Methods and Software

Stochastic biochemical reactions

Intracellular reactions are modelled as stochastic biochemical reactions. Each reaction \(i\) has an exponential waiting time and changes the number of molecules \(X_j\) by the stoichiometric amount \(S_{j,i}\) with the propensity \(w_i(X)\), where \(X\) is the vector of copy number for all modelled species.

Biochemical reactions were simulated using Gillespie's next reaction method. To correctly model the multicellular nature of the system, well-mixed assumptions are only applied at the individual cell level. In other words, each cell was treated separately in evaluating propensities and executing reactions.

Signalling pathways

Hydrodynamics

2D diffusion with active degradation

The STU simulator

A simulator as part of a broad Signal Transmission Undertaking (STU). The STU simulator integrates intracellular stochastic biochemical reactions with extracellular diffusion and cell movement including cell-cell interactions. Hence STU simulator captures the stochastic, continuous, discrete, and spatial phenomena that underlie signal transmission in cell populations. This was not an easy task as the numerical stability of each simulator component involves requirements on spatial and temporal granularity. For details on simulator implementation see Software.

Simulations results

The following STEW simulation study includes the most tasking scenarios to truly push the robustness limits of the IOD band system. Within STEW a laminar flow regime was created in a hemispherical channel. A circulating tumor cell mockup was positioned in the center of the channel. The CTC was free to rotate but remained in the same location through the entire simulation.

Simulation start was marked by the introduction of IODs at a fixed density through the left channel entrance. For the duration of the simulation IODs are acted on by hydrodynamics forces colliding with each other and with the CTC. At the same time IODs generate signalling molecules that diffuse through the medium. When a collision between any two cells occurs, the cell-cell interaction may lead to binding of complementary location tags (antigens displayed on the surface of the IOD cells or the CTC).

Simulation outcome is either true or false depending on whether or not clumping of cells was observed. Clumping of cells may occur around the CTC or elsewhere in the medium. A good IOD band design should lead to clumping only around the CTC and only if the CTC has the targeted marker profile.

This simulation test of IOD band designs is challenging for several reasons:

• Laminar flow maintains constant distance between cells for an extended period of time. Cells that start together stay together as if they were collocated on a CTC.
• Unidirectional flow tends to generate a layer of cells on the forefront of the CTC trapping cells that normally would remain suspended.
• Boolean signalling pathways lack temporal filtering functions capable of suppressing false positives in the case of erroneous binding.

Three different designs were tuned and analysed in terms of response time, robustness, and accuracy. As expected, the structure of the intercellular signalling network is critical in achieving a reliable response.

‘’’Single step auto-activation’’’

‘’’Cross-activation’’’

‘’’Double step auto-activation’’’