The two‐state photoreceptor model, which includes ground‐ and active‐state (Sg and Sa) photoreceptors (aka sensors), photoconversion rates k1 and k2, and dark reversion rate kdr, is converted to a “sensing model” for in vivo environments by adding a Sg production rate kS that captures both gene expression and holo‐protein formation, and a dilution rate kdil for both Sa and Sg due to cell growth and sensor degradation (Materials and Methods). The hollow blue pentagon represents a chromophore in the ground state, while the filled blue pentagon represents that in the activated state.
Photoconversion rates are determined by the overlap integral of the spectral flux density of the light source (nlight) and the Sg and Sa photoconversion cross sections σg and σa (Materials and Methods).
The sensing model converts nlight into the active ratio of light sensors Sa/Sg which feeds into an “output model” with a simplified model of TCS signaling that regulates the production rate kG of the target protein G, which is diluted due to cell growth and proteolysis at rate kdil (Materials and Methods).
Figure 2.Characterization and model parameterization for CcaSR
A. Schematic of CcaSR TCS with sfGFP output. Wavelength values represent in vitro measured absorbance maxima.
B–E Training data for the full CcaSR system model (Fig 1C). Experimental observations (“Expt.”) and simulations of the best‐fit model (“Model”) are shown for each set. In particular, the response dynamics to step (B) increases from dark to eight different intensities and (C) decreases from eight different intensities to dark were evaluated using the λc = 526 nm LED. Time points are distributed unevenly to increase resolution of the initial response. (D, E) Steady‐state intensity dose‐response to a set of 23 “spectral LEDs” with λc spanning 369 nm to 958 nm. (D) Forward photoconversion is primarily determined by the response to the spectral LEDs. (E) Reverse photoconversion is analyzed by including light from a second, activating LED (λc = 526 nm at 1.25 μmol m−2 s−1). The λc = 369 nm LED is not capable of reaching the brightest intensities, and thus, those data points are not included. Light intensities are shown in units of 0.1 × log2 μmol m−2 s−1 scale (e.g., a value of 1 corresponds to 10 × 21 = 20 μmol m−2 s−1). sfGFP fluorescence is calibrated to MEFL units (Materials and Methods). Each row of measurements in panels (B–E) was collected in a single 24‐well plate. The 40 plates required to produce the training dataset were randomly distributed across eight LPAs over five separate trials (Materials and Methods and Dataset EV2). Each color patch represents the arithmetic mean of a single population of cells.
F, G Best‐fit model parameters produced via nonlinear regression of the model to training data (Materials and Methods and Table EV4). are unit photoconversion rates (10−3 × min−1/(μmol m−2 s−1), that is, , where I is the LED intensity in μmol m−2 s−1). Uncertainty in the least‐significant digits are indicated in parenthesis.
Figure 3.Estimation of the CcaS photoconversion cross section and spectral validation of the CcaSR model
We estimate the continuous ground‐ and active‐state PCSs of CcaS (, lines) by regressing cubic splines to minimize the difference between experimentally determined photoconversion rates (points) and those predicted via (Materials and Methods, Appendix Figs S5 and S6, and Dataset EV5). Error bars indicate the standard error of the best‐fit values of the photoconversion rates that were determined during model parameterization of CcaSR (Fig 2). The normalized spectral flux densities of the spectral LEDs are shown at bottom.
Using to predict photoconversion rates for light sources not in the spectral LED training set. Predicted photoconversion rates are integrated into the CcaSR model by keeping all other parameters (Fig 2F) fixed, enabling prediction of the intensity dose‐response of CcaSR to the new light source (i.e., G(I)pred.).
Spectral validation of the CcaSR model and consists of prediction of the intensity dose‐response for eight challenging, broad‐spectrum light sources constructed by applying colored filters over white‐light LEDs (Materials and Methods, Tables EV1, EV2 and EV3, and Dataset EV3). Measured nlight, predicted (10−3 × min−1/(μmol m−2 s−1)), measured and predicted intensity dose‐response curves, and RMSE between model and prediction are shown for each LED (Materials and Methods). The forward and reverse intensity responses are determined using the filtered LED alone (circles) and in the presence of a second activating LED (λc = 526 nm at 1.25 μmol m−2 s−1, triangles). The simulated responses are determined using the calculated photoconversion rates (Materials and Methods). RMSE relative errors are expressed in log10 decades (Materials and Methods). Data were collected across four LPAs, and the forward (circles) and reverse (triangles) intensity responses were collected over two separate experimental trials (Materials and Methods and Dataset EV2). Each data point represents the arithmetic mean of a single population of cells.
We compare model predictions of dynamical CcaSR sfGFP output to experimental measurements for time‐varying light inputs from UV (purple line; λc = 389 nm), green (λc = 526 nm), or green plus red (λc = 657 nm) light. In all cases, the light programs (top) are produced using the light program generator algorithm (LPG, Materials and Methods). The LPG uses the model of the system to produce a light program that drives a gene expression simulation (bottom, green line) which closely matches the reference signal (bottom, black line). The simulation (i.e., model prediction), is then compared to the experimentally measured response (bottom, data points). The reference signal consists of a ramp up, hold, and ramp down on a logarithmic scale (Dataset EV6).
