Effect of pH on the ternary solution behavior of beta-lactoglobulin

Ternary phase diagrams (TPDs) were constructed for aqueous beta-lactoglobulin solutions containing ethanol and (NH4)2SO4 at pHs of 7, 5, and 3 for temperatures between 20 and 70 degrees C. The addition of (NH4)2SO4 generally led to the production of a reversible precipitate, a transformation that was not strongly influenced by temperature or pH. In contrast, at pH 7 and 20 degrees C, ethanol concentrations >12% led to the formation of a molten-globule structure, which gelled at protein concentrations >10%. Destabilization of beta-lactoglobulin structure occurred at lower ethanol concentrations as temperature was increased, until at 70 degrees C, all solutions that were previously liquid at room temperature had transformed into a gel. At pH 5.0, near beta-lactoglobulin's isoelectric point, demixing dominated, leading to the creation of either irreversible precipitates or a paste-like microgel. Elevated temperatures caused the previously liquid morphology to transform into either a reversible aggregate or microgel. Solution behavior at pH 3 had characteristics of what was observed at pHs 7 and 5. At moderated protein and ethanol concentrations, a paste-like microgel was observed, whereas at higher ethanol concentrations, beta-lactoglobulin formed a gel. This work demonstrates how small changes in protein structure at the molecular level can have a dramatic effect on macroscopic morphology.     

Tension response in skinned Ca-activated skeletal muscle fibers of the frog to temperature jump following stepwise changes in the fiber length

Joulean temperature jump from 4-7 degrees to 20-25 degrees completed in 0.2 ms was applied to suspended in the air chemically skinned Ca-activated (pCa = 5.5-6) skeletal muscle fibres of the frog 2 ms after stepwise length changes (duration 0.3 ms, amplitudes --6. +3 nm per half sarcomere). The temperature jump induced a biphasic rise of tension, as was described earlier. Neither the time constant of the 2nd slow phase, nor maximum tension after the temperature jump were dependent on the length step amplitude. The amplitude and time constant of the 1st phase (1.2-0.28 ms) decreased after the fibre release. It shows that the 1st phase of the tension rise induced by the temperature jump is due to conformation in cross-bridges attached to thin filaments.     

Salt-dependent monomer-dimer equilibrium of bovine beta-lactoglobulin at pH 3

Although bovine beta-lactoglobulin assumes a monomeric native structure at pH 3 in the absence of salt, the addition of salts stabilizes the dimer. Thermodynamics of the monomer-dimer equilibrium dependent on the salt concentration were studied by sedimentation equilibrium. The addition of NaCl, KCl, or guanidine hydrochloride below 1 M stabilized the dimer in a similar manner. On the other hand, NaClO(4) was more effective than other salts by about 20-fold, suggesting that anion binding is responsible for the salt-induced dimer formation, as observed for acid-unfolded proteins. The addition of guanidine hydrochloride at 5 M dissociated the dimer into monomers because of the denaturation of protein structure. In the presence of either NaCl or NaClO(4), the dimerization constant decreased with an increase in temperature, indicating that the enthalpy change (DeltaH(D)) of dimer formation is negative. The heat effect of the dimer formation was directly measured with an isothermal titration calorimeter by titrating the monomeric beta-lactoglobulin at pH 3.0 with NaClO(4). The net heat effects after subtraction of the heat of salt dilution, corresponding to DeltaH(D), were negative, and were consistent with those obtained by the sedimentation equilibrium. From the dependence of dimerization constant on temperature measured by sedimentation equilibrium, we estimated the DeltaH(D) value at 20 degrees C and the heat capacity change (DeltaC(p)) of dimer formation. In both NaCl and NaClO(4), the obtained DeltaC(p) value was negative, indicating the dominant role of burial of the hydrophobic surfaces upon dimer formation. The observed DeltaC(p) values were consistent with the calculated value from the X-ray dimeric structure using a method of accessible surface area. These results indicated that monomer-dimer equilibrium of beta-lactoglobulin at pH 3 is determined by a subtle balance of hydrophobic and electrostatic effects, which are modulated by the addition of salts or by changes in temperature.     

