Physical Constraints in Intracellular Signaling: The Cost of Sending a Bit

Many biological processes require timely communication between molecular components. Cells employ diverse physical channels to this end, transmitting information through diffusion, electrical depolarization, and mechanical waves among other strategies. Here we bound the energetic cost of transmitting information through these physical channels, in $k_{B}T/\mathrm{bit}$, as a function of the size of the sender and receiver, their spatial separation, and the communication latency. These calculations provide an estimate for the energy costs associated with information processing arising from the physical constraints of the cellular environment, which we find to be many orders of magnitude larger than unity in natural units. From these calculations, we construct a phase diagram indicating where each strategy is most efficient. Our results suggest that intracellular information transfer may constitute a substantial energetic cost. This provides a new tool for understanding tradeoffs in cellular network function.

Figure 1

An overview of spatial communication. (a) An abstract transmission scheme that sends information from a sender $I$ to a receiver $O$. The sender locally modifies the density field $\lambda$ with current density $J$, which propagates to the receiver where it is measured as a local perturbation $O(t)$. The input current density $J$ is normalized to separate the effects of the input signal strength and its spatial distribution. The output $O$ is not normalized, reflecting the fact that the receiver’s ability to resolve the signal increases with its size. (b) Outline of calculation for the energetic cost of communication, which depends on the signal transmission strength ${\chi }^{OI}$, the thermal noise $S^O(\omega )$ in the output measurement, and the dissipation kernel $\mathcal{D}(\omega )$ of the input process. (c) Electrical communication between two ion channels in a membrane. The input signal $I(t)$ is the time-varying current flowing through the input ion channel. The output $O(t)$ is the excess charge accumulated at the output ion channel. The density field $\lambda$ is the surface charge density on the membrane. (d) Diffusive signaling in 2D between two proteins embedded in a membrane.

Figure 2

An illustration of the energetic cost of communication for four signaling mechanisms: 2D diffusive signaling (purple), 3D diffusive signaling (red), electrical-membrane signaling (blue), and acoustic signaling in saline water (yellow). Here, the sender-receiver sizes are fixed at ${\sigma }_I={\sigma }_O=5\mathrm{nm}$. Diffusion: $D=0.1\mathrm{\mu }{\mathrm{m}}^2/\mathrm{s}$ ($d=2$), $D=50\mathrm{\mu }{\mathrm{m}}^2/\mathrm{s}$ ($d=3$), typical values in the plasma membrane and cytoplasm [50]. Electrical: $\alpha ={10}^{-6}\mathrm{S}/\mathrm{\mu }\mathrm{m}$ [51], $c={10}^{-14}\mathrm{F}/\mathrm{\mu }{\mathrm{m}}^2$ [52]. Acoustic: $c=1.5\times {10}^9\mathrm{\mu }\mathrm{m}/\mathrm{s}$, $\eta =0.21$, ${\tau }^{\eta }=8.9\times {10}^{-5}$ ($s^{\eta }$) (extracted from ultrasound measurements in blood, see Supplemental Material Sec. 5.2 [32]). (a) The optimality phase space. For each value of signal distance and frequency, the color of the optimal signaling mechanism is displayed. (b) The characteristic length scale $\ell$ is plotted for each signaling mechanism. These draw exclusion zones dictating where signaling mechanisms become prohibitively expensive. (c) The energetic cost of sending information is plotted for each signaling mechanism as a function of distance at a transmission frequency of 0.1 Hz (top) and 1 kHz (bottom).