Multi-input distributed classifiers for synthetic genetic circuits

Abstract

For practical construction of complex synthetic genetic networks able to perform elaborate functions it is important to have a pool of relatively simple modules with different functionality which can be compounded together. To complement engineering of very different existing synthetic genetic devices such as switches, oscillators or logical gates, we propose and develop here a design of synthetic multi-input classifier based on a recently introduced distributed classifier concept. A heterogeneous population of cells acts as a single classifier, whose output is obtained by summarizing the outputs of individual cells. The learning ability is achieved by pruning the population, instead of tuning parameters of an individual cell. The present paper is focused on evaluating two possible schemes of multi-input gene classifier circuits. We demonstrate their suitability for implementing a multi-input distributed classifier capable of separating data which are inseparable for single-input classifiers, and characterize performance of the classifiers by analytical and numerical results. The simpler scheme implements a linear classifier in a single cell and is targeted at separable classification problems with simple class borders. A hard learning strategy is used to train a distributed classifier by removing from the population any cell answering incorrectly to at least one training example. The other scheme implements a circuit with a bell-shaped response in a single cell to allow potentially arbitrary shape of the classification border in the input space of a distributed classifier. Inseparable classification problems are addressed using soft learning strategy, characterized by probabilistic decision to keep or discard a cell at each training iteration. We expect that our classifier design contributes to the development of robust and predictable synthetic biosensors, which have the potential to affect applications in a lot of fields, including that of medicine and industry.

Fig 1. Scheme of a two-input linear classifier circuit.

x ₁, x ₂—inputs inducing the corresponding promoters, RBS_A1 and RBS_A2—ribosome binding sites determining the strengths of the input branches, A—intermediate transcription factor (same in both input branches), GFP—reporter gene.

Fig 2. Hard classification technique.

P ₁, P ₂, P ₃—positive classes of individual linear classifiers, D—negative class of the collective classifier.

Fig 3. Training a distributed classifier with a linear target border.

(A) Target classes: P—positive, D—negative. (B) Trained ensemble region on the plane of parameters: hatched area.

Fig 4. Simulation results for hard classification.

Response of a trained distributed classifier in the space of inputs. Black-white dashed line—target (predefined) class border, white (black) filled circles—samples from the negative (positive) class, color—number of the positively responding cells (quantities 40 and above marked with same color).

Fig 5. Scheme of a two-input classifier circuit with a bell-shaped response.

x ₁, x ₂—inputs inducing the corresponding promoters, RBS_U1 and RBS_U2—ribosome binding sites determining the strengths of the input branches, U₁, U₂—intermediate repressor/activator factors, Z₁, Z₂—outputs of the individual branches, GFP—reporter gene.

Fig 6. Simulation results for soft classification strategy applied to separable classes.

(A) Untrained (master) population output (color). (B) Trained population output (color). White (black) filled circles—samples from the negative (positive) class, black-white dashed line—classification border of the trained classifier.

Fig 7. Simulation results for soft classification strategy applied to inseparable classes.

Notations same as in Fig 6.