Heat shock and cold shock
In the in vivo behavioral experiments presented in our work, the impairment of coordination and mobility of the fish was recorded under extreme changes in body temperature equal to the ambient temperature. Previously, it was shown that the violation of cyclic changes in membrane fluidity caused by a sharp increase or decrease in ambient temperature will lead to the termination of synaptic transmission, which can be recorded by the loss of the righting reflex . Impaired coordination unequivocally indicates impaired nerve conduction, in particular from the optic receptor to the muscle. Indeed, disturbances in neural conduction not only in the brain, but also in peripheral neurons can cause a loss of equilibrium in the Atlantic cod Gadus morhua  Considering that each cycle of synaptic exocytosis includes reversible phase transitions of lipids of the presynaptic membrane due to entry and subsequent removal of calcium ions from the presynaptic terminal [5, 6], as well as the temperature dependence of coordination disorders , it can be stated that the temperature, at which loss of coordination is recorded is the temperature of the phase transition of the lipid-protein complex of the synaptic membrane. At a temperature of heat shock, the membrane remains in a state of liquid crystal, at a temperature of cold shock in a state of gel, and reversible phase transitions of lipids of a presynaptic membrane with changes in intracellular calcium are impossible. At the body level, this condition is recorded as a loss of righting reflex .
The conducted experiments confirmed the known linear dependence of critical temperatures (maximum and minimum) on the temperature of the long-term acclimation in the range from 20 °C to 30 °C [30, 34]. It is noteworthy that even minor deviations from definitely tolerable temperatures between 20 °C and 30 °C evoked shock reactions in fish Danio rerio. Shock proteins expressed both in cold and heat stress were found not only in humans but also in various species of fish, including zebrafish . With a slight increase in temperature in zebrafish, the expression of hsp70 mRNA can increase tenfold, however, the expression of the HSP70 protein increases only at potentially harmful temperatures . Heat shock proteins are expressed in zebrafish at 33 °C as early as 1 h after the temperature rise [36, 37]. Exposure of zebrafish to 18 °C for 4 h caused a cold stress, an increase in the content of 29 mRNA, a decrease in the content of 26 mRNA, an increase in the activity of 908 genes encoding proteins, and a decrease in the activity of 468 genes encoding proteins . Note that two-thirds of the recorded range of vital activity of zebrafish Danio rerio (Fig. 4) lies in the region of extreme temperatures leading to the activation of stress mechanisms.
Kinetics of temperature adaptation
Adaptation to a new ambient temperature is accomplished by regulatory reactions altering the membrane fluidity. In the frames of our notions [5, 6, 30], these processes are related with changes of intracellular Ca2+ concentration [14, 15] and expression of genes responsible for the processes determining the lipid composition of presynaptic membrane and synaptic vesicles [35, 37, 39]. Our experiments (Fig. 3) showed that a change in membrane fluidity occurs within a few days after being placed in an environment with a new temperature. This means that the composition of the lipid and protein components of the membrane is continuously changing for at least this time.
It was shown earlier [40,41,42] that new values of membrane potential and intracellular concentrations of inorganic ions were established within one hour after the switching off of the active transport. In particular, in human fibroblasts incubated in the presence of 1 µM ouabain for 1 h, membrane potential decreased from – 50 to – 10 mV [41, 42]. Calculations on the model system showed that such depolarization can cause an increase in the intracellular Ca2+ concentration from 10–4 to 10–1 mM, which is close to the increase of the intracellular Ca2+ concentration during the action potential or upon cooling by 10–15 °C [14, 15]. This means that new values of the membrane potential and ionic concentrations are established within tens of minutes.
Considering that the processes of the membrane lipid composition change may take a few days [35, 37, 39], it can be expected that the changes in TH and TC within the first hour after the temperature change are determined only by the current concentration of the intracellular Ca2+. In all plots (Fig. 3a and b), changes of TH and TC within the first hour after the sharp shift of the temperature amounted about a half of the whole range of the shock temperature changes and apparently were mostly determined by changes of the intracellular Ca2+ concentration [14, 15].
During adaptation to extremal high temperatures 30 °C ≤ TA ≤ 38 °C, changes of the intracellular Ca2+ concentration did not seem to occur, but the impairment of the mechanisms responsible for the synthesis or incorporation into the membranes of the long-chain hard-melting lipids was recorded, and non-selective mechanism of the removal and utilization of lipids was functioning. The increase in TC (●) and TH (○) observed over several days (Fig. 3d, e) is apparently the result of an increase in the phase transition temperature of the remaining part of the membrane lipids.