Formation of domains of cationic or anionic lipids in binary lipid mixtures increases the electrostatic coupling strength of water-soluble proteins to supported bilayers

The electrostatic binding strength of water-soluble proteins having either an excess positive (cytochrome c) or negative (beta-lactoglobulin) electric charge to oppositely charged supported planar bilayers (SPBs) was studied as a function of the bilayer phase state (fluid or gel phase) by IR-ATR spectroscopy. The bilayer consisted of mixtures of zwitterionic DEPC with either cationic DMTAP or anionic DMPG. We observed drastic differences in the binding strength of both proteins for the two bilayer phase states, with the gel phase exhibiting a higher binding strength than the fluid phase, under conditions where the two lipid components had different hydrophobic chain lengths resulting in a nonideal mixing behavior. In addition, for beta-lactoglobulin we observed a strong binding to a gel phase SPB comprising DEPC/DMTAP, while raising the temperature of the SPB above the chain melting transition temperature of the mixture resulted in a complete unbinding of the protein. In contrast, for DMPC/DMTAP having the same cationic charge content but no hydrophobic chain mismatch, no phase-dependent coupling strength of the protein to the SPB was observed. Our results suggest that the formation of charge-enriched domains by partial demixing of the bilayer lipids at the transition to the gel state is crucial for modulation of the protein binding strength to the SPB, while the intrinsic charge of the solid support surface is of minor importance.     

A kinetic study of protein-protein interactions.

Kinetic studies have been carried out of the monomer-dimer interaction of insulin, beta-lactoglobulin, and alpha-chymotrypsin using stopped-flow and temperature-jump techniques. The pH indicators bromothymol blue, bromophenol blue, and phenol red were used to monitor pH changes associated with the monomer-dimer interaction. In all three cases a kinetic process was observed which could be attributed to a simple monomer-dimer equilibrium, and association (k1) and dissociation (k-1) rate constants were determined. The results obtained are as follows: for insulin at 23 degrees C, pH 6.8, 0.125 M KNO3, k1 = 1.14 X 10(8) M-1 s-1, k-1 - 1.48 X 10(4)s(-1); for beta-lactoglobulin AB at 35 degrees C, pH 3.7, 0.025 M KNO3, d1 = 4.7 X 10(4) M-1 s-1, k-1 = 2.1 s-1; for alpha-chymotrypsin at 25 degreesC, pH 4.3, 0.05 M KNO3 k1 - 3.7 X 10(3) M-1 s-1, k-1 - 0.68 s-1. The kinetic behavior of the separated beta-lactoglobulin A and B was similar to that of the mixture. In the case of chymotrypsin, bromophenol blue was found to activate the enzyme catalyzed hydrolysis of p-nitrophenyl acetate, and a rate process was observed with the temperature jump which could be attributed to a conformational change of the indicator-protein complex. The association rate constant for dimer formation of insulin approaches the value expected for a diffusion-controlled process, while the values obtained for the other two proteins are below those expected for a diffusion-controlled reaction unless unusally large steric and electrostatic effects are present.     

Interaction mode specific reorganization of gel phase monoglyceride bilayers by beta-lactoglobulin.

The interaction between beta-lactoglobulin and sonicated aqueous dispersions of the gel phase forming monoglyceride monostearoylglycerol were studied using isothermal titration calorimetry, direct binding experiments, differential scanning calorimetry, leakage of a fluorescent dye and solid-state (31)P- and (2)H-NMR. In the absence of a charged amphiphile, monostearoylglycerol forms a precipitate. Under these conditions, no interaction with beta-lactoglobulin was observed. In the presence of the negatively charged amphiphile dicetylphosphate, the gel phase monostearoylglycerol formed stable and closed, probably unilamellar, vesicles with an average diameter of 465 nm. beta-Lactoglobulin interacts with these bilayer structures at pH 4, where the protein is positively charged, as well as at pH 7 where the protein is negatively charged. Under both conditions of pH, the binding affinity of beta-lactoglobulin is in the micromolar range as observed with ITC and the direct binding assay. At pH 4, two binding modes were found, one of which is determined with ITC while the direct binding assay determines the net result of both. The first binding mode is observed with ITC and is characterized by a large binding enthalpy, a decreased enthalpy of the MSG L(beta) to L(alpha) phase transition and leakage of a fluorescent dye. These characteristics are explained by a beta-lactoglobulin induced partial L(beta) to coagel phase transition that results from a specific electrostatic interaction between the protein and the charged amphiphile. This explanation is confirmed by solid-state (2)H-NMR using 1-monostearoylglycerol with a fully deuterated acyl chain. Upon interaction with beta-lactoglobulin, the isotropic signal in the (2)H-NMR spectrum of the monostearoylglycerol-dicetylphosphate mixture partially transforms into a broad anisotropic signal which could be assigned to coagel formation. The second binding mode probably results from an aspecific electrostatic attraction between the negatively charged bilayer and the positively charged protein and causes the precipitation of the dispersion. At pH 7, only the first binding mode is observed.     

