Energy Transfer

N- or C-terminal NanoLuc/Kinase fusions were encoded in pFN31K or pFC32K expression vectors (Promega), including flexible Gly-Ser-Ser-Gly linkers between Nluc and each full-length kinase. Optimal orientations for each construct are described in Table S1. For cellular BRET target engagement experiments, HEK-293 or HeLa cells were transfected with NLuc/target fusion constructs using FuGENE HD (Promega) according to the manufacturer’s protocol. Briefly, Nluc/target fusion constructs were diluted into Transfection Carrier DNA (Promega) at a mass ratio of 1:10 (mass/mass), after which FuGENE HD was added at a ratio of 1:3 (μg DNA: μL FuGENE HD). 1 part (vol) of FuGENE HD complexes thus formed were combined with 20 parts (vol) of HEK-293 cells suspended at a density of 2 x 10⁵ per mL, followed by incubation in a humidified, 37°C/5% CO₂ incubator for 20 hr. For broad kinase profiling experiments, kinase transfections were performed in 96-well plates using plasmid DNAs arrayed based on energy transfer probe affinity. To simplify the work flow, energy transfer probes were binned based on their optimal concentrations for each kinase target. Based on these groupings, the work flow could be simplified and 178 individual kinases could be queried by a single person, in a single day. The analysis can be performed without any automated liquid handling instruments or robotics. Following transfection, cells were washed and resuspended in Opti-MEM. BRET assays were performed in white, 96-well plates (Corning) at a density of 2 x 10⁴ cells/well. All chemical inhibitors were prepared as concentrated stock solutions in DMSO (Sigma-Aldrich) and diluted in Opti-MEM (unless otherwise noted) to prepare working stocks. Cells were equilibrated for 2 hr with energy transfer probes and test compound prior to BRET measurements. Energy transfer probes were prepared at a working concentration of 20X in tracer dilution buffer (12.5 mM HEPES, 31.25% PEG-400, pH 7.5). For target engagement analysis, the energy transfer probes were added to the cells at concentrations optimized for each target, as described in Table S1. For analysis of DDR1 and DDR2 with compound 6j, energy transfer probe 6 was used at a concentration of 300 nM and 330 nM, respectively. To measure BRET, NanoBRET NanoGlo Substrate and Extracellular NanoLuc Inhibitor (Promega) were added according to the manufacturer’s recommended protocol, and filtered luminescence was measured on a GloMax Discover luminometer equipped with 450 nm BP filter (donor) and 600 nm LP filter (acceptor), using 0.5 s integration time. Milli-BRET units (mBU) are calculated by multiplying the raw BRET values by 1000. Apparent tracer affinity values (EC₅₀) were determined using the sigmoidal dose-response (variable slope) equation available in GraphPad Prism (Equation 1);
Competitive displacement data were then plotted with GraphPad Prism software and data were fit to Equation 1 to determine the IC₅₀ value.
For fractional occupancy determination in kinase profiling experiments, the following equation (Equation 2) was used; where X = BRET in the presence of the test compound and energy transfer probe, Y = BRET in the presence of only energy transfer probe, and Z = BRET in the absence of the energy transfer probe and test compound. Predicted biochemical occupancy at the chosen drug dose for kinase profiling experiments was determined from the K_d value reported previously (Davis et al., 2011 (link)) using a variation of the Langmuir Isotherm (Hulme and Trevethick, 2010 (link)) (Equation 3);
For all BRET data shown, no individual data points were omitted.

We now consider an alternate estimate of energy associated with burrowing. Consider a cylindrical burrow perpendicular to the sediment–water interface in which the sediment is excavated from the substrate and redeposited at the sediment–water interface. At a minimum, burrow excavation does work against gravity by lifting particles toward the sediment–water interface:
$$\begin{array}{c}\hfill E_{\mathit{gr}}=mgz,\end{array}$$
where E_gr is the change in gravitational energy [J], m is the mass of sediment moved [M], g is the gravitational acceleration [L] [t⁻²], and z is the vertical distance [L]. The (buoyant?) mass of some portion of the cylindrical burrow with a vertical thickness of Δz is
$$\begin{array}{c}\hfill m=(1-\varphi )({\rho }_s-{\rho }_w)\pi b^2\mathrm{\Delta }z,\end{array}$$
where ϕ is the porosity of the sediment, ρ_s and ρ_w are the densities of sediment and water, respectively, b is the burrow radius, and z is the distance from the center-of-mass to the sediment–water interface. The work of lifting n segments is
$$\begin{array}{c}\hfill \sum _{i=1}^n{E}_{\mathit{gr}}=\sum _{i=1}^n\left[(1-\varphi )({\rho }_s-{\rho }_w)\pi b^2\mathrm{\Delta }z\right]g{z}_i.\end{array}$$
Taking the limit as n goes to infinity and Δz goes to zero, the work for excavating a cylindrical burrow that extends to some depth d below the sediment–water interface is
$$\begin{array}{c}\hfill \begin{array}{cc}\hfill E_{\mathit{gr}}& ={\int }_0^d\left[(1-\varphi )({\rho }_s-{\rho }_w)\pi b^{2}dz\right]gz\hfill \\ \hfill & =\frac{1}{2}(1-\varphi )({\rho }_s-{\rho }_w)\pi b^{2}g{d}^2.\hfill \end{array}\end{array}$$
The result in Eq. 19 is the same as if we had used the entire mass of the burrow in Eq. 17 and raised the center-of-mass from half the burrow depth to the surface.
We now consider the work done in excavating n identical burrows:
$$\begin{array}{c}\hfill E_{\mathit{gr}}=n\left[\frac{1}{2}(1-\varphi )({\rho }_s-{\rho }_w)\pi b^{2}g{d}^2\right]\end{array}$$
If we approximate the rate at which new burrows are created as a continuous process, then
$$\begin{array}{c}\hfill \frac{E_{\mathit{gr}}}{\mathit{dt}}=\frac{\mathit{dn}}{\mathit{dt}}\left[\frac{1}{2}(1-\varphi )({\rho }_s-{\rho }_w)\pi b^{2}g{d}^2\right].\end{array}$$
Under this approximation, the rate at which new burrows are created is related to the linear burrowing velocity by
$$\begin{array}{c}\hfill \frac{\mathit{dn}}{\mathit{dt}}=\frac{1}{d}\frac{\mathit{dz}}{\mathit{dt}}.\end{array}$$
Using Eq. 14, the relationship to the volumetric burrowing rate reported by (22 ) is
$$\begin{array}{c}\hfill \frac{\mathit{dn}}{\mathit{dt}}=\frac{R}{\pi b^{2}d}.\end{array}$$
Substituting Eq. 23 into Eq. 21, we arrive at
$$\begin{array}{c}\hfill \frac{d{E}_{\mathit{gr}}}{\mathit{dt}}=\frac{1}{2}(1-\varphi )({\rho }_s-{\rho }_w)Rgd.\end{array}$$
Dimensional analysis shows that Eq. 24 has units of [J] [L⁻²] [t⁻¹]. The interpretation of these units is the same as for Eq. 15 in the preceding section: a rate of energy transfer per unit area of the sea floor.

Experimental work by ref. 38 (link) shows that burrowing in cohesive substrates can be modeled as propagating a fracture tip. Under these conditions, the work done on the substrate is
$$\begin{array}{c}\hfill E_{\mathit{cr}}=G_{c}wz,\end{array}$$
where E_cr is the work [J] required to propagate the crack, z is the distance [L] the crack propagates, G_c [J] [L⁻²] is the fracture toughness, and w [L] is the width of the crack, which is assumed to be equal to the diameter of the burrow.
If the fracture tip propagates at some linear velocity $\frac{\mathit{dz}}{\mathit{dt}}$ , then the rate of working on the sediments is
$$\begin{array}{c}\hfill \frac{d{E}_{\mathit{cr}}}{\mathit{dt}}=G_{c}w\frac{\mathit{dz}}{\mathit{dt}}.\end{array}$$
Further interpretation of Eq. 13 requires information about how burrowing rates are measured and reported in the literature. The values used here were reported by ref. 22 as a volume of sediment [L³] reworked by a population of organisms with a certain density at or below the seafloor [individuals] [L⁻²]. This quantity, which we refer to as the volumetric reworking rate R, has units of [L³] [L⁻²] [t⁻¹].
To adapt Eq. 13 to the volumetric reworking rate R, we need information regarding body size, specifically the cross-sectional area of the organism which sets the burrow width w. A common method is to approximate an animal’s body by fitting an ellipsoid with a circular cross-section (59 (link)). The relationship between the linear burrowing rate $\frac{\mathit{dz}}{\mathit{dt}}$ and the volumetric reworking rate R is then
$$\begin{array}{c}\hfill \frac{\mathit{dz}}{\mathit{dt}}=\frac{R}{\pi b^2},\end{array}$$
where the burrow radius, b is half the burrow width w in Eq. 13. Combining Eqs. 13 and 14 casts $\frac{d{E}_{\mathit{cr}}}{\mathit{dt}}$ in terms of the volumetric reworking rate R:
$$\begin{array}{c}\hfill \frac{d{E}_{\mathit{cr}}}{\mathit{dt}}=\frac{2G_{c}R}{\pi b}.\end{array}$$
Dimensional analysis of Eq. 15 shows that $\frac{d{E}_{\mathit{cr}}}{\mathit{dt}}$ has units of [J] [L⁻²] [t⁻¹]. These units represent a rate of energy transfer per unit surface area, which we interpret as the rate at which animals transfer energy across the sediment–water interface.

All BRET assays were performed in white, tissue-culture treated 96-well plates (Corning #3917) using adherent HEK-293 cells at a density of 2 × 10⁴ cells per well. All chemical inhibitors were prepared as concentrated stock solutions in DMSO (Sigma-Aldrich) and diluted in Opti-MEM to prepare working stocks. Cells were equilibrated for 2 h with the appropriate energy transfer probe and test compound prior to BRET measurements. Energy transfer probes were prepared at a working concentration of 20× in Tracer dilution buffer (12.5 mM HEPES, 31.25% PEG-400, pH 7.5). Individual kinase NanoBRET assays used the following energy transfer probes and concentrations: PLK1, probe 11 (0.2 μM); PLK2, probe 11 (1.0 μM); PLK3, probe 11 (1.0 μM); WEE1, tracer K10 (Promega, 0.13 μM). To measure BRET, NanoBRET NanoGlo Substrate and Extracellular NLuc Inhibitor (Promega) were added according to the manufacturer’s recommended protocol, and filtered luminescence was measured on a GloMax Discover luminometer equipped with 450 nm BP filter (donor) and 600 nm LP filter (acceptor), using 0.5 s integration time. BRET ratios are calculated by dividing the acceptor luminescence by the donor luminescence. Milli-BRET (mBRET) units (mBU) are calculated by multiplying the raw BRET ratios by 1,000. Broad spectrum profiling on 192 kinases was performed using the K192 NanoBRET Target Engagement assay (Promega) with tracer K10 using the published protocol [24 (link)].