Fig. 1: The introduction of CryoTRANS.

a CryoTRANS leverages a high-resolution initial map denoted by f₀ and a lower-resolution target map denoted by f₁ as inputs. It then utilizes a neural network-parameterized velocity field \(\vec{V}\) to construct a pseudo-trajectory within the 3D coordinate space of the initial map. This pseudo-trajectory is achieved by discretizing a governing ODE into ten pseudo-time points. During training, the model minimizes a loss function that incorporates the Wasserstein distance between the final generated map \(\hat{{f}_{1}}\) and the target map f₁. The gradient of this loss function is backpropagated through the neural network to optimize its parameters. b Diagram of the Wasserstein Distance: quantifies the minimum effort required to transform the densities in the generated map \({\hat{f}}_{1}\) to match those in the target map f₁. c The intermediate density maps at different pseudo-time points generated by CryoTRANS using the trained velocity field \(\vec{V}\). This pseudo-trajectory, visualized as an orange cube, represents the path of a specific voxel within the density map. These example maps are simulations derived from atomic models of Mm-cpn^34,35 in two conformations: the closed state (PDB 3J03) and the open state (PDB 3IYF).