How precisely can we sense temperature differences?

How precisely can we sense temperature differences?

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We have thermoreceptors, thus we can sense temperature (both warm and cold). I'm interested in the sensitivity of our thermoreceptors -
What is the smallest temperature difference that we can sense?
I assume that different parts / organs may have different sensitivity (eg. lips vs fingers), thus I'd like to narrow my focus on the palms / fingers. But if someone has comparative data, that is welcomed too.

Short answer
Temperature differences of 0.02 degrees Celcius can be distinguished, dependent on various factors including experimental conditions and bodily location.

The ability to discriminate temperature differences depends on whether it is a cooling or heating pulse, the skin temperature, the duration of the temperature stimulus, age, bodily location among other factors. Unfortunately I cannot access the primary literature other than a few isolated smaller studies. However, Scholarpedia has a very nice entry and associated references, and I quote:

The thermal sensory system is extremely sensitive to very small changes in temperature and on the hairless skin at the base of the thumb, people can perceive a difference of 0.02-0.07 °C in the amplitudes of two cooling pulses or 0.03-0.09 °C of two warming pulses delivered to the hand. The threshold for detecting a change in skin temperature is larger than the threshold for discriminating between two cooling or warming pulses delivered to the skin. When the skin at the base of the thumb is at 33 °C, the threshold for detecting an increase in temperature is 0.20 °C and is 0.11 °C for detecting a decrease in temperature.

The rate that skin temperature changes influences how readily people can detect the change in temperature. If the temperature changes very slowly, for example at a rate of less than 0.5 °C per minute, then a person can be unaware of a 4-5 °C change in temperature, provided that the temperature of the skin remains within the neutral thermal region of 30-36 °C. If the temperature changes more rapidly, such as at 0.1 °C/s, then small decreases and increases in skin temperature are detected. [… ]

You also were interested in the palmar skin: here average difference limens are 0.02 - 0.06 °C, dependent on the temperature step used. These values were obtained using cooling pulses. In other words, differences in two cooling pulses of 0.02 - 0.06 °C were discernible, with higher limens needed for higher pulses. Baseline temperatures (29 - 39 °C) had little effect (Darian-Smith et al., 1977).

Darian-Smith et al., J Invest Dermat 1977;69:146-53

The Stevens, J. C., & Choo, K. K. (1998). Temperature sensitivity of the body surface over the life span. Somatosensory & motor research, 15(1), 13-28 article as commented on by Corvus is indeed a must-read, but my uni library does not have access to it unfortunately

Difference Between Heat and Temperature

The concept of heat and temperature are studied together in science, which is somewhat related but not alike. The terms are very common, due to their wide usage in our day to day life. There exist a fine line which demarcates heat from temperature, in the sense that heat is thought of, as a form of energy, but the temperature is a measure of energy.

The fundamental difference between heat and temperature is slight but significant, heat is the overall energy of the molecular motion, whereas temperature is the average energy of the molecular motion. So, let’s take a look at the article given below, in which we have simplified the two for you.

It’s Getting Hot in Here

© ISTOCK.COM/KTSIMAGE/ERAXION E ven the earliest scientists knew that temperature was an important vital sign, signifying sickness or health. In the 17th century, Italian physiologist Sanctorio Sanctorius invented an oral thermometer to monitor patients. Now, 21st-century researchers have set themselves a new, more challenging task: taking the temperatures of individual cells.

&ldquoTemperature is one kind of basic physical parameter which regulates life,&rdquo says Mikhail Lukin, a physicist at Harvard University who has developed a diamond-based intracellular temperature sensor. &ldquoIt determines the speed of all sorts of processes which occur inside living systems.&rdquo

But although temperature is a basic vital sign, scientists have a relatively poor understanding of how it varies among and within cells. &ldquoIt turns out that to measure temperature reliably inside the cell is not easy,&rdquo says Lukin. &ldquoYou cannot stick a large thermometer in there and maintain the cell viability.&rdquo

In the last five years, however.

Although temperature differences within the body tend to vary on the order of a few degrees, at most, researchers are beginning to suspect that small differences can alter cells’ chemistry and function, or tip off doctors to cancerous growth. Here, The Scientist profiles several methods for examining how temperature influences what’s going on inside cells.

Hitting on Hotspots
HOT STUFF: (Top panel) Design of a miniature fluorescent thermometer developed in Seiichi Uchiyama’s lab. When the thermometer is cool, its polymer backbone (green) maintains an open structure. Water molecules quench the fluorescent unit (shown here as a star). As temperatures rise, the thermometer folds and protects the fluorescent unit from water, allowing it to glow. (Bottom panel) The thermometer reveals that the nucleus of a cultured monkey cell is, on average, one degree hotter than the cytoplasm. NAT COMMUN, 3:705, 2012 Researchers: Seiichi Uchiyama, University of Tokyo Madoka Suzuki, Waseda University, Singapore

Goal: Temperature influences myriad processes in the cell, from gene expression to protein-protein interactions. Suzuki, Uchiyama, and their colleagues seek to measure slight variations in temperature between different parts of cells. This may shed light on how heat is generated in the body and how local variation in temperature changes a cell’s chemistry.

Approach: Sensors containing fluorescent dyes, quantum dots, or other glowing materials can change in brightness depending on temperature. In the past several years, researchers have built tiny fluorescent thermometers that cells can ingest. Using microscopy, researchers can detect the thermometers’ glow and evaluate intracellular temperature.

Uchiyama first started mapping temperature distribution inside single cells in 2012, publishing his design for a fluorescent polymeric thermometer (Nat Commun, 3:705). The thermometer consisted of a fluorescent molecule attached to a polyacrylamide chain whose conformation changes with temperature, either quenching or activating fluorescence. The researchers were able to show that the nucleus is warmer than the cytoplasm and that the mitochondria radiate substantial heat in a monkey kidney–derived cell line. (These findings are controversial see “Temperature Quandary” below.)

Uchiyama has since published other fluorescent sensor designs, most recently developing a faster fluorescent polymeric thermometer that relies on looking at the fluorescence ratio of a temperature-sensitive fluorophore to a temperature-insensitive one (Analyst, 140:4498-506, 2015). The researchers used the sensor to measure temperature in human embryonic kidney cells, finding that the nucleus was approximately 1 °C warmer than the cytoplasm.