Determining the optimal whole-body vibration dose-response relationship for muscle performance

Da Silva-Grigoletto, ME, de Hoyo, M, Sa?udo, B, Corrales, L, and García-Manso, JM. Determining the optimal whole-body vibration dose-response relationship for muscle performance. J Strength Cond Res 25(12): 3326-3333, 2011-The aim of this investigation was twofold: first, to determine the optimal duration of a single whole-body vibration (WBV) exposure (phase 1) and second to find out the ideal number of sets per intervention to maximize muscle performance (phase 2). All participants were young (age: 19.4 ± 1.6 years), healthy, physically active men. In both studies, a 30-Hz frequency and a 4-mm peak-to-peak displacement were used. In phase 1, subjects (n = 30) underwent 3 sets of different durations (30, 60, and 90 seconds), whereas in phase 2, subjects (n = 27) underwent 3 interventions where the duration remained fixed at 60 seconds, and the number of sets performed (3, 6, or 9) was modified. The recovery time between sets was set at 2 minutes. In all interventions, each set consisted of 1 isometric repetition in a squat position with knees flexed at 100°. Before and after each session, jump height (countermovement jump [CMJ] and squat jump [SJ]) and power output in half squat (90° knee flexion) were assessed. In phase 1, an improvement in jump ability and power output was observed after the 30- and 60-second intervention (p < 0.01), whereas the 90 second intervention, participants just experienced a decrease in SJ and CMJ (p < 0.05). When comparing the different protocols, the greatest response was achieved using 60 seconds (p < 0.05), which was therefore considered as the optimal duration to be used in phase 2. In the second phase, improvements in jump ability and power output were found with 3 and 6 sets (p < 0.05), whereas with 9 sets, participants actually experienced a decrease in these variables. Intergroup comparison showed a greater effect for the program of 6 sets (p < 0.05). In conclusion, a WBV intervention consisting of six 60-second sets produces improved muscle performance measured by SJ, CMJ, and power output.     

ESR study of aqueous dispersions of beta-lactoglobulin and spin-labelled glyceryl monostearate.

From the ESR spectra of aqueous dispersions of synthetic glyceryl monostearate (spin labelled at C-12) a critical micelle concentration of 30 mumol/l at room temperature was obtained, which agrees with that deduced from surface tension measurements. At monoglyceride concentrations smaller or larger than the critical micelle concentration, the monomers show increased motional restriction with increasing molar ratio of beta-lactoglobulin to monoglyceride up to a value of 10, as determined from calculated rotational correlation times; A similar progressive interaction was deduced from spectral changes observed on equimolar dispersions of beta-lactoglobulin and monoglyceride on raising the temperature to 55 degrees C at which the protein and monoglyceride coprecipitate. The relevance of these finding for non-labelled monoglyceride dispersions is indicated by the similarity of the pH-dependent flocculation behaviour of labelled and non-labelled monoglycerides, both in the absence and presence of beta-lactoglobulin; In addition, proton magnetic resonance and mechanical stability measurements suggest that spin-labelled glyceryl monosterate behaves analogously to non-labelled glyceryl monooleate.     

Unfolding kinetics of beta-lactoglobulin induced by surfactant and denaturant: a stopped-flow/fluorescence study

The beta-->alpha transition of beta-lactoglobulin, a globular protein abundant in the milk of several mammals, is investigated in this work. This transition, induced by the cationic surfactant dodecyltrimethylammonium chloride (DTAC), is accompanied by partial unfolding of the protein. In this work, unfolding of bovine beta-lactoglobulin in DTAC is compared with its unfolding induced by the chemical denaturant guanidine hydrochloride (GnHCl). The final protein states attained in the two media have quite different secondary structure: in DTAC the alpha-helical content increases, leading to the so-called alpha-state; in GnHCl the amount of ordered secondary-structure decreases, resulting in a random coil-rich final state (denatured, or D, state). To obtain information on both mechanistic routes, in DTAC and GnHCl, and to characterize intermediates, the kinetics of unfolding were investigated in the two media. Equilibrium and kinetic data show the partial accumulation of an on-pathway intermediate in each unfolding route: in DTAC, an intermediate (I(1)) with mostly native secondary structure but loose tertiary structure appears between the native (beta) and alpha-states; in GnHCl, another intermediate (I(2)) appears between states beta and D. Kinetic rate constants follow a linear Chevron-plot representation in GnHCl, but show a more complex mechanism in DTAC, which acts like a stronger binding species.     

