and 778 within 10% of maximum performance. A similar set of simulations was also conducted except that the initial means for the one thousand runs were randomly chosen, thereby starting with different parts of the combination space. All one thousand runs converged within 21% of the maximum. 557 runs converged to within 5% of the maximum performance, whereas 776 converged within 10% of the maximum performance.

A similar set of simulations was also conducted in which the number of samples per iterations was increased to 100 samples, thereby sampling the combination space with a higher density. The results show that with all runs starting from the same initial set of means and standard deviations, all runs converged to combinations with a performance within 13% of the maximum performance. Out of the one thousand runs 730 converged within 5% and 922 within 10%. Starting with randomly chosen means at the beginning of every run resulted in similar numbers with all one thousand runs converging within 13% of the maximum performance, with 735 runs converging within 5% and 935 converging within 10%.

In the above simulations, the algorithm used the performances of the top performing 16% of the samples within each iteration to update the means and standard deviations. Decreasing the number to 8% with 100 samples per iteration the algorithm converged within 12% of the maximum performance for all one thousand runs starting with the same initial set of means and standard deviations. 850 converged within 5% and 987 converged within 10%. Starting from randomly chosen means convergence was to within 16% of the maximum performance with 859 runs converging within 5% and 984 runs within 10%.

In all, the simulations suggest that the optimization algorithm is capable of consistently identifying top performing combinations without requiring to test many samples. This also introduces an important question on whether the algorithm can be utilized to drive a set of experimental trials to optimize the reactivation of the virus reactivation. Such a result would provide validation of the computational approach and would also suggest a direct experimental approach that can be used to optimize drug combinations through a sequence of trials.