When Suzuki first began to design a thermometer he remembers just gently pressing a glass microneedle that had a fluorescent dye enclosed in its tip against the membranes of cells and seeing if the fluorescence changed as temperature rose (Biophys J, 92:L46-L48, 2007). Eventually, he and his colleagues began to experiment with making fluorescent nanoparticles they could introduce into cells. The fluorescent molecules cannot be exposed to the chemical environment of the cell, because this can alter their brightness. “The nanothermometers should read out temperature change and should not respond to [other] environmental changes,” says Suzuki.

To protect the fluorescent reporters, the researchers embedded the molecules in a hydrophobic polymer and then encased this hydrophobic core within a hydrophilic polymer shell, creating particles that were, on average, 140 nm in diameter. To further guard against misinterpretation, Suzuki included two types of fluorophores, one sensitive to heat and one not. By measuring the ratio of the two fluorophores’ brightness, the team found that in cultured human cancer cells stimulated with a chemical that spurs cells to produce heat, the temperature varied locally (ACS Nano, 8:198-206, 2014).

The team has since developed a small-molecule thermometer composed of a yellow fluorescent dye that specifically targets mitochondria, the engines of heat generation in the cell (Chem Commun, 51:8044-47, 2015). Another small-molecule thermometer targets the endoplasmic reticulum—an organelle that also appears to help the cell to generate heat (Sci Rep, 4:6701, 2014).

Suzuki hopes to someday be able to develop intracellular thermometers with faster response times and greater temperature sensitivity so that they can identify other hotspots of heat production in the cell. For now, he says, sensors struggle to capture small bursts of heat that diffuse quickly. “The mitochondria and endoplasmic reticulum are considered as heat sources,” says Suzuki, as is actomyosin in muscle cells. “There might be other heat sources which we have never imagined.”

Shine bright like a diamond
BLINGED-OUT CELLS: Mikhail Lukin and his colleagues heat cells by shining lasers on gold particles and measure internal temperatures of the cells by detecting the spin states of defects in nanodiamonds. NATURE, 500:54-58, 2013 Researcher: Mikhail Lukin, Harvard University

Goal: Lukin and his collaborators dream of using intracellular temperature to sort healthy cells from sick ones, and of regulating cellular processes by heating them up or cooling them down. “It opens a broad array of possibilities,” he says.

Approach: Lukin, a physicist, sought to differentiate himself from the pack by making thermometers out of diamond nanocrystals rather than fluorescent dyes or polymers. “We made use of basically quantum defects in diamonds, which are the so-called nitrogen-vacancy centers,” he explains. “It’s a defect where nitrogen substitutes [for] carbon.”

Nitrogen-vacancy centers have atomic spin states that change orientation when perturbed by light, magnetic fields, or, it turns out, temperature. “If the temperature of the nanocrystal changes, then what happens is that the separation between carbon atoms in the nanocrystal changes a little bit,” altering the spin state of electrons, says Lukin. When the researchers shine a laser on the diamond nanocrystals, the impurities glow, emitting varying fluorescence depending on their spin state and temperature. (See “Monitoring Magnetic Bugs,” The Scientist, October 2013.)

To test their method, the researchers also introduced gold nanoparticles into cells and heated the particles with lasers, allowing Lukin and his team to both control the temperatures of cells and monitor how their temperature control was working. The researchers found that they could detect changes as small as 0.0018 °C (Nature, 500:54-58, 2013).

Lukin and collaborators are now using temperature to explore and control the development of worms.

“It might allow you to selectively regulate various processes inside the cell,” he says. “It might allow you to accelerate development of some processes, decelerate development of others, or kill the cell if you don’t want this specific cell to play a role anymore.”

Cancer killers
MULTIPURPOSE BEAD: Millán and Carlos have constructed tiny beads that both heat cells and take their temperatures. Fluorescent ions (red) reveal temperature. They coat magnetic nanoparticles (orange) that provide heat when exposed to a magnetic field. For protection, a polymer shell (green and blue) encases the combined heater-thermometer. ACS NANO, 9:3134-42, 2015 Researcher: Luís Carlos, University of Aveiro, Portugal Angel Millán, Institute of Materials Science of Aragón, CSIC-University of Zaragoza, Spain

Goal: Carlos and Millán are trying to kill tumors by selectively applying lethal levels of heat to cancer cells, creating temperature gradients that destroy biomolecules and trigger cell death. But efforts to kill cancer cells using hyperthermia tend to falter for lack of a good way to ensure that cancer cells get hot enough while the surrounding tissue remains sufficiently cool.

Approach: Carlos and Millán recently designed a nanoparticle that is both a heater and a thermometer (ACS Nano, 9:3134-42, 2015). Researchers hoping to both heat and take the temperatures of cells have generally used separate particles for the two tasks. Carlos and Millán wanted to make sure they were measuring temperature exactly at the heat source, as heat can quickly dissipate over short spaces in cells. “If we don’t have the thermometer really in contact with the heater, we will not be able to measure the effective local temperature,” Carlos says.

The heater consists of a magnetic bead that heats up when exposed to a magnetic field. The thermometer consists of two fluorescent ions, one of which changes brightness with shifts in temperature. These are all enclosed in a polymer shell.

There are already clinical trials testing the use of magnetic bead–induced heating to kill cancer. But the researchers think that with their combined heater-thermometers they can heat cells more precisely, reducing both the number of nanoparticles needed and collateral damage beyond the tumor.

“If you internalize the nanoparticles specifically inside cancer cells, maybe just a few are enough to induce cell death,” says Millán. The researchers are currently heating cells in culture and monitoring their temperature and reactions.

More than skin-deep
GOING DEEP: Jaque and his colleagues have created a nanothermometer that can sense temperature underneath skin. (Top left) The thermometer is composed of temperature-sensitive quantum dots and temperature-insensitive fluorescent nanoparticles, all embedded in a biocompatible polymer. (Left and above) Transmission electron microscopy image of the nanothermometer ADV MATER, 27:4781-87, 2015 Researcher: Daniel Jaque, Autonomous University of Madrid

Goal: Jaque’s team hopes to develop methods to measure temperature beneath animals’ skin and eventually in human tissue in vivo by using temperature sensors that give off fluorescent signals that penetrate flesh.