The stabilization of beta-lactoglobulin by glycine and NaCl

Effect of glycine and NaCl on the thermal denaturation of beta-lactoglobulin was examined. The results showed that the transition temperature of beta-lactoglobulin is increased by the addition of glycine and NaCl at 0.5 and 1M. This observed stabilization by glycine and NaCl was interpreted in terms of their favorable interactions with the native state of beta-lactoglobulin and unfavorable interactions with the denatured state.     

Characterization of beta-lactoglobulin A gelation in the presence of sodium caprate by ultrasound spectroscopy and electron microscopy

The effect of sodium caprate (a fatty acid salt) on the formation of beta-lactoglobulin A gels was studied at constant temperature (30 or 35 degrees C) using ultrasonic spectroscopy. During incubation at these temperatures, ultrasonic attenuation increased with the addition of sodium caprate, and reached a plateau after 5-7 h of incubation. Comparing beta-lactoglobulin A with and without sodium caprate, a decrease in net ultrasonic velocity was observed. These results suggested that aggregation occurred during incubation with sodium caprate, and the sample showed an increase in compressibility. Transmission electron microscopy with negative staining showed the formation of filamentous aggregates of beta-lactoglobulin A at around 3-4.5 h of incubation with sodium caprate. These results demonstrated that sodium caprate induced the formation of structures with unique gel properties compared to those formed by heating beta-lactoglobulin in the presence of NaCl alone.     

Influence of preactivity and eccentric muscle activity on concentric performance during vertical jumping

The purpose of this investigation was to observe the influence of increasing amounts of preactivity and eccentric muscle activity imposed by three different jump types on concentric vertical jumping performance. Sixteen athletes involved in jumping-related sports at Appalachian State University, which is a Division IA school, performed a static jump (SJ), counter-movement jump (CMJ), and drop jump (DJ). Force, power, velocity, and jump height were measured during each jump type. In addition, muscle activity was measured from two agonist muscles (vastus lateralis, vastus medialis) and one antagonist muscle (biceps femoris). Preactivity and eccentric phase muscle activity of the agonist muscles (average integrated electromyography) was significantly (p < or = 0.05) higher during the DJ (preactivity, 0.2 +/- 0.11 mV; eccentric phase, 1.00 +/- 0.36 mV) in comparison with the CMJ (preactivity, 0.11 +/- 0.10 mV; eccentric phase, 0.45 +/- 0.17 mV). Peak concentric force was highest during the DJ and was significantly different among all three jump types (SJ, CMJ, DJ). Maximal jump height was significantly higher during the DJ (0.41 +/- 0.05 m) and CMJ (0.40 +/- 0.06 m) compared with the SJ (0.37 +/- 0.07 m). However, no significant difference in jump height existed between the CMJ and DJ. A positive energy balance, as assessed by force-displacement curves during the eccentric and concentric phases, was observed during the CMJ, and a negative energy balance was observed during the DJ. The data from this investigation indicate that a significant increase in concentric vertical jump performance is associated with increased levels of preactivity and eccentric phase muscle activity (SJ to CMJ). However, higher eccentric loading (CMJ to DJ) leads to a negative energy balance during the eccentric phase, which may relate to a non-significant increase in vertical jump height, even with coincidental increases in peak concentric force. Practitioners may want to focus on improving eccentric phase muscle activity through the use of plyometrics to improve overall jumping performance in athletes.     

Effect of Temperature on Growth, Development and Reproduction of Meloidogyne hapla in Lettuce

Temperature was an important factor in growth, development and reproduction of Meloidogyne hapla in lettuce. Growth, as measured by increase in diameter of females, was not appreciably different at the intermediate (21.1 C night and 26.7 C day) and high (26.7 C night and 32.2 C day) temperature regimes, but was considerably less at the low temperature regime (15.5 C night and 21.1 C day) than at the two higher temperature regimes. Second-stage female larvae developed into adults 14 days after inoculation at the high, 18 days at the intermediate and 34 days at the low temperature regime. Eggs were observed 20 days after inoculation at the high, 26 days at the intermediate and 54 days at the low temperature regime. Number of eggs and larvae after 6 weeks was greater at the high than at the intermediate temperature regime and no eggs or larvae occurred at the low temperature regime during the observed 6 weeks.     