If the mechanism of the lipid removal and utilization was functioning, then a decrease in TH(◊) to the level of 27 °C and a decrease in TC(♦) to 6.5 °C, which was observed within a few days (Fig. 3e and F), can be explained by a decrease in the phase transition temperature of the remaining part of the membrane lipids [5, 6]. It is of note that upper limits of the thermal niche of the fishes are very sensitive to the water hypoxia , however, in our experiments all aquariums with fishes were actively aerated.
It is important to note that recorded motor impairments are easily reversible. After the fish return to the vessel with a long acclimation temperature, mobility and coordination are restored within a few seconds. Note that if the characteristic times of membrane phase transitions, with regard of the establishment of the ambient temperature in the synapse region, do not exceed tens of seconds , then even the change in the content of intracellular ions – a process inevitably accompanying temperature changes—has characteristic times of the order of tens of minutes [40,41,42].
Gene expression after a change in temperature develops in the fish Danio rerio [37, 38] and Carassius auratus  during the first 4 h, and adaptation changes in lipid-protein complexes of synaptic membranes take tens of hours (Figs. 2 and 3). This means that the coordination disorder during a sharp change in temperature is exclusively associated with the absence of phase transitions of the membranes, which leads to the impairment of nerve conduction. An alternative assumption of impaired fusion and rupture of any other cell membranes, for example, of vascular endothelial cells, which affects many metabolic parameters, is beneath criticism, because such effects cannot be develop and disappear within a few seconds.
Long-term exposure to extreme temperatures below 10 °C or above 38 °C in our experiments was deleterious for a part of the population. Recall that in our experiments we used young fish 20–30 mm long, and such fish can tolerate extreme temperatures better than larvae or adults . Fishes refused food, appeared sluggish and exhausted; abdomen was retracted, and a spinal curvature was observed. In particular, at 38 °C half of the population died out within 3 days. However, the surviving fishes could tolerate the temperature 41 °C – 42 °C for several days. A similar pattern was observed at extremely cold temperatures. It is noteworthy that the metabolism activity at 20 °C is definitely higher than at 10 °C, but fasting for several days at 20 °C did not have a significant impact on the fishes' habitus. It seems likely that the observed processes are related with disturbances in the lipid metabolism. In normal conditions, the main oxidation substrates in fishes are aminoacids, carbohydrates, and fatty acids. During adaptation to extremal temperatures in the conditions of a high O2 content, all ectotherms including fishes actively utilize not only lipids of the cell membranes  but also use lipids from fat deposits in liver and muscles . It has been shown in early works that the mechanisms of interaction of lipid and protein components of cell membranes are similar in a wide variety of organisms from yeast to mammals [46, 48].
Reversible phase transitions
The viability polygon for Danio rerio (Fig. 5) suggests that the temperature of the phase transition of the most hard-melting lipid-protein composition with a 1000-fold increase in [Ca+ 2] is reduced by (43 °C–27 °C) = 16 °C, and the temperature of the phase transition of the most low-melting lipid-protein composition with an increase in [Ca+2] decreases by (27–6 °C) = 21 °C. Accordingly, the temperature ranges of the phase transition are different and depend on the intracellular activity of Ca+2 ions. The range of temperatures of the phase transition in the lipid-protein composition at a high calcium concentration near [Ca+2] > 10–1 mM is wider than the temperature range in a calcium-free medium at [Ca+2] < 10–4 mM. The ratio of the intervals between the temperature of the thermopreferendum and the extremely high and extremely low temperatures can be estimated as 1.3.
In compliance with the notion of the reversible phase transitions of lipids of the presynaptic membrane in the process of the synaptic exocytosis [5,6,7, 30], it can be said that:
The range of the phase transition temperatures of lipids of the presynaptic membrane with calcium content below 10–4 mM extends from 27 °C to 42 °C and amounts about 15 °C.
The range of the phase transition temperatures of lipids of the presynaptic membrane with calcium content above 10–1 mM extends from 6.5 °C to 27 °C and is about 20 °C.
This means that a temperature decrease by 15–20 °C is equivalent to a 1000-fold increase in the intracellular calcium concentration. These results qualitatively correspond to the theoretical estimates made on the simplest model of the cell ionic-osmotic homeostasis with an account of the activity of the Na,K-APTase and Na-Ca-exchanger [14, 15]. The model predicts that at the activation energy for the ionic transport of the order of 30 kcal/mole, a cell with a membrane potential of about 60 mV at 37 °C after cooling to 26 °C, it is depolarized by 10 mV and increases the content of intracellular calcium from 10–4 mM to 10–2 mM, and a cell with membrane potential of – 60 mV at 26 °C after cooling to 7 °C, is depolarized by 20 mV and increases the content of intracellular calcium from 10–4 mM to 10–1 mM. These dependencies are analyzed in detail in works [14, 15] that provide formulas and specific graphical dependencies.
