Closed-loop control of cellular functions using combinatory drugs guided by a stochastic search algorithm

Abstract

A mixture of drugs is often more effective than using a single effector. However, it is extremely challenging to identify potent drug combinations by trial and error because of the large number of possible combinations and the inherent complexity of the underlying biological network. With a closed-loop optimization modality, we experimentally demonstrate effective searching for potent drug combinations for controlling cellular functions through a large parametric space. Only tens of iterations out of one hundred thousand possible trials were needed to determine a potent combination of drugs for inhibiting vesicular stomatitis virus infection of NIH 3T3 fibroblasts. In addition, the drug combination reduced the required dosage by approximately 10-fold compared with individual drugs. In another example, a potent mixture was identified in thirty iterations out of a possible million combinations of six cytokines that regulate the activity of nuclear factor kappa B in 293T cells. The closed-loop optimization approach possesses the potential of being an effective approach for manipulating a wide class of biological systems.

Fig. 1.

Iterative cycle of the closed-loop optimization approach. At each iteration, the cells are stimulated by a drug mixture from a predetermined set of concentrations. The biological activity of interest is then evaluated. The information is then fed into a stochastic search algorithm to determine the drug combination for the next iteration. The cycle repeats iteratively until a potent drug mixture is identified.

Fig. 2.

The principle and procedure of the Gur Game are illustrated by searching drugs with potent antiviral activities. The antiviral activity (AVA) refers to the percentage of cells not being infected by the virus. (a) Assume the drug concentrations, C1 and C2, have AVA of 40% and 80%, respectively (Top). The procedure of performing the Gur Game for searching for the best concentration of the antiviral drug is shown in Middle and Bottom. In the experiment, the AVA is first tested and expressed as a number between 0 (0% AVA) and 1 (100% AVA). A random number between 0 and 1 is generated after each test. If the AVA is smaller than the random number, then the concentration will be switched in the next iteration. Otherwise, the drug concentration will stay in the next iteration. In this example, the system has a higher chance to stay at concentration C2 and to switch at concentration C1. This asymmetric decision provides the “bias” of the search that leads the concentration toward high AVA. The random number introduces “randomness” in the decision, because the concentration of the drug may switch even at a high AVA. As a result, the search will not be trapped at a drug concentration of a local maximal biological response. (b) A hypothetical experiment is shown to illustrate the procedure. In this example, it can be proven mathematically that the chance of the system to choose the drug concentration C2 (AVA = 0.8) will be 0.75, whereas the probability of choosing drug concentration C1 (AVA = 0.4) is 0.25 (see SI Appendix). (c) The procedure can be extended to multiple drugs with different concentration levels each. An example of two drugs with four concentrations each is shown. Each drug is assigned with a set of discrete concentrations, represented by −2, −1, 1, and 2. After each experiment, a random number is generated for each drug. If the random number is larger than AVA, the concentration will be switched. Otherwise, the concentration will either stay or be switched in an attempt to further improve the performance (see SI Appendix). The random number introduces randomness in the search and the system collectively “biases” toward drug combinations with potent antiviral effects. Therefore, the procedure implements a “bias random walk” of drug concentrations to search for potent drug cocktails.

Fig. 3.

Optimizing antiviral drug combinations with the Gur Game. Inhibition of viral activity is defined as the percentage of uninfected cells (indicated by GFP expression). (a) Four sets of experiments were performed to determine potent drug cocktails. Set 2 converges in <10 iterations and identifies a potent combination that inhibits the viral activity completely. Set 3 and set 4 converge at the 12th and 14th iteration, respectively. (b) Bright field and fluorescence micrographs of NIH 3T3 cells treated with VSV at 1 multiplicity of infection (moi) with and without the drug combination identified in set 2.

Fig. 4.

Searching for a cytokine mixture that optimizes NF-κB activity. (a) Concentration of individual cytokines TNFα (gray filled square), TNFβ (red filled circle), IL-1α (green filled triangle), IL-1β (blue inverted triangle), EFG (cyan open square), and BAFF (magenta open triangle) applied at different iterations. The initial concentration of all of the cytokines was 2.5 ng/ml. (b) Normalized GFP intensity at different iterations. Iterations 17, 23, and 28 are labeled with black open squares. (c) Dynamic response of NF-κB activity for cells treated with the cytokine combination (blue filled circle), TNFα 50 ng/ml (green asterisk), and control (red open circle). Data are normalized to the maximum intensity for cells treated with the cytokine combination. Data represent the mean ± SEM from at least 100 cells inside the microfluidic channels. (d) Searching paths for TNFα and TNFβ and (e) searching paths for IL-1α and IL-1β. Black open squares represent cytokine concentrations at iteration 17. Each color represents a particular path.

Fig. 5.

Effectiveness of drug cocktails. (a) Low dosages of combinatory drugs for inhibiting 100% of the virus activity. After optimization, the optimal drug combination contains IFNα and IFNγ with concentrations orders of magnitude smaller than ribavirin and puromycin; therefore, they are not visible in the plot. All of the concentrations are labeled in the plot. (b) When drug is applied individually, a high concentration of ribavirin or puromycin is required to completely inhibit VSV activity. (c) Percentages of inhibition by individual drugs at the concentrations found in the potent drug combination. Red line represents inhibition of viral activity by using the potent drug combination. Red dots present inhibition of viral activity by individual drugs.

Fig. 6.

Sensitivity analysis of individual cytokines in the potent cytokine combination. Concentrations of TNFα (a), TNFβ (b), IL-1α (c), IL-1β (d), EGF (e), and BAFF (f) were varied while keeping the other cytokine concentrations constant. Data show mean ± SEM of at least 300 cells. Experiments were conducted in 96-well plates. The cells were stimulated with the appropriate concentration of cytokines for one hour and washed with fresh media. Fluorescence measurements were carried out seven hours after stimulations.