Localized cooling of stems induces latewood formation and cambial dormancy during seasons of active cambium in conifers

Background and Aims In temperate regions, trees undergo annual cycles of cambial growth, with periods of cambial activity and dormancy. Environmental factors might regulate the cambial growth, as well as the development of cambial derivatives. We investigated the effects of low temperature by localized cooling on cambial activity and latewood formation in two conifers, Chamaecyparis obtusa and Cryptomeria japonica.Methods A plastic rubber tube that contained cooled water was wrapped around a 30-cm-wide portion of the main stem of Chamaecyparis obtusa and Cryptomeria japonica trees during seasons of active cambium. Small blocks were collected from both cooled and non-cooled control portions of the stems for sequential observations of cambial activity and for anatomical measurements of cell morphology by light microscopy and image analysis.Key Results The effect of localized cooling was first observed on differentiating tracheids. Tracheids narrow in diameter and with significantly decreased cambial activity were evident 5 weeks after the start of cooling in these stems. Eight weeks after the start of cooling, tracheids with clearly diminished diameters and thickened cell walls were observed in these stems. Thus, localized low temperature induced narrow diameters and obvious thickening of secondary cell walls of tracheids, which were identified as latewood tracheids. Two months after the cessation of cooling, a false annual ring was observed and cambium became active again and produced new tracheids. In Cryptomeria japonica, cambial activity ceased earlier in locally cooled portions of stems than in non-cooled stems, indicating that the cambium had entered dormancy sooner in the cooled stems.Conclusions Artificial cooling of stems induced latewood formation and cessation of cambial activity, indicating that cambium and its derivatives can respond directly to changes in temperature. A decrease in the temperature of the stem is a critical factor in the control of cambial activity and xylem differentiation in trees.     

The pH jump study of enzyme proteins. I. Liquefying alpha-amylase from Bacillus subtilis.

Rapid conformational changes due to pH jump were studied kinetically at 25 degrees mainly by the stopped-flow method using liquefying alpha-amylase from Bacillus subtilis [EC 3.2.1-.1, liquefying]. First, the conformational change due to a pH jump produced by mixing with alkali was monitored as a function of time at 245 nm through the ionization of phenolic hydroxyl groups of tyrosine residues which were originally buried and finally become exposed due to the pH jump. Three distinct phases of conformational change were clearly recognized by this method by varying the final pH values. Each phase involved the exposure of an essentially definite number of tyrosine residues, whose rate constant was crucially dependent on pH. Second, these phases of conformational change were subjected to examination in terms of the optical rotation change at 411 nm and the reversibility upon reverse pH jump with respect to conformational reconstitution, as observed through the protonation ofphenolic hydroxyl groups of ionized tyrosine residues and the enzyme activity. The first phase, which occurs above pH 12.5, involves no change in the optical rotation and is reversible as observed by the above two monitoring methods. In contrast, the other two phases, which are observed above pH 12.7, are accompanied by an optical rotation change and no appreciable reversibility was detected by these methods.     

The diversity of the liquid ordered (Lo) phase of phosphatidylcholine/cholesterol membranes: a variable temperature multinuclear solid-state NMR and x-ray diffraction study

To investigate the properties of a pure liquid ordered (Lo) phase in a model membrane system, a series of saturated phosphatidylcholines combined with cholesterol were examined by variable temperature multinuclear (1H, 2H, 13C, 31P) solid-state NMR spectroscopy and x-ray scattering. Compositions with cholesterol concentrations>or=40 mol %, well within the Lo phase region, are shown to exhibit changes in properties as a function of temperature and cholesterol content. The 2H-NMR data of both cholesterol and phospholipids were used to more accurately map the Lo phase boundary. It has been established that the gel-Lo phase coexistence extends to 60 mol % cholesterol and a modified phase diagram is presented. Combined 1H-, 2H-, 13C-NMR, and x-ray scattering data indicate that there are large changes within the Lo phase region, in particular, 1H-magic angle spinning NMR and wide-angle x-ray scattering were used to examine the in-plane intermolecular spacing, which approaches that of a fluid Lalpha phase at high temperature and high cholesterol concentrations. Although it is well known for cholesterol to broaden the gel-to-fluid transition temperature, we have observed, from the 13C magic angle spinning NMR data, that the glycerol region can still undergo a "melting", though this is broadened with increasing cholesterol content and changes with phospholipid chain length. Also from 2H-NMR order parameter data it was observed that the effect of temperature on chain length became smaller with increasing cholesterol content. Finally, from the cholesterol order parameter, it has been previously suggested that it is possible to determine the degree to which cholesterol associates with different phospholipids. However, we have found that by taking into account the relative temperature above the phase boundary this relationship may not be correct.     

