Modelling ordinary differential equations using a variational auto encoder

A computer system comprising storage and one or more processors, the storage storing code arranged to run on at least one of the processors, wherein the code is configured so as when run on the at least one processor to perform operations of:

• from each of multiple trials, obtaining a respective series of observations y(t) of a subject over time t;
• implementing a variational auto encoder to model an ordinary differential equation, ODE, wherein the variational auto encoder comprises an encoder for encoding the observations into a latent vector z and a decoder for decoding the latent vector, the encoder comprising at least a first neural network and the decoder comprising one or more second neural networks, wherein the ODE as modelled by the decoder has a state x(t) representing one or more physical properties of the subject which result in the observations y, and the decoder models a rate of change of x with respect to time t as a function f of at least x and z:
• dx/dt=f(x, z);
• and
• operating the variational auto encoder to learn the function f based on the obtained observations y by tuning weights of the first and second neural networks, the learning comprising performing variational inference over the latent vector z, whereby z has a plurality of dimensions and in the encoder each dimension is constrained to comprising one or more samples of a predetermined type of probabilistic distribution parameterized by a respective one or more parameters.

A genetic engineering facility comprising:

• a computer system comprising storage and one or more processors, the storage storing code arranged to run on at least one of the processors, wherein the code is configured so as when run on the at least one processor to perform operations of:
• from each of multiple trials, obtaining a respective series of observations y(t) of a subject over time t;
• implementing a variational auto encoder to model an ordinary differential equation, ODE, wherein the variational auto encoder comprises an encoder for encoding the observations into a latent vector z and a decoder for decoding the latent vector, the encoder comprising at least a first neural network and the decoder comprising one or more second neural networks, wherein the ODE as modelled by the decoder has a state x(t) representing one or more physical properties of the subject which result in the observations y, and the decoder models a rate of change of x with respect to time t as a function f of at least x and z:
• dx/dt=f(x, z);
• and
• operating the variational auto encoder to learn the function f based on the obtained observations y by tuning weights of the first and second neural networks, the learning comprising performing variational inference over the latent vector z, whereby z has a plurality of dimensions and in the encoder each dimension is constrained to comprising one or more samples of a predetermined type of probabilistic distribution parameterized by a respective one or more parameters;
• wherein the subject comprises a device of a genetic circuit inserted into a cell for producing one or more proteins, the device comprising one or more cassettes each comprising at least one respective gene and at least one respective promoter;
• and wherein the one or more properties comprises one or more of:
• a density of copies of the cell in a population from which the observations are observed in the respective trial, and/or an intercellular concentration of any one or more proteins or other species between cells in the population from which the observations are observed in the respective trial;
• wherein the multiple trials comprise trials under conditions of different variants d of the device and/or different external signals u applied to the device, where f is further modelled as a function of one or both of d and u:
• dx/dt=f(x,z,d), dx/dt=f(x,z,u) or dx/dt=f(x,z,d,u), the variants d of the device comprising different cassettes or different combinations of cassette, and/or the different external signals u comprising one or more different treatments or combinations of treatments applied to the device;
• and
• wherein the code is further configured so as, following said learning, to either:
• a) for a given candidate variant of a device d, treatment or treatments u applied to the device, or combination of the variant of the device d and treatment or treatments u, predicting what time profile of x or y would be caused by the candidate device, treatment or treatments, or combination;
• or
• b) for a desired time profile of x or y, inferring what the variant of the device d, treatment or treatments u, or combination of the variant of the device d and treatment or treatments u, would cause the desired time profile;
• wherein the genetic engineering facility further comprises in vitro genetic engineering equipment arranged to produce a genetic circuit based on the running of the program, the production comprising:
• engineering a genetic circuit including the candidate or the inferred variant of the device d in a cell, and thereby causing the cell to produce said one or more proteins with the predicted or desired time profile, respectively;
• engineering a genetic circuit including the variant of the device d in a cell, applying the candidate or inferred treatment or treatments to the device, and thereby causing the cell to produce said one or more proteins with the predicted or desired time profile, respectively;
• engineering a genetic circuit including the candidate or the inferred variant of the device d in a cell, applying the candidate or inferred treatment or treatments to the variant of the device d, and thereby causing the cell to produce said one or more proteins with the predicted or desired time profile, respectively;
• engineering a genetic circuit including in a cell a first additional device approximated by the candidate or inferred variant of the device d, and thereby causing the cell to produce at least one protein resulting from the first additional device;
• engineering a genetic circuit including in a cell a second additional device approximated by the variant of the device d, and applying the candidate or inferred treatment or treatments to the variant of the device d, thereby causing the cell to produce at least one protein resulting from the second additional device;
• or
• engineering a genetic circuit including in a cell a third additional device approximated by the candidate or the inferred variant of the device d, applying the candidate or inferred treatment or treatments to the variant of the device d, and thereby causing the cell to produce at least one protein resulting from the third additional device.