Approach: Most nanothermometers have a major limitation: they emit light waves in the visible range. This works fine for observing cells in culture or even in vivo in relatively transparent creatures, such as worms. But visible light cannot tell researchers much about cells below the skin in intact, opaque organisms. Much of the infrared spectrum, meanwhile, is highly absorbed by water, which is abundant in tissue.

There are, however, ranges of wavelengths that do penetrate tissue and avoid the water absorption problem. Light between 650 and 950 nm—red verging into infrared—is considered one biological window. Infrared light between 1,000 and 1,350 nm makes up a second biological window.

Jaque and his colleagues have been developing a thermometer that relies on fluorescence that can be excited and read in these biological windows. Most recently, Jaque, postdoc Emma Martín Rodríguez, and colleagues designed a thermometer that is excited in the first biological window and emits signals in the second (Adv Mater, 27:4781-87, 2015).

The thermometer is made up of quantum dots, whose fluorescence is quenched with rises in temperature, and temperature-insensitive fluorescent nanoparticles, all encapsulated in an FDA-approved polymer.

With current technologies, it is possible to sense temperature around 1?cm below animals’ skin. But to move to medical applications in humans, researchers will need to sense temperatures at much deeper levels. “We are just at the beginning of the history,” says Jaque.

Eventually, Jaque hopes to use nanothermometers to guide heat treatment for cancer. “You introduce nanoparticles that give a real-time measurement of temperature inside your body,” he says. Then, as you heat the tumor, “you can adjust the treatment not to burn the body.”


Baffou objected to the high levels of heat generation depicted in this image from Uchiyama’s 2012 Nature Communications paper. The image shows large local temperature spikes (white arrows) near mitochondria in a living monkey cell. The letter N marks the nucleus. NAT COMMUN, 3:705, 2012 Researchers including Madoka Suzuki and Seichii Uchiyama have recently measured what appear to be substantial temperature increases in living cells. In some cases, the temperature differences reach a few degrees Celsius—despite the absence of any outside heating of the cells. In September 2014, a group of French researchers challenged these findings, sparking a lively, year-long back-and-forth in the pages of Nature Methods (11:899-901, 2014 12:801-03, 2015).

The French group performed calculations that seemed to show that a single cell just does not have enough energy to so quickly generate such a large temperature differential on its own. “Glucose is a molecule inside cells where energy comes from,” says coauthor Guillaume Baffou of Aix-Marseille University’s Institut Fresnel. “If you fill the whole volume of the cell with glucose, which is obviously not the case, and if you burn glucose, you will not achieve a temperature increase of one degree.”

“If we apply the conventional laws of thermodynamics . . . we arrive to the conclusion that it is not possible to have differences in temperature inside the cell around one degree coming from internal reactions,” agrees Luís Carlos of the University of Aveiro in Portugal, who was not involved in the correspondence. “But from an experimental point of view, there are several works done by several authors around the world showing differences in temperature greater than one degree.”

One possibility is that researchers observing large temperature increases in cells simply were making experimental errors. “The other hypothesis is that there is something that happens at the micro- and nanoscales concerning heat transfer that [is] not well-described by the conventional thermodynamics,” says Carlos.

Suzuki agrees that it is impossible for a whole cell to get hotter by a whole degree without outside heat input. However, “the calculation should not consider the temperature of the whole cell, the water ball, but a small volume inside the cell where the heat is produced and the temperature is measured.” Suzuki says that the next step will be measuring the thermal conductivity of living cells, with all their organelles and proteins filling the interior. This might help explain whether and how local areas of cells can heat up while the cell overall does not experience radical temperature change.

“Thermal biology is still at its infancy,” says Baffou. “There is no reliable temperature mapping for cells.”

Q10 in Circadian Biology

In circadian biology, we are interested in understanding the biological processes which "tick" off time and give rise to an organism's free-running period (FRP). If those processes' rates were to increase with temperature, then the clock would run fast, and it would take less time to "tick." We would then expect the FRP to decrease as temperature increases. But in fact, organisms' FRPs tend to have a Q10 which is close to (but not exactly) 1: FRPs change comparatively little with changes in temperature. This is illustrated in the figure below. The blue line plots how much an FRP would vary with increasing temperature if it had a Q10=1.1 The red line plots how much an FRP would vary with increasing temperature if it had a Q10=2.0. The data one would observe for most circadian rhythms looks more like the blue line than the red line.

To say that for circadian rhythms, Q10𕚳 is more precise way of expressing that the clock is temperature compensated.

Although circadian clocks are temperature compensated, acute changes in environmental temperature can in fact function as zeitgebers, and many organisms’ clocks can be entrained to a regular temperature cycle, or to a repeated increase or decrease of temperature. This is especially true for organisms that do not regulate their own body temperature. In organisms (like mammals) which do regulate body temperature, changing environmental temperature has less of an effect. For most organisms, light is by far a stronger zeitgeber than temperature. However, because temperature can have an effect on the clock, one can expect some individual variation in FRPs (even in organisms of the same species) if they are subjected to different temperatures.

To sum up this section: it is an oversimplificaiton to think that all organisms of the same species have precisely the same FRP, since factors like lighting intensity, aftereffects, and temperature can all produce individual variations.

3.2. Criteria for Entrainment, Skeleton Photoperiods, and Phase Response Curves

It is important to understand that entrainment – the synchronization of the clock to the environmental conditions – involves an effect of the zeitgeber on the actual “gears” of the biological clock that is, a change in the internal, molecular mechanisms that regulate an organism’s activities. Masking (see ڈ.2 in Part II) must be carefully distinguished from genuine entrainment. There are four established criteria for determining when an organism is entrained to a cue. We have touched upon each of them above, but will now state them more clearly. A review of all four criteria is also available in the video below, called “Properties of Entrainable Oscillators."

First, in order to claim that an organism is entrained to a specific zeitgeber schedule, there must be no other time cues present to the organism. For example, if one wants to show that plants entrain to light-dark cycles, then one must control for temperature cycles: if one subjected the plant simultaneously to synchronized temperature and light cycles, then even if the plant entrained, there would be no way to confirm that the plant was entrained to light, and not to temperature. There would be no strong support for claiming that light was acting as the zeitgeber.