The obtained viability polygon (Fig. 5) qualitatively coincide with the results obtained for Danio rerio using other methods . Traditionally, the polygon of the tolerance temperatures was limited by the values of the critical heat maximum Ctmax and critical cold minimum Ctmin obtained for a given fish species at different values of acclimation temperature TA . Determination of Ctmax implies determination of the maximal temperature, at which the fish subjected to constant linear increase in the water temperature remains alive after the return to the temperature of preliminary return to the temperature of the preliminary long-term acclimation, TA. Method of critical temperatures requires determination of temperatures in an immediate proximity of the temperature of the physiological death, which depends both on TA and on the speed of the temperature change and even on the housing conditions of the parents [49, 50]. Maximal differences between the values of Ctmax  and TH  are observed at TA below 27 °C and between temperature Ctmin  and TC , at TA above 27 °C. The viability range determined by the methodology of loss of righting reflex , stretched from 6 °C to 43 °C, and the range of tolerable temperatures  obtained by the critical temperature method, from 4.5 to 42.0 °C. Main differences between values of Ctmax and TH can be explained by incorrect determination of the temperature of physiological death. At temperatures higher than TH but lower than Ctmax, the excitation propagation through the synapse is not possible [5,6,7, 30] and the nervous system of the organism is not able to accomplish coordination of organs and tissues, although the organs and tissues still can function independently at this temperature for some time. Similarly for temperatures lower than TC but higher Ctmin.
In the natural area of distribution in India and Bangladesh, fishes Danio rerio prefer brooks, lakes, ponds, and rice fields [51, 52]. The water temperature in these reservoirs generally ranges from 16.5 °C to 34.0 °C . Minimal temperature of 12.3 °C was recorded in a brook and maximal temperature of 38.6 °C, in a rice field [51, 52]. This means that the fishes are able to live at these temperatures for several hours or even days, and when possible, can leave the area of extremal temperatures and gather in the area with temperature between 20 and 30 °C.
Note that any living system emits heat and that the temperature of the fish brain in our experiments is higher than the water temperature, but not more than by 1.0 °C. However, when considering the results of other researchers, one should expect that the values of the limiting temperatures will be underestimated by several degrees. This is because brain temperature of Danio rerio recorded in our experiments and body surface temperature recorded in most other studies can differ by several degrees.
In our gradient bath experiments, the thermal preferential temperature for zebrafish has been shown to be between 25 and 27 °C. This temperature of 28 °C is optimal for the cultured zebrafish embryonic cell line . At this temperature, the current density in the Na+ channels of zebrafish myocytes and the rate of development of the action potential were similar to those in human heart myocytes at 37 °C . The optimum temperature for other fish species living at a wide range of temperatures, in particular for Lophiosilurus alexandri  or Nile tilapia , is also 28 °C. Furthermore, the temperature of 25 ± 2 °C is a thermopreferendum for frogs (Rana esculenta) . The optimal metabolic rate and the maximal rate of larva formation in nematode Caenorhabditis elegans , the maximal regeneration rate in planaria Girardia tigrina , the maximal mobility in planaria Schmidtea mediterranea  are in the same temperature range from 25 to 27 °C.
It was shown in our experiments (Fig. 3), that the temperature of the thermopreferendum TPR is equal to the minimum value of the heat shock temperature (TH)min and the maximum value of the cold shock temperature (TC)max, which corresponds to the phase transition temperature of the most hard-melting lipid-protein composition in a calcium-containing medium and the most low-melting lipid-protein composition in a calcium-free medium. It means that the revealed viability range for zebrafish 6 °C to 43 °C is employed by an overwhelming majority of living organisms found in middle latitudes.
It is difficult to explain, but interestingly the thermoneutral zone, in which the heating rate is equal to the rate of heat release into the environment, and the metabolic rate and substrate consumption are minimal, is located in the temperature range from 25.5 to 28 °C for both humans and mice [62,63,64], which coincides with the thermal preferendum for zebrafish.