Thermal unfolding and refolding of beta-lactoglobulin. An intrinsic andextrinsic fluorescence study.

The conformational features of beta-lactoglobulin, refolded by cooling from a thermally perturbed state, has been characterized by intrinsic and extrinsic fluorescence measurements on the protein. It is found that even at 85-90 degrees C, beta-lactoglobulin does not completely lose its folded structure. The unfolding and refolding of beta-lactoglobulin as observed through intrinsic tryptophan fluorescence is nearly reversible because the native beta-lactoglobulin and its refolded form, following heating and cooling, show nearly identical tryptophan fluorescence properties. However, the fluorescence properties of an extrinsic probe 1-anilino 8-naphthalene sulfonic acid (ANS) for the native and refolded forms are quite different from each other. Significant increase in fluorescence intensity and blue shifts in emission maxima of ANS bound to refolded beta-lactoglobulin is observed compared to that of the native form. Our results indicate that beta-lactoglobulin, refolded after heating to above 70 degrees C, has deep hydrophobic pockets which can be accessed by ANS. These pockets are either nonexistent or inaccessible to ANS in native beta-lactoglobulin. The opening of the central cavity collapses at pH close to the isoelectric pH of the protein. This indicates that electrostatic repulsion is necessary to keep this access open.     

Thermoelastic properties of cross-bridges in skinned skeletal muscle fibers of the frog under a condition of rigor

Thermoelastic properties of cross-bridges were measured by application of small sinusoidal length perfurbations and submillisecond Joulean temperature jump to chemically skinned muscle fibre removed from rigor solution. The thermal expansion coefficient of fibres was 4.2 +/- 1.0 X 10(-5) K-1. We have observed neither rubber-like stiffness increase, nor tension increase and stiffness decrease (which are expected if alpha-coil melting occurs) after temperature jump.     

A jump in an Arrhenius plot can be the consequence of a phase transition. The binding of ATP to myosin subfragment 1

The temperature dependence of the kinetics of the binding of ATP to myosin subfragment-1 was studied by an ATP chase technique in a rapid-flow-quench apparatus: (formula; see text) A temperature range of 30 degrees C to -15 degrees C was obtained with ethylene glycol as antifreeze. The Arrhenius plot of k2 is discontinuous with a jump at 12 degrees C. Above the jump delta H+ = 9.5 kcal/mol, below delta H+ = 28.5 kcal/mol. Few such Arrhenius plots are recorded in the literature but they are predicted from theory. Thus, we explain our results as a phase change of the subfragment 1-ATP system at 12 degrees C. This is in agreement with certain structural studies.     

Modeling temperature entrainment of circadian clocks using the Arrhenius equation and a reconstructed model from Chlamydomonas reinhardtii

Endogenous circadian rhythms allow living organisms to anticipate daily variations in their natural environment. Temperature regulation and entrainment mechanisms of circadian clocks are still poorly understood. To better understand the molecular basis of these processes, we built a mathematical model based on experimental data examining temperature regulation of the circadian RNA-binding protein CHLAMY1 from the unicellular green alga Chlamydomonas reinhardtii, simulating the effect of temperature on the rates by applying the Arrhenius equation. Using numerical simulations, we demonstrate that our model is temperature-compensated and can be entrained to temperature cycles of various length and amplitude. The range of periods that allow entrainment of the model depends on the shape of the temperature cycles and is larger for sinusoidal compared to rectangular temperature curves. We show that the response to temperature of protein (de)phosphorylation rates play a key role in facilitating temperature entrainment of the oscillator in Chlamydomonas reinhardtii. We systematically investigated the response of our model to single temperature pulses to explain experimentally observed phase response curves.