Second, whenever a zeitgeber is present, the organism must synchronize its rhythms, so that their period matches the zeitgeber’s period. (This is sometimes called the requirement of period control by the zeitgeber). For example, if an experimenter imposes a zeitgeber with the (artificial) periodicity of 24.3 hours (a “long day” that would not naturally occur), a mouse ought to be able to entrain to that cycle. If the zeitgeber is actually effective, we would expect the mouse’s onset of activity to occur once every 24.3 hours. In most cases, the requirement for period control is evident by adjusting the FRP to match a normal 24h zeitgeber.

Third, an effective zeitgeber must be shown to have its synchronizing effect reliably. For example, if we take the same organism and again subject it to the same zeitgeber schedule, then the organism ought to entrain to it again, with the same relative timing to the zeitgeber cycle. We should see again (for example) that onset of activity occurs once every 24.3 hours, and (if it is a nocturnal organism like a mouse) the onset of activity should occur at the start of the night phase. (This is called the requirement of a stable and repeatable phase relationship between the zeitgeber and the endogenous rhythm).

Fourth, if an organism is genuinely entrained to a zeitgeber, then when we remove the zeitgeber, two things should happen. First, the organism ought to begin to free-run, since the entraining and synchronizing cues are no longer present. Second, if the "gears" of the clock have actually been affected by the prior entrainment, then the organism should begin to free-run in a way that is determined by, and predictable from, its previous entrainment. (This is called the requirement of phase control.) This is what enables us to rule out mere masking as an alternative explanation for (merely apparent) entrainment in which only the “hands” of the clock are affected.

All four requirements are illustrated schematically in figure 3.2 below.

Figure 3.2 Criteria for Entrainment.

(a) A diurnal organism is free-running with a characteristically long (>24h) period in constant darkness, and all other zeitgebers that can be controlled are constant.

(b) The organism quickly entrains to an imposed LD12:12 cycle. Yellow shading indicates the light phase. (One sometimes needs to read captions: the conventional black and white bars are not always shown to indicate LD cycles). Since other zeitgebers have been removed (see a above), this is partial evidence that a light-dark cycle is an effective zeitgeber. The organism synchronizes to the LD cycle as evident by activity onsets aligning vertically. Thus, the period of the activity rhythm matches the period of the zeitgeber (24h) meeting the condition of period control.

(c) The LD cycle is removed, and the organism again free-runs. The FRP is >24h as before, but the onset of activity is predictable based on the prior, entrained phase of activity in b. Note the red line through successive onsets in part a does not align with the similar line for part c. Thus, entrainment in b exerted control over the clock's phasing to produce a several hour offset in the intervals of free-running, demonstrating phase control by light.

(d) A HotCold12:12 temperature cycle is imposed to mimic the prior LD cycle (red shading indicates time of high temperatures). During the HotCold cycle, the organism is in constant darkness so that light and temperature effects can be examined separately. At first glance, it appears that activity synchronizes to the temperature cycle. To see if this is really entrainment, however, again we must remove the putative zeitgeber (temperature) to see what happens.

(e) The temperature cycle is removed, and the organism free-runs. Note that the onset of activity is not predictable from the prior onset of activity during the temperature cycle in d: there is no evidence of phase control by temperature. Instead, comparing c to e by following the red line, the organism's clock has been free-running throughout d: the merely apparent synchronization to the temperature cycle was simply a form of masking.

(f) The LD cycle is imposed again, and the organism rapidly entrains again, demonstrating a stable and repetable phase relationship.

Thus far, we have discussed entrainment to LD cycles in which light is present throughout a long duration. In an LD12:12 cycle, the organism receives 12 whole hours of light. But notice that the four criteria for entrainment do not require that the zeitgeber resemble a natural day in this way (just as a zeitgeber does not have to have T =24h). A regular schedule of short pulses of light can also meet the criteria for entrainment. In extremely light-sensitive organisms, it has been shown that a regular daily pulse of light of only 1 sec in duration is sufficient to maintain entrainment. In many organisms, entrainment can be maintained with a daily light pulse of 15 - 60 minutes duration. For reasons that will become apparent later, investigators will sometimes investigate entrainment under skeleton photoperiods in which two light pulses are given daily. Instead of a full 12h light phase, for example, an investigator might replace 12h of light with two 1 hour pulses: one at the beginning and one at the end of the 12 h period. Under such conditions, entrainment is very similar to that seen with the a 12h photoperiod. This indicates that light at dawn and dusk (beginning and end of day) is doing most of the work of entrainment. An example is shown in Fig. 3.3 below.

Figure 3.3: A double-plotted actogram, showing an organism entrained to a skeleton photoperiod.
Black and white bars at the top indicate when lights are on and off.

In both LD cycles and skeleton photoperiods, the organism is exposed to the periodic influence of some zeitgeber. But skeleton photoperiods show that isolated pulses of light can be effective in influencing and entraining the clock. A corollary of this is that entrainment may be study-able under highly simplified conditions whereby we investigate what happens to an organism when it is subjected only to a very brief and non-repeating light pulse (instead of a full 1 h photophase that repeats every 24h, as in the skeleton photoperiod above). Scientists are always looking to find the simplest conditions that elicit a particular effect because this allows all extraneous influences to be excluded.

In the case of circadian entrainment, application of brief (or "acute") light pulses to organisms reveals a fascinating and fundamental property of circadian clocks: brief light pulses cause circadian clocks to be reset, and the timing of the light pulse determines whether the light pulse will cause the resetting to be earlier, later or have no effect. In other words, there is a circadian rhythm in the response to a light pulse. Put another way, the effect that an isolated zeitgeber has on the clock depends upon the circadian time (CT) at which it is administered. Moreover, there is an adaptive logic to this rhythm: over evolutionary time, if there was a bright light in the environment it almost certainly came from the sun (lightning might be one possible exception). If an organism’s internal sense of time predicted that it was daytime, then experiencing bright light does not indicate that anything is counter to expectation. However, if the internal sense of time predicted that it was nighttime, the presence of sunlight indicates a mismatch with the environment that should be corrected. In the course of our evolution, the internal clock was less infallible than the rhythm of sunlight. Thus, our clocks evolved to reset themselves whenever their predictions of the current time of day were of sync with the lighting environment. With this evolutionary perspective in mind, we can begin to understand an important data graphic called a phase response curve.