Arctic and tropical organisms
In arctic fish Salvelinus alpinus, living at 10–11 °C, the oxygen consumption and hydrogen peroxide production by mitochondria almost doubles at temperatures above 20 °C . This temperature can be considered extreme for this species of fish. The ratio of the intervals between the temperature of the thermopreferendum and the highest and lowest shock temperatures equals to 1.3. According to our notion, the thermopreferendum temperature for this species is TPR ≈ 11–12 °C, maximal temperature is about 20 °C, and a minimal temperature of the lipid phase transition is not lower than 5 °C. Similarly, for a cold-water trout Salvelinus namaycush, living at 8–10 °C, a decrease of the maximal rate of metabolism and a dramatic reduction in the metabolic recovery rate was observed at temperatures above 19 °C .
A tropical tilapia Alcolapia grahami from the lake Magadi (Kenya) lives in rapid stream sources with water temperature of up to 43 °C. The value of the critical heat maximum Ctmax, measured according to the methodology of critical temperatures , was 45.6 °C for this population . Considering that at temperatures above 43 °C the tertiary and quaternary structure of many proteins is violated [68, 69], these results should be treated with caution. If an upper temperature limit is taken as 43 °C and thermopreferendum, as 37 °C, then a lower temperature limit, in analogy with mammalians [70, 71], will amount about 30 °C. The metabolism rate measured in these tilapias, exceeds the parameters ever recorded in ectotherms and lays within the basic range of metabolic rates of small mammals . Note that the considered species live in narrow temperature ranges below 15 °C.
Ectothermes and endothermes
The majority of mammalians and birds maintain the temperature of the visceral organs, such as brain and heart, considerably higher than the ambient temperature. To minimize the heat loss, their bodies are covered with hair or feathers. However, in different periods of life these organisms can lower the metabolic rate and, consequently, the body temperature. During the diurnal rest period, the metabolism rate estimated by oxygen consumption, in most mammalians decreases by about 20% and a body temperature, by 0.5–2.0 °C. In birds, metabolism rate can decline by 30%, and a light circadian hypothermia can reach 4.0 °C. Furthermore, a considerable number of mammalian and birds can come into a much more prolonged periods of hypometabolism and hypothermia . Assuming that the thermopreferendum temperature in mammalians is 36–38 °C and the upper limit is 43 °C, then, considering that the temperature interval ratio is close to 1,0, we can expect that the lower temperature limit will be about 30 °C. This temperature is a low temperature limit recorded in many mammalian species; in particular, American black bear Ursus americanus during seasonal hibernation reversibly cools down to 30 °C in the circadian cycles lasting many days [70, 71]. In a closely related species, brown bear Ursus arctos, body temperature drops down to 6 °C and in the inter-bout arousal increases up to 30 °C .
Winter hibernation in many hibernators, including rodents, bats, lemurs, marsupials, hedgehogs, and brown bears (Ursus arctos) consists of a series of multi-day periods of catalepsy alternating with arousal periods. During catalepsy lasting 10–20 days, the body temperature is about 5–7 °C and during arousal lasting 1–2 days, the body temperature grows up to 30 °C [71, 72, 74]. In this hypometabolic state at 30 °C, in a brown bear Ursus arctos the metabolic activity judged by the oxygen consumption is 4 times lower than the metabolic activity in summer. The creation of similar hypometabolic state during prolonged surgical operations or under conditions of cranio-cerebral trauma in humans may turn very helpful .
The brain temperature of many organisms living in mid-latitudes easily varies in the range from 6 to 43 °C; the brain temperature of cold-water organisms ranges from 6 to 20 °C, and the brain temperature of most mammals and birds can vary from 30 up to 43 °C. This means that living organisms are able to exist in each of three temperature ranges, which differ in the mechanisms of synthesis, incorporation and utilization of membrane lipids. At the same time, the area of the viability polygon for cold-water species or for endothermic organisms, including humans, is 6–8 times less than the maximum possible area obtained for zebrafish in our experiments.
It is noteworthy that the survival range evaluated on the basis of the phase transition temperatures of lipids coincide with the functional activity ranges for most enzymes. The activities of all enzymes decrease upon cooling, and growing density of water at low temperatures, reaching maximum at 3–6 °C, favors the enzyme blockade. At these temperatures the metabolic activity virtually stops [68, 75]. At temperatures higher than 43 °C, the tertiary and quaternary structure of proteins is impaired, and this determines the upper limit of the viability range [68, 69].
The presented experimental results indicate that the upper temperature limit in cold-water fish [65, 66] and the lower temperature limit in some warm-water fish , mammals and birds [72,73,74, 76] are determined only by the phase transition temperature of membrane lipid-protein compositions, and not by a blockade of enzymatic activity.