“UV mono”. The LPG‐generated UV light signal drives the CcaSR system along a trajectory predicted to follow the reference signal.
“Green mono”. The green LED alone provides an optimized input signal.
“Red perturbation”. The green LED provides the “Green mono” signal, while the red LED generates a sinusoidal perturbative signal (center) with a 240‐min period and 20 μmol m−2 s−1 peak‐to‐peak amplitude.
“Red compensation”. The red perturbative signal is again present. However, the LPG redesigns the green light signal to account for its presence.
Data information: Light signals are shown in units of log10 μmol m−2 s−1, and RMSE relative errors are expressed in log10 decades (Materials and Methods). Error bars correspond to the standard deviation in fluorescence measurements over three independent experimental trials (Table EV4 and Dataset EV2).
Figure EV2.Cph8‐OmpR characterization and model parameterization
A–G Figure details are described in Fig 2, and data are available in Dataset EV7. Note that the reverse action spectrum measurements (E) contain only four intensities of the spectral LEDs rather than the full set of 12 used in the CcaSR experiments.
Figure 5.Characterization and modeling of a multiplexed CcaSR/Cph8‐OmpR system
CcaSR and Cph8‐OmpR are co‐expressed in a single strain. CcaSR regulates the expression of sfGFP, while Cph8‐OmpR regulates the expression of mCherry. Wavelength values are as in Fig 2A.
Training data for the multiplexed model (“Experiment”, Dataset EV8) consists of a two‐dimensional steady‐state intensity dose‐response to green (λc = 526 nm) and red (λc = 657 nm) light. The light intensities are logarithmically distributed, with the green light varying on a 0.05 × log2 μmol m−2 s−1 scale (e.g., a value of −1 corresponds to 20 × 2−1 = 10 μmol m−2 s−1) and the red light varying over a 0.05 × log3 μmol m−2 s−1 scale (e.g., a value of −1 corresponds to 20 × 3−1 = 6.67 μmol m−2 s−1). The different intensity ranges are used to maintain a high‐resolution measurement despite the differences in the intensity dose‐responses of the two systems. The four missing intensity values (white boxes) were not collected. The training data were used to re‐fit the a, b, n, and K Hill function parameters for the CcaSR and Cph8‐OmpR models (Table EV6). Simulated steady‐state responses to the same light environments for the best‐fit dual‐system models (Table EV6) are shown (“Model”). mCherry fluorescence is calibrated to MECY units (Molecules of Equivalent Cy5, Materials and Methods). RMSE relative errors are expressed in log10 decades (Materials and Methods). Data were collected in one experimental trial, and the 192 samples were randomly distributed across eight LPAs (Materials and Methods, Table EV6, and Dataset EV8). Each color patch represents the arithmetic mean of a single population of cells.
Figure 6.Validation of the multiplexed system model
Predicted responses of the multiplexed system (Fig 5A) to time‐varying signals of green (λc = 526 nm) and red (λc = 657 nm) light are compared to experimental results. Reference signals, light programs, and experimental data are as in Fig 4.
“Green mono”. The green LED alone provides an optimized input signal for CcaSR.
“Red mono”. The red LED alone provides an optimized input for Cph8‐OmpR.
“Sum”. The “Green mono” and “Red mono” programs are used simultaneously without any compensation, leading to a substantial deviation of the CcaSR output from the reference trajectory.
“Compensated sum”. The “Red mono” program is used; however, the green light program is produced while incorporating red light program into the LPG (above).
Data information: RMSE relative errors are expressed in log10 decades (Materials and Methods). Error bars correspond to the standard deviation in fluorescence measurements over three separate experimental trials (Table EV6 and Dataset EV8).
Figure 7.Multiplexed biological function generation
The LPG is used to program CcaSR and Cph8‐OmpR outputs to independently follow different reference signals. Red light (λc = 657 nm) programs are optimized first using the LPG, and then, the “Compensated” approach (Fig 6D) is utilized to generate the green light (λc = 526 nm) program (Materials and Methods).
“Dual‐sines”. The sfGFP and mCherry reference trajectories are sinusoids with different periods, amplitudes, and offsets.
“Sine and stairs”. The mCherry signal follows the same sinusoid in “Dual‐sines”, but the sfGFP reference is a stepped trajectory with several plateaus and increasing linear ramps.
“Dual‐stairs”. The sfGFP signal follows the same stair‐shape in “Sine and stairs”; however, the mCherry response is a decreasing stair‐shape.
“Time‐shifted waveform”. The sfGFP and mCherry reference trajectories both follow the same arbitrary waveform consisting of ramps, holds, and a sinusoid, with sfGFP trailing mCherry by 40 min.
Data information: RMSE relative errors are expressed in log10 decades (Materials and Methods). Error bars correspond to the standard deviation in fluorescence measurements over three independent experimental trials (Table EV6 and Dataset EV8).