Modeling non-genetic information dynamics in cells using reservoir computing

TL;DR

It is proposed that environmental signals are transmitted into the cell by ion fluxes along pre-existing gradients through gated ion-specific membrane channels to enable a dynamic and versatile biological system that acquires, analyzes, and responds to environmental information.

Abstract

Virtually all cells use energy and ion-specific membrane pumps to maintain large transmembrane gradients of Na$^+$, K$^+$, Cl$^-$, Mg$^{++}$, and Ca$^{++}$. Although they consume up to 1/3 of a cell's energy budget, the corresponding evolutionary benefit of transmembrane ion gradients remain unclear. Here, we propose that ion gradients enable a dynamic and versatile biological system that acquires, analyzes, and responds to environmental information. We hypothesize environmental signals are transmitted into the cell by ion fluxes along pre-existing gradients through gated ion-specific membrane channels. The consequent changes of cytoplasmic ion concentration can generate a local response and orchestrate global or regional responses through wire-like ion fluxes along pre-existing and self-assembling cytoskeleton to engage the endoplasmic reticulum, mitochondria, and nucleus. Here, we frame our hypothesis through a quasi-physical (Cell-Reservoir) model that treats intra-cellular ion-based information dynamics as a sub-cellular process permitting spatiotemporally resolved cellular response that is also capable of learning complex nonlinear dynamical cellular behavior. We demonstrate the proposed ion dynamics permits rapid dissemination of response to information extrinsic perturbations that is consistent with experimental observations.

Figures (8)

• Figure 1: Intracellular information dynamics model. a. Change in external potassium ion concentration changes potassium diffusive/efflux force, which changes the energy required to maintain the internal potassium concentration resulting in an information signal that gets passed into the cell via conducting cytoskeleton b. Two-dimensional cross-section of a three-dimensional spherical cell model consisting of cell membrane, peripheral cytoplasm, cell-organelles, and cytoskeleton for minimally capturing the intracellular information dynamics. c. Change in local ion-concentration can result in re-assembly of cytoskeletons. d. Mechanism for propagation of information via the cytoskeleton for inducing appropriate cell response. e. Low-resolution animation of information dynamics where the information took 5-time steps (each time step is simulated to be in the range of 2-20$\mu$s) to travel from cell boundary to the central organelle through a random network of cytoskeletons.
• Figure 2: Cell Geometry and Cell-Reservoir. a. 3D spherical cell composed of voxels. b. 2D cross section of cell showing cell membrane (CM), peripheral cytoplasm (PC), cytoskeleton (CS), and central organelle (CO). c. UMAP projection of 3D cell into 2D Space, where the three rows correspond to projections on same cell with all components, without CM, and without CM and PC, respectively, while the right column shows the UMAP nearest neighbor (NN) connection. d. Cell-Reservoir $G(V,E)$ discretizes physical 3D space into $n\times n\times n$ voxels (vertices) by assigning them to the even indices $(2i,2j,2k)$ of a 3D tensor of size $2n-1 \times 2n-1 \times 2n-1$. Each voxel is surrounded by 26 edges. A voxel is either empty ($v=0$) or filled ($v=1$). A cubic R-ball of size $5\times 5\times 5$ can traverse through Cell-Reservoir for locating the NN and their inter-relationships. Each filled vertex has two states that stores the physical signal $I_i$ and the memory signal $S_i$.
• Figure 3: Cell-Reservoir Electrical Properties:a. 2D cross-sectional conductance map of Cell-Reservoir edges, which represents the connection strength between two neighboring voxels. b. A log-normally distributed conductance was assigned to the Cell-Reservoir edges. c-h are Cell-Reservoir potential map, Cell potential map, and Cell information signal map for point source and spherical source respectively. Potential distribution follows the $\exp(-kr)/r$ law and the information flow follow Ohm’s and Kirchhoff’s current laws.
• Figure 4: Reservoir Computing for Cellular Decision-Making. a. Cell-Reservoir has a decision-making (Readout) layer for learning various intracellular decision-making tasks. Information on environmental perturbation, $\delta q^t$, at time $t$ is propagated through the cytoskeleton which reaches the organelle surface node at time $t+\delta t$. The organelle memory state signal, $S^{t+\delta t}$, also shown for a spherical source, can be fed into a Readout Layer for decision-making. The cell decisions, $y^{t+\delta t}$ is then used for appropriate cell response. b. Cell-Reservoir learning sine wave response and c. square wave response for a cosine wave input via linear, lasso, ridge, and artificial neural network readout layer. The left columns show the training mode, and the right columns show the testing mode. Each figure includes the root mean square error between the ground truth and prediction value.
• Figure 5: Spatiotemporally resolved Intracellular Information Dynamics. Snapshots of information flow in a $81\times 81\times 81$ Cell-Reservoir or a $41\times 41\times 41$ Cell for a. Point Source for 40 time-steps (each time steps is about $0.05-0.5 \mu s$) and b. Spherical Source for 12-time steps, color coded with signal strength. Central organelle surface signal map and signal histogram for c. point source and d. spherical source.