Exclusive integral parameter
At the cellular and brain levels, there are numerous complex signaling mechanisms. However, a violation in the processes of coordination of the activity of different muscles of the fish body, recorded in our behavioral experiments, unambiguously indicates that signals in the form of sequences of nerve impulses from the visual receptor or from the vestibular apparatus do not enter at least one muscle of the body. The impairment of coordination will be recorded for any disorder in nerve conduction, both at the receptor level, and in various brain structures or at the level of the neuromuscular synapse.
It is important to note that recorded motor impairments are easily reversible. After the fish return to the vessel with a long acclimation temperature, mobility and coordination are restored within a few seconds. Note that if the characteristic times of membrane phase transitions, with regard the time of the establishment of the ambient temperature in the synapse region, do not exceed tens of seconds , then even the change in the content of intracellular ions has characteristic times of the order of tens of minutes [40,41,42]. Gene expression after a change in temperature develops in the fish Danio rerio [37, 38] or Carassius auratus  during the first 4 h, and adaptation changes in lipid-protein complexes of synaptic membranes take tens of hours (see Fig. 3). This means that the coordination disorder during a sharp change in temperature is exclusively associated with the absence of phase transitions of the membranes, which leads to the impairment of nerve conduction. An alternative assumption of impaired fusion and rupture of any other cell membranes, for example, of vascular endothelial cells, which affects many metabolic parameters, is beneath criticism, because such effects cannot be develop and disappear within a few seconds.
Our experiments (see Figs. 1 and 4) showed that any investigated TA corresponded to well-defined temperatures of phase transitions TC and TH. Many researchers have long tried to determine the effect of the temperature of long-term acclimation TA on the components of lipid membrane [77,78,79,80,81,82,83,84,85]. It has been shown that adaptation to any TA occurs simultaneously with changes in many combinations of lipid and protein components. A comparative analysis of the fatty acid composition of the brain of 17 species of teleost fish obtained from Antarctic, temperate and semi-tropical waters, as well as from rats, turkeys, mammals and birds as typical was carried out. Analysis of the lipid composition of the brain has shown that the relative amounts and ratios of different lipids are the main factors contributing to the maintenance of proper fluidity [77, 78]. Cold adaptation correlated with an increase in the proportion of unsaturated fatty acids, mainly polyunsaturated fatty acids , as well as highly unsaturated phospholipids . The complexity of the analysis of the mechanisms of membrane homeostasis is determined by the presence of many mechanisms that control the properties of the membrane and adjust its composition . Note that some lipids are intermediate products of cellular metabolism and modulators of certain metabolic pathways . Moreover, not only proteins, but also peptides, change the structure of the membrane, creating domains of liquid crystals in the membrane , and the activity of membrane enzymes, in turn, depend on the fluidity and lipid composition of the membranes . A change in temperature of the membrane phase transition can occur, for example, when a part of cholesterol is transferred from the plasma membrane to the endoplasmic reticulum  or when cholesterol-independent domains are formed under the action of saturated long-chain phospholipids C24 and C16 . It is assumed that temperature adaptation of the brain is associated with the aggregation of monomers of acetylcholinesterase and its dissociation of their tetramers . The task is complicated by the fact that more than 40.000 lipids can be identified  and more than 5.000 different membrane proteins  were detected in the composition of cell membranes. It is practically impossible to predict the behavior of such a complex system from the standpoint of biochemistry.
The listed facts allow us to state that many variants of lipid and protein components of synaptic membranes can correspond to any specific TA value. Moreover, our experiments (Fig. 3) showed that the change in membrane fluidity occurs within a few days after being placed in an environment with a new temperature. This means that the composition of the lipid and protein components of the membrane is continuously changing for at least this time. Many variants of the composition of lipid and protein components of the synaptic membrane seem to depend on the type of organism and on the temperature prehistory (heating or cooling) of the nervous system.
The loss of righting reflex methodology allows us to characterize the state of the membrane using only one parameter. The advantage of our method of recording temperature shock is the possibility of detecting phase transitions of membrane lipids in a behavioral experiment in vivo. We assume that the minimum phase transition temperature of the most low-melting lipid-protein composition at a high calcium concentration does not exceed 7 °C, and the maximum phase transition temperature of the highest-melting lipid-protein composition is 27 °C, which is the minimum phase transition temperature of the most low-melting lipid protein composition in a calcium-free medium. The maximum temperature of the phase transition of the most refractory lipid-protein composition in a calcium-free medium is 43 °C, and at a high calcium concentration it is 27 °C. Mammals, birds, and many organisms from polar or tropical waters live in much narrower temperature ranges.
Apparently, narrow temperature ranges of vital activity correspond to narrower temperature ranges of phase transitions and different values of the thermopreferendum. The phase transition temperature is the exclusive integral parameter characterizing the functional state of membrane lipids.