Skeleton photoperiods show that brief light pulses are sufficient to support entrainment. An evolutaionary perspective enables us to conceptually understand why entrainment can occur in response to acute light pulses. If the clock of an organism currently predicts that it is day and the organism then experiences a bright light pulse, there is no indication that anything is amiss. The clock has no reason to make a correction. Empirically, across a vast array of species, a pulse of light in the subjective day has minimal effects on the circadian clock. Now suppose that a nocturnal rat wakes up to begin its nighttime activities. What does a bright light in the sky indicate to that rodent, when the organism is anticipating subjective night? Probably that it arose too early, because that bright light is probably the sun, which has not yet set. As a corrective, the rat might wish to make an adjustment to its internal sense of time and reset the clock so that the next day it gets up a little bit later. This kind of adjustment to the clock is called a phase delay. Conversely, consider a rat that has woken up and has been pursuing its activities in darkness for several hours. Everything seems in order: the rat anticipates subjective night, and the enfironment is dark. Suppose after several hours of activity, the rat’s internal sense of time indicates that it has 2 more hours of darkness to continue its nighttime activities. But if at this time, there is exposure to a bright light, the circadian system will interpret this as a sunrise. Clearly, the circadian system is running late and should have started and finished activity early than it did. Remarkably, a bright light pulse late in the subjective night causes organisms to reset their clocks so that their active phase begins earlier in the next cycle. This adjustment to the clock is called a phase advance. As these examples indicate, under natural conditions, small adjustments to the clock are usually made around dawn and dusk as clocks may deviate slightly from the proper phase. Organisms would rarely experience conditions where the clock became multiple hours out of alignment with the day-night cycle. Thus, what happens in response to light in the middle of the subjective night is not of great relevance to natural entrainment.

By graphing how much the circadian clock shifts in response to an acute zeitgeber, depending on the circadian time of the organism, we can produce what are called phase response curves (PRCs) . A schematic example is shown below. The X axis tracks the time at which a zeitgeber is applied, and on the Y axis, we plot how much it affected the clock.

Figure 3.4: The basic shape of a PRC.

A phase response curve (PRC) can summarize a tremendous amount of data regarding how a zeitgeber affects an organism’s clock. Two videos, embedded below, explain how PRCs are constructed. First, a video on “Naming Conventions” explains the terminology of “phase shifts.” Second, a video on “Phase Response Curves” explains how a PRC summarizes data about phase shifts in response to a zeitgeber. We will briefly review the basics below, using an example in which light is used as a zeitgeber.


To gather the data for a PRC, scientists experiment with variations on light-dark cycles by using acute light pulses, during which the lights go on for a predetermined period of time before going out. For example, a light pulse might be fifteen minutes long, much less than the light duration of light in a natural daily cycle. These light pulses cause phase shifts , or changes in the timing of the onset, offset, peak, or other notable feature of a circadian rhythm. For example, an acute light pulse to a free-running rat might alter when its next onset of activity occurs.

A PRC relies on the fact that phase shifts can be precisely quantified. By convention, phase shifts are distinguished as positive or negative. A negative phase shift signifies a delay. For example, suppose a rat is free-running, and its onset of activity is occuring with a short period, once every 23.5h. We now apply an acute light pulse, and we find that after the pulse, the next onset of activity occurs 23.9h after the previous onset of activity. The onset of activity was delayed by 0.4h compared to when we would have predicted its occurence on the basis of FRP. We would say that the light pulse caused a negative phase shift of 0.4h. Conversely, a positive phase shift indicates an advance. Suppose a light pulse caused the rat's next onset of activity to occur 23h after its previous onset of activity. The onset of activity was advanced by 0.4h. We would say the light pulse caused a positive phase shift of 0.4h. 

What we have illustrated in these brief examples is that whether a light pulse causes a positive or a negative phase shift depends on when the pulse is delivered with respect to the organism’s circadian time . An pulse of light during the organism's subjective day will have a different effect than an identical pulse of light during the organism's subjective night. In our example above, it could have been the very same light pulse (the same duration, the same light intensity, etc.) that caused a positive phase shift or a negative phase shift of 0.4h: the organism's response depends on the phase of circadian time in when the pulse is applied. The phase response curve provides a quantitative representation of this phenomenon, plotting phase shifts as a function of circadian time.

With the way that an organism's clock and its PRC is built, an organism is always able to change its internal clock to fix itself when put in a periodically light and dark environment. The "dead zone" is the organism's "sweet spot," and the clock will reset itself so that the dead zone aligns with the middle of the light phase. If light ever occurs with too much deviation from the sweet spot, the PRC shows us how the organism's clock will phase shift positively or negatively until the "dead zone" matches mid-day.

What is temperature and what does it truly measure?

Everybody has used a thermometer at least once in their lives, but even without one, our bodies are decent sensors for measuring how hot or cold things are upon contact. We refer to this property as temperature which, in more technical terms, represents the average kinetic energy of the atoms and molecules comprising an object.

Heat or temperature?

Before we go any further with our discussion, it’s important to get something out of the way.

Often heat and temperature are used interchangeably — this is wrong. While the two concepts are related, temperature is distinct from heat.

Temperature describes the internet energy of a system, whereas heat refers to the energy transferred between two objects at different temperatures.

But, as you might have noticed, heat can be very useful when describing temperature.

Imagine a hot cup of coffee. Before pouring the hot elixir of life, the cup had the same temperature as the air surrounding it. However, once it came in contact with the liquid, heat was transferred, increasing its temperature. Now, if you touch the cup, you can feel that it’s hot.

But, given enough time, both the cup and its contents will reach thermal equilibrium with the ambient air. Essentially, they all have the same temperature, which is another way of saying there is no longer a net transfer of energy. Physicists call this the “zeroth law of thermodynamics”. By this principle, heat can only flow from a body that has a higher temperature than another body with which it is in contact — and never the other way around.

