Breakdown of Mass-Action Laws in Biochemical Computation

  • Fidel Santamaria
  • Gabriela Antunes
  • Erik De Schutter


The objective of this chapter is to describe conditions where the classical laws of mass action and diffusion no longer apply to biological systems, particularly neurons and other types of cells. This type of phenomena typically takes place at the nano- to micro-scale levels. An increasing number of studies show that the classical diffusion process dominated by Brownian motion cannot be directly applied to cells. Instead, a process called anomalous diffusion seems to be fundamental to the propagation of biochemical signals. Anomalous diffusion implies an increase in the correlation of movement among the diffusing molecules, which is the basis of the deviation from classical diffusion phenomena. Such a process has important consequences not only on the diffusion of molecules inside cells but also on their reaction rates. We first describe structural causes of anomalous diffusion and stochastic simulation algorithms that can be used to computationally simulate its effects. We end the chapter by describing another cause of anomalous diffusion, molecular crowding, and speculations on the significance of these phenomena for neural function.


Dendritic Spine Mean Square Displacement Anomalous Diffusion Stochastic Simulation Algorithm Spine Head 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



FS was supported by NSF-HDR 0923339 and EF-1137897. GA and ADS were supported by OISTPC.


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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Fidel Santamaria
    • 1
  • Gabriela Antunes
    • 2
  • Erik De Schutter
    • 2
    • 3
  1. 1.Department of BiologyUniversity of Texas at San AntonioSan AntonioUSA
  2. 2.Computational Neuroscience UnitOkinawa Institute of Science and TechnologyOkinawaJapan
  3. 3.Laboratory of Theoretical NeurobiologyUniversity of AntwerpAntwerpBelgium

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