Figure 4.

Information encoding in the noisy harmonic oscillator model. (A) Oscillator at position $x\left(t\right)$ is subjected to random thermal forcing as well as deterministic forcing, $F\left(t\right)$ (Eq. 3). Four force magnitudes, $g_{\mathrm{1,2,3,4}}=\left\{0.6,1.2,1.8,\text{and}2.4\text{pN}\right\}$, serve as input, and $x\left(t\right)$ is output. Other parameters are $t_1=10$ s, $t_2=60$ s, and $\beta =0.01$ s⁻¹. (B) Two sample trajectories (red and green curves) and the average of 5000 trajectories (black curves) corresponding to $g_4=2.4$ pN. Upper: Overdamped oscillators with $m=0.4m_{\text{c}}$, where $m_{\text{c}}={\gamma }^2\text{/}\left(4k\right)=0.25$ mg is the mass at critical damping, $\gamma =1$ pN s/μm, and $k=$ 1 pN/μm. Lower: Underdamped oscillators with $m=9m_{\text{c}}$. Other parameters are $k_{\text{B}}T$ = 0.5 pN μm and $\delta k=0.2$ pN/μm. (C and D) Vectorial mutual information, $M{I}_{\text{v}}$, as a function of sampling start time, $t_{\text{s}}$, at different sampling rates, r (color bar), and memory capacity $n=2$ for (C) overdamped and (D) underdamped oscillators. The black curve represents the scalar mutual information, $M{I}_{\text{s}}$, at each time point. (E) $M{I}_{\text{v}}$ as a function of n at fixed sampling rate $r=1/30$ Hz and sampling start time (black curve, $t_{\text{s}}=0$; red curve, $t_{\text{s}}=40$ s). $n=$ 1 corresponds to $M{I}_{\text{s}}$. (F) Maximal $M{I}_{\text{v}}$ over all $t_{\text{s}}$ values as a function of r for fixed memory capacity $n=2$. Error bars in (C)–(F) represent the mean ± SD of 20 independent trials for each condition. To see this figure in color, go online.