The dance of molecules

Everything in this universe is in motion, and motion begets kinetic energy. The faster a particle is moving, the more kinetic energy it has. In fact, kinetic energy increases exponentially with particle velocity.

Where does temperature fit into all of this? Well, temperature is simply an average measure of the kinetic energy for particles of matter. Another way of putting it would be that temperature simply describes the average vibration of particles.

Because the motion of all particles is random, they don’t all move at the same speed and in the same direction. Some bump into each other and transfer momentum, further increasing their motion. For this reason, not all particles that comprise an object will have the same kinetic energy.

In other words, when we measure an object’s temperature, we actually measure the average kinetic energy of all the particles in the object. However, it’s just an approximation.

Within this line of reasoning, the higher the temperature, the higher the motion of the particles. Conversely, when the temperature drops, the motion of the particles is slower. For instance, dyes spread faster through hot water than cold water.

This is why at a temperature of absolute zero, the motion of particles grinds to a halt. Absolute zero is just a theoretical construct and, in practice, it can never be achieved. However, physicists have been able to cool things to a fraction of a degree above zero, trapping atoms and molecules, or creating exotic phases of matter such as the Bose-Einstein condensate (BEC).

It’s important to note that temperature isn’t dependent on the number of molecules involved. A boiling cup of water has the same temperature as a boiling pot of water — both containers have water molecules with the same average kinetic energy, regardless of the quantity of matter involved.

Temperature scales

There are various scales used to describe temperature. In the United States, the most commonly used unit for temperature is Fahrenheit, while much of the rest of the world uses Celsius (or Centigrade). Physicists often prefer to measure temperature in Kelvin, which is also the standard international unit for temperature.

For the Kelvin scale, zero refers to the absolute minimum temperature that matter can have, whereas in the Celsius scale, zero degrees is the temperature at which water freezes at a pressure of one atmosphere (273.15 Kelvin). At 100 degrees Celsius, water begins to boil at a pressure of one atmosphere, offering a neat, linear and relatable scale for describing temperature.

A worthy mention goes to the Rankine scale, which is most often used in engineering. The degree size is the same as the Fahrenheit degree, but the zero of the scale is absolute zero. Often just R for “Rankines” rather than °R is used for expressing Rankine temperatures. The zero of the Rankine scale is -459.67°F (absolute zero) and the freezing point of water is 491.67R.

How temperature is measured

Because of our innate ability to sense how hot or cold things are, humans have had little use for precise measurements of temperature throughout history. However, there have always been mavericks bent on learning about things just for the sake of unraveling nature or getting a kick out of doing science.

Hero, a Greek philosopher and mathematician, is credited with the idea for the first thermometer, writing in the 1st century CE about the relationship between temperature and the expansion of air in his work Pneumatics.

The ancient text survived the degradation of the Roman Empire and the dark ages that followed, until it resurfaced during the Renaissance.

An assortment of Galileo thermometers of various sizes. The bigger the size, the more precise the instrument. Credit: Amazon.

It is believed that Hero’s work inspired Galileo Galilei to invent the first device that precisely measures temperature. The Galileo thermometer is composed of multiple glass spheres each filled with a colored liquid mixture that often contains alcohol but can even be simply water with food coloring added.

Each bubble has a metal tag attached to it that indicates temperature, which also serves as a calibrated counterweight that’s slightly different from the others. These floating balls sink or float inside the surrounding water sinking or climb up the water column slowly and gracefully. People still use them to this day, mostly for decorative purposes.

For more precise measurements, there’s the traditional mercury thermometer whose fluid expands at a known rate as it gets hotter and contracts as it gets cooler. It’s then just a matter of reading the measurement indicated by where the column of liquid ends on the scale.

Robert Fludd, an English physician, is credited with designing the first thermometer in 1638 that had a temperature scale built into the physical structure of the device. Daniel Fahrenheit designed the first mercury-based thermometer in 1714 that ultimately went on to become the gold standard of temperature measurement for centuries.

What happens at absolute zero?

The curious things that happen at low temperatures keep on throwing up surprises. Last week, scientists reported that molecules in an ultra-cold gas can chemically react at distances up to 100 times greater than they can at room temperature.

In experiments closer to room temperature, chemical reactions tend to slow down as the temperature decreases. But scientists found that molecules at frigid temperatures just a few hundred billionths of a degree above absolute zero (−273.15°C or 0 kelvin) can still exchange atoms, forging new chemical bonds in the process, thanks to weird quantum effects that extend their reach at low temperatures.

“It’s perfectly reasonable to expect that when you go to the ultra-cold regime there would be no chemistry to speak of,” says Deborah Jin from the University of Colorado in Boulder, whose team reported the finding in Science (DOI&colon 10.1126/science.1184121). “This paper says no, there’s a lot of chemistry going on.”


New Scientist takes a look at the weird and wonderful realm of the ultra-cold.

Why is absolute zero (0 kelvin or −273.15°C) an impossible goal?

Practically, the work needed to remove heat from a gas increases the colder you get, and an infinite amount of work would be needed to cool something to absolute zero. In quantum terms, you can blame Heisenberg’s uncertainty principle, which says the more precisely we know a particle’s speed, the less we know about its position, and vice versa. If you know your atoms are inside your experiment, there must be some uncertainty in their momentum keeping them above absolute zero – unless your experiment is the size of the whole universe.

What is the coldest place in the solar system?

The lowest temperature ever measured in the solar system was on the Moon. Last year, NASA’s Lunar Reconnaissance Orbiter measured temperatures as low as −240°C in permanently shadowed craters near the lunar south pole. That’s around 10 degrees colder than temperatures measured on Pluto so far. Brrrrrrrrr.

What is the coldest natural object in the universe?

The coldest known place in the universe is the Boomerang Nebula, 5,000 light years away from us in the constellation Centaurus. Scientists reported in 1997 that gases blowing out from a central dying star have expanded and rapidly cooled to 1 kelvin, only one degree warmer than absolute zero. Usually, gas clouds in space have been warmed to at least 2.7 kelvin by the cosmic microwave background, the relic radiation left over from the big bang. But the Boomerang Nebula’s expansion creates a kind of cosmic refrigerator, allowing the gases to maintain their unusual cool.

