How does biology maintain its function when parameters change?
It has long been shown that different parameter sets give rise to the same function. What we’ve observed in biology supports this – as cells grow, their functions remain robust, despite the fact that its parameters must have changed drastically. How does biology accomplish that? In this paper, the authors show that excitability is dependent on two key parameters S (structure) and K (kinetic), and doesn’t appear to have a higher-dimensional structure. Structural parameters include parameters such as membrane surface area, number of conductance g(V) or ionic concentrations, while kinetic parameters include the rate constants of channels.
The authors first show that any randomly chosen parameter set of the Hodgkin-Huxley model may be easily pushed towards a different outcome (i.e. active/inactive/oscillatory), meaning that it is very sensitive to changes of individual parameters. Next, by doing a parameter sweep and plotting histograms of each outcome as a function of its parameters (see Fig. 3(b) in the original paper), it is observed that the state seems to be dependent on (1) rates of Na and K channels and (2) maximal conductance of Na and K. Therefore S and K is defined as S=g_Na/(g_Na+g_K) and K=(α_n+β_m)/(α_n+β_n+α_m+β_m) respectively. Plotting the results of the parameter sweep in the S-K space yields a structure where the outcome is clearly distinguishable (see Fig. 4(b) in the original paper). The borders of the phases are steep, implying that the system is relatively robust to changes in S (maximal conductance) in extreme statuses.
While very insightful, there are still a lot of questions concerning this subject. For example, what are the homeostatic mechanisms that control these parameter changes? The authors argue that slow inactivation is a local homeostatic mechanism that stabilizes excitability by adjusting S and K. Another question is that some neurons are flexible, so how does biology balance between robustness of function and flexibility? There are still a lot of work required to answer these questions.
Written by Pei-Hsien Liu.
Original paper: Ori, Hillel, et al. “Cellular Function given Parametric Variation in the Hodgkin and Huxley Model of Excitability.” Proceedings of the National Academy of Sciences, vol. 115, no. 35, 2018, doi:10.1073/pnas.1808552115.
The authors first show that any randomly chosen parameter set of the Hodgkin-Huxley model may be easily pushed towards a different outcome (i.e. active/inactive/oscillatory), meaning that it is very sensitive to changes of individual parameters. Next, by doing a parameter sweep and plotting histograms of each outcome as a function of its parameters (see Fig. 3(b) in the original paper), it is observed that the state seems to be dependent on (1) rates of Na and K channels and (2) maximal conductance of Na and K. Therefore S and K is defined as S=g_Na/(g_Na+g_K) and K=(α_n+β_m)/(α_n+β_n+α_m+β_m) respectively. Plotting the results of the parameter sweep in the S-K space yields a structure where the outcome is clearly distinguishable (see Fig. 4(b) in the original paper). The borders of the phases are steep, implying that the system is relatively robust to changes in S (maximal conductance) in extreme statuses.
While very insightful, there are still a lot of questions concerning this subject. For example, what are the homeostatic mechanisms that control these parameter changes? The authors argue that slow inactivation is a local homeostatic mechanism that stabilizes excitability by adjusting S and K. Another question is that some neurons are flexible, so how does biology balance between robustness of function and flexibility? There are still a lot of work required to answer these questions.
Written by Pei-Hsien Liu.
Original paper: Ori, Hillel, et al. “Cellular Function given Parametric Variation in the Hodgkin and Huxley Model of Excitability.” Proceedings of the National Academy of Sciences, vol. 115, no. 35, 2018, doi:10.1073/pnas.1808552115.
留言
張貼留言