Dual specificity protein kinase activity catalyzing autophosphorylation and phosphorylation of exogenous substrates on both serine/threonine and tyrosine residues (PubMed:10207045). Regulates the cellular cytoskeleton by enhancing actin stress fiber formation via phosphorylation of cofilin and by preventing microtubule breakdown via inhibition of TAOK1/MARKK kinase activity (PubMed:18216281, PubMed:11555644). Inhibits podocyte motility via regulation of actin cytoskeletal dynamics and phosphorylation of CFL1 (By similarity). Positively regulates integrin-mediated cell spreading, via phosphorylation of cofilin (By similarity). Suppresses ciliogenesis via multiple pathways; phosphorylation of CFL1, suppression of ciliary vesicle directional trafficking to the ciliary base, and by facilitating YAP1 nuclear localization where it acts as a transcriptional corepressor of the TEAD4 target genes AURKA and PLK1 (By similarity). Probably plays a central role at and after the meiotic phase of spermatogenesis (PubMed:8537404). ATP + L-seryl-[protein] = ADP + H(+) + O-phospho-L-seryl-[protein] ATP + L-threonyl-[protein] = ADP + H(+) + O-phospho-L-threonyl-[protein] ATP + L-tyrosyl-[protein] = ADP + H(+) + O-phospho-L-tyrosyl-[protein] Activated by autophosphorylation on Ser-215. Kinase activity is inhibited by SPRED1. Interacts (via both C- and N-termini) with SPRY4 (via C-terminus); the interaction inhibits TESK1 kinase activity (PubMed:17974561). Interacts with TAOK1; the interaction inhibits TAOK1 kinase activity (PubMed:18216281). Interacts (via C-terminus) with SPRED1 (via C-terminus); the interaction inhibits TESK1 kinase activity (PubMed:17974561, PubMed:18216281). Interacts (via C-terminus) with PARVA/PARVIN (via C-terminus); the interaction inhibits TESK1 kinase activity (PubMed:15817463). Interacts with YWHAB/14-3-3 beta; the interaction is dependent on the phosphorylation of TESK1 Ser-439 and inhibits TESK1 kinase activity (PubMed:11555644). Interacts with SPRY1, SPRY3 and SPRED2 (PubMed:17974561). Interacts (via C-terminus) with SPRY2 (via C-terminus); the interaction disrupts SPRY2 interaction with PPP2CA/PP2A-C, possibly by vesicular sequestration of SPRY2 (PubMed:17974561). Therefore dephosphorylation of SPRY2 by the serine/threonine-protein phosphatase 2A (PP2A) holoenzyme is lost, inhibiting its interaction with GRB2 (PubMed:17974561). Colocalizes with SPRY4 in vesicular spots in the cytoplasm (By similarity). Localized to F-actin-rich lamellipodia at the cell periphery following fibronectin-mediated cell adhesion of Schwann cells (PubMed:22302232). Weakly expressed in sciatic nerves (at protein level) (PubMed:22302232). Highly expressed in testicular germ cells (PubMed:8537404, PubMed:10207045). Expressed at low levels in brain, lung, heart, liver and kidney (PubMed:10207045). Induced by fibronectin-mediated cell adhesion of Schwann cells (PubMed:22302232). Induced by sciatic nerve crush injury, expression peaks 2 weeks post-injury and returns to normal at 4 weeks post-injury in the macrophages of promyelinating Schwann tubules (PubMed:22302232). The extracatalytic C-terminal part is highly rich in proline residues. Autophosphorylated on serine and tyrosine residues. Belongs to the protein kinase superfamily. TKL Ser/Thr protein kinase family.