What is the coldest object in space?

If you count artificial satellites, things get chillier still. Some instruments on the European Space Agency’s Planck space observatory, launched in May 2009, are frozen down to 0.1 kelvin, to suppress microwave noise that would otherwise fog the satellite’s vision. The space environment, combined with mechanical and cryogenic refrigeration systems using hydrogen and helium, chill the coldest instruments to 0.1 kelvin in four sequential steps.

What is the lowest temperature ever achieved in the laboratory?

The lowest temperature ever recorded was back here on Earth in a laboratory. In September 2003, scientists at the Massachusetts Institute of Technology announced that they’d chilled a cloud of sodium atoms to a record-breaking 0.45 nanokelvin. Earlier, scientists at the Helsinki University of Technology in Finland achieved a temperature of 0.1 nanokelvin in a piece of rhodium metal in 1999. However, this was the temperature for just one particular type of motion – a quantum property called nuclear spin – not the overall temperature for all possible motions.

What weird behaviour can gases display near absolute zero?

In everyday solids, liquids and gases, heat or thermal energy arises from the motion of atoms and molecules as they zing around and bounce off each other. But at very low temperatures, the odd rules of quantum mechanics reign. Molecules don’t collide in the conventional sense instead, their quantum mechanical waves stretch and overlap. When they overlap like this, they sometimes form a so-called Bose-Einstein condensate, in which all the atoms act identically like a single “super-atom”. The first pure Bose-Einstein condensate was created in Colorado in 1995 using a cloud of rubidium atoms cooled to less than 170 nanokelvin.

How can we measure light precisely and how can the universe expand?

How is it possible that we can measure the speed of light so precisely?? The speed of something can only ve measured in reference to another object, can't we just measure the speed of light in two directions and have the exact speed at which that point in the earth is moving ( C - measured C = speed of that point of earth.

Extra question: How is it that the universe is expanding? I have a big theory on this but how is it that we can measure the expansion of the universe?? That doesn't make any sense to me because if the universe is expanding we are also expanding, how can we know that what we percieved as 10 meters is now 20 meters if our instruments for measures also expanded and our own body, mind, eyes, atoms, and even the photons in the universe also expanded?

I say this cause scientists say the universe expands faster than the speed of light.

Extra extra bonus final boss easy question

How can something not pass the speed of light if the momentum formula is f=m.v being f force, m mass and v volume. To move something of 1 kg faster than the speed of light you need more newtons than speed of light, does a newton always take the same energy to achieve or does one newton take more energy in relation to the one that was applied before??

Thanks in advance for clearing my mind! I think a lot about this things but school is shit, I'm 16 and we are learning movement, I wanna learn about plancks not fucking a.t+iv=fv, that's easy boring shit. (Sorry for small rant)

Edit: that's my record of internet points in this site, thanks to everyone for answering.

The speed of something can only ve measured in reference to another object, can't we just measure the speed of light in two directions

The speed of light is always the same, even if you're moving. It's only speeds below the speed of light which are relative.

What you're describing is almost exactly the Michelson-Morley experiment - measuring the speed of light in two directions. But it doesn't work because light is always measured to be moving at c, even by two people who are measuring the same light but moving at different speeds themselves.

Space and time "rotate" into one another as you change your speed in a way which essentially conspires to maintain the speed of light as you measure it. What one experimenter sees as space (and time) is not quite the same as what another (relatively moving) experimenter sees as space (and time).

Hijacking this top comment to pose another related question:

We know that the effects of time dilation increase exponentially as we approach c, with time quite literally "freezing" at C (which we know is impossible for any object with mass). In a theoretical universe where c travel is possible, travel from any two points in the universe is literally instantaneous. With this in mind, and with the obvious understanding that light has no concept of "time," wouldn't we assume that light emitted from the big bang reached the edge of the current universe. instantly? As in, the age of the universe is 0? How do we meld our perception of time and the measured age of the universe With the fact that the reference frame containing light emitted from the big bang has experienced no passage of time?

I guess a more direct way to ask this question is this: I understand the experience of time is entirely relative, and that in essence the calculated age of the universe shouldn't be thought of in our concept of how "long" a year is-- it's literally the number of times the earth has circled the sun (or would have if it existed), which is objective and measurable. But I just cant wrap my mind around the fact that in existant reference frames the age of the universe remains null

Would anything weird happen if light somehow traveled at a lower or higher speed? Would it eventually become something different from light?

To the first question. You can measure the speed by synchronizing two clocks, taking one very far away and then sending an object from one to the other at a very specific moment in time and then counting how long it takes before it arrives. If your measurements are sufficiently fast you can even measure the delay of light in very small distances in processors for example.

To the second question. I don't know much of the details behind the mechanisms of the expansion of the universe but it isn't so much that everything just gets larger but that the space in which objects are located gets larger. It acts like a sort of force accelerating content inside space out. As long as the forces holding objects together are larger, the objects will not grow in size themselves. We know it is expanding because distant objects move away from us which causes a doppler shift in the frequency at which they send their light. They look more red if they fly away from us and more blue if they move towards us. Similar to how an ambulance sounds different when it comes to you and moves away from you.

The formula f=mv is not correct. It should be F=ma. Where everything is the same but a is the acceleration. These equations however need to be corrected if you account for relativity which limits our velocity and those equations get much more complicated to a point where I'm not comfortable going into detail and I also don't think it would help you too much at this point. I think the most important lesson for you to take away from this is that some equations in physics aren't perfect but just sufficiently good within certain conditions and as long as you are not going a significant fraction of the speed of light for example. The principles that will happen once you start reaching the speed of light is that time doesn't move equally fast for different frames of reference which causes all kinds of non-relativistic physics to stop working properly.

If something goes really fast (99.99% speed of light for example), its time from the perspective of a stationary observer would ɺlmost' stand still. You might see the problem with definitions of force here.

"The formula f=mv is not correct. It should be F=ma."

As the OP mentioned Momentum, I think the correction in his equation isn't "v" to "a", but "f" to "p". p=mv is the correct equation for momentum

The first experiment you talked about doesn't make sense in my mind, what does sending an object between two points have to do if you can't send it at the speed of light.

Then from your second answer how is it that things expand but they don't if gravity is stronger between them?? Objects far away have gravity towards their own particles, if the forces that are "pulling them apart" are stronger than the gravity they have towards the universe then they aren't expanding, they are just travelling in a direction, I recall reading that the universe is expanding at an increasing rate so it's either expanding with its own atoms also expanding so it's a logical fallacy (can't be proven wrong), or it's not expanding and it's just being pulled apart by other stuff outside the universe, or there are other factors that we aren't taking into account. I used to think that we can't see stuff very far from us since we aren't in the centre of the universe and light hasn't traceled here yet but idk.

You cleared my mind on the third question and produced me more questions for the other two so thank you so much for replying.

We can just measure the speed of light like we can measure any other speed. The speed of light is only 300,000,000 meters per second. We can easily make things that make measurements at 1000 times per second or more. So all you would need to measure the speed of light is a distance 150 kilometers long, a mirror and a sampling rate of 1000 times per second. This is exactly how we got our first measurement of the speed of light. We created a pulsing light beam and then shot it at a mirror, then had a spinning disc that we could change the RPM of next to the emitter, this lets us measure very precisely what the travel time of the pulses are.

Our own bodies, atoms, and eyes are not expanding. The force pushing everything away from each other is ridiculously weak and almost any object's gravity can overcome it. The space between galaxies is very very big though, much bigger than the space inside of galaxies, so the dark energy force that is causing the universe to expand is greater than the incredibly tiny force pulling galaxies towards each other, so galaxies move away from each other, but the forces inside galaxies and between very close galaxies like our own local group is more than enough to keep those things together.

The speed of light does not work the way you think it works, and has nothing to do with light itself. What we call the speed of light is actually the speed of causality. Light in it's own reference frame moves almost infinite distance in almost zero time. Light moves much much much much faster than the speed of light in it's own reference frame. So f=ma works until infinity in your own reference frame. It is only outside stationary observers that see things moving at the speed of light. We don't really know what causes this, but one theory is that it's the Higgs field. The Higgs field is a sea of quantum particles that fills the universe and imparts mass to objects in the universe, letting them interact with other objects.

If you're familiar with how the speed of sound in a medium works, we get the speed of sound because it is the maximum speed that particles in air, steel, or water can transmit a wave from one particle to another. The speed of light/the speed of causality is thought to work in the same way. When you move from one location to another in the universe your mass has to go with you before you can move again. So as you move faster and faster the Higgs field has trouble handing off your mass from the particles at your previous position, to your new position fast enough. Because you cannot experience time without mass you do not experience these delays with the Higgs field updating your position, but outside observers see you moving in slow motion much like watching a laggy video on YouTube that is constantly buffering. Just because people watching a video of an SR-71 Blackbird with very slow buffering see it taking much more time to cross a distance, doesn't mean the plane in the video is going any bit slower. The plane is still moving ridiculously fast, it's just that you as an outside observer experience it moving much slower due to the buffering. Likewise outside observers see things moving at or near the speed of light with progressively more buffering. Those things going near the speed of light are still moving incredibly fast, quadrillions of meters per second or more in their own reference frames, but we can only update their positions at a maximum speed of about 300 million meters per second when we observe those objects.


Receptors are biological transducers that convert energy from both external and internal environments into electrical impulses. They may be massed together to form a sense organ, such as the eye or ear, or they may be scattered, as are those of the skin and viscera. Receptors are connected to the central nervous system by afferent nerve fibres. The region or area in the periphery from which a neuron within the central nervous system receives input is called its receptive field. Receptive fields are changing and not fixed entities.

Receptors are of many kinds and are classified in many ways. Steady-state receptors, for example, generate impulses as long as a particular state such as temperature remains constant. Changing-state receptors, on the other hand, respond to variation in the intensity or position of a stimulus. Receptors are also classified as exteroceptive (reporting the external environment), interoceptive (sampling the environment of the body itself), and proprioceptive (sensing the posture and movements of the body). Exteroceptors report the senses of sight, hearing, smell, taste, and touch. Interoceptors report the state of the bladder, the alimentary canal, the blood pressure, and the osmotic pressure of the blood plasma. Proprioceptors report the position and movements of parts of the body and the position of the body in space.

Receptors are also classified according to the kinds of stimulus to which they are sensitive. Chemical receptors, or chemoreceptors, are sensitive to substances taken into the mouth (taste or gustatory receptors), inhaled through the nose (smell or olfactory receptors), or found in the body itself (detectors of glucose or of acid-base balance in the blood). Receptors of the skin are classified as thermoreceptors, mechanoreceptors, and nociceptors—the last being sensitive to stimulation that is noxious, or likely to damage the tissues of the body.

Thermoreceptors are of two types, warmth and cold. Warmth fibres are excited by rising temperature and inhibited by falling temperature, and cold fibres respond in the opposite manner.

Mechanoreceptors are also of several different types. Sensory nerve terminals around the base of hairs are activated by very slight movement of the hair, but they rapidly adapt to continued stimulation and stop firing. In hairless skin both rapidly and slowly adapting receptors provide information about the force of mechanical stimulation. The Pacinian corpuscles, elaborate structures found in the skin of the fingers and in other organs, are layers of fluid-filled membranes forming structures just visible to the naked eye at the terminals of axons. Local pressure exerted at the surface or within the body causes deformation of parts of the corpuscle, a shift of chemical ions (e.g., sodium, potassium), and the appearance of a receptor potential at the nerve ending. This receptor potential, on reaching sufficient (threshold) strength, acts to generate a nerve impulse within the corpuscle. These receptors are also activated by rapidly changing or alternating stimuli such as vibration.

All receptors report two features of stimulation, its intensity and its location. Intensity is signaled by the frequency of nerve impulse discharge of a neuron and also by the number of afferent nerves reporting the stimulation. As the strength of a stimulus increases, the rate of change in electrical potential of the receptor increases, and the frequency of nerve impulse generation likewise increases.

The location of a stimulus, whether in the external or internal environment, is readily determined by the nervous system. Localization of stimuli in the environment depends to a great extent on pairs of receptors, one on each side of the body. For example, children learn very early in life that a loud sound is probably coming from a nearer source than a weak sound. They localize the sound by noticