Probability distributed time delays: integrating spatial effects into temporal models.

Area of Science:

• Computational Biology
• Biochemical Modeling
• Systems Biology

Background:

• Accurate cell modeling requires balancing physical phenomena representation with computational cost.
• Spatial inhomogeneities significantly impact cellular system behavior.
• Spatially-resolved stochastic methods offer biological realism but are computationally expensive.

Purpose of the Study:

• To develop computational methods that accurately model spatial processes in cells.
• To reduce the computational expense of complex cellular simulations.
• To enable exploration of cellular dynamics over extended timescales.

Main Methods:

• Incorporation of spatial information via probability distributed time-delays.
• Utilizing a delay stochastic simulation algorithm (DSSA).
• Development of an alternative approach using delay differential equations (DDE) for high concentration scenarios.

Main Results:

• The proposed methods achieve a balance between computational cost and accurate representation of spatial processes like diffusion.
• Successfully integrated spatial information into temporal stochastic and deterministic simulations.
• Demonstrated feasibility of exploring cellular scenarios with diffusion and stochasticity over significantly larger time spans.

Conclusions:

• The novel methodologies accurately capture spatial processes, enhancing simulation accuracy at reduced computational costs.
• These methods overcome the limitations of current spatially-resolved simulators regarding achievable simulation time spans.
• Enables previously unfeasible exploration of cellular dynamics influenced by diffusion and stochasticity.