Table 1. Maximum likelihood fits of transition rates in wild type C. elegans.

Each cohort was fitted separately; values are expressed as mean ± sem (n = 5 cohorts). Data from wild type cohorts were obtained on the same days as the experimental cohorts for which they served as controls (Tables 3 and 4), but experimental cohorts in this study were separated by weeks to months. All transition rates were constrained to be ≥0. Transition rates that were calculated using the synaptic constraints (Equation 35) are shaded orange; other constrained values are shaded grey. Mean dwell times and state probabilities were calculated from the transition rates. Column A shows fits using the standard model, which has 8 rate constants with two synaptic constraints, resulting in 6 free parameters that determine the 6 synaptic weights (Figure 2C,D; Materials and methods Equations 31–35). Column B shows fits to a model that has only one pause state (X); this model was derived from the standard model by imposing two more constraints: ${\displaystyle a_{FY}=a_{RY}\cong 0}$, yielding 4 free parameters. To allow comparison of models A and B by the likelihood ratio test, which requires tht model B be a special case of model A, ${\displaystyle a_{RY}}$ and ${\displaystyle a_{FY}}$ were set slightly >0 (10^-10 s^-1), thereby avoiding infinite values for ${\displaystyle a_{YF}}$ and ${\displaystyle a_{YR}}$ when applying the synaptic constraints, while maintaining a vanishingly small probability of being in state Y (${\displaystyle p_Y<}$ 10^-18). The log_e likelihood (summed over the 5 cohorts) for model B was 1854 less than for model A, with 30 degrees of freedom for model A (6 per cohort × 5 cohorts) and 20 degrees of freedom for model B (4 per cohort × 5 cohorts). Applying the likelihood ratio test, the difference was highly significant (p<10^-100; p=Chi-squared(2L, df), where L  = 1854 and df  = 30–20 =10. Model C is the most general 3-state (F, R, P) model, which allows all six transitions between the three states. The fitted transition rates for model C were nearly identical to model B. Likelihood values are relative to model A.

	A	B	C
	2 pause states6 free parameters	1 pause state4 free parameters	1 pause state6 free parameters
Δ loge likelihood	0	-1854	-1836
Degrees of freedom	30	20	30
	mean ± sem (n  = 5)	mean ± sem (n  = 5)	mean ± sem (n  = 5)
${\displaystyle a_{XR}}$ (s-1)	1.201 ± 0.099	1.019 ± 0.085	1.008 ± 0.090
${\displaystyle a_{XF}}$ (s-1)	1.115 ± 0.087	1.915 ± 0.152	1.914 ± 0.152
${\displaystyle a_{RX}}$ (s-1)	0.025 ± 0.008	0.507 ± 0.013	0.507 ± 0.013
${\displaystyle a_{RY}}$ (s-1)	0.490 ± 0.015	10-10
${\displaystyle a_{FX}}$ (s-1)	0.182 ± 0.007	0.198 ± 0.009	0.196 ± 0.008
${\displaystyle a_{FY}}$ (s-1)	0.007 ± 0.002	10-10
${\displaystyle a_{YR}}$ (s-1)	0.411 ± 0.019	>109
${\displaystyle a_{YF}}$ (s-1)	4.575 ± 0.533	>109
${\displaystyle a_{FR}}$ (s-1)			0.001 ± 0.001
${\displaystyle a_{RF}}$ (s-1)			0.000 ± 0.000
${\displaystyle d_F}$ (s)	5.329 ± 0.245	5.096 ± 0.235	5.135 ± 0.227
${\displaystyle d_R}$ (s)	1.945 ± 0.043	1.975 ± 0.049	1.976 ± 0.049
${\displaystyle d_X}$ (s)	0.441 ± 0.032	0.349 ± 0.026	0.351 ± 0.027
${\displaystyle d_Y}$ (s)	0.208 ± 0.019	<10-9
${\displaystyle p_F}$	0.762 ± 0.015	0.7641 ± 0.015	0.764 ± 0.014
${\displaystyle p_R}$	0.158 ± 0.007	0.158 ± 0.007	0.155 ± 0.007
${\displaystyle p_X}$	0.063 ± 0.006	0.081 ± 0.008	0.080 ± 0.008
${\displaystyle p_Y}$	0.017 ± 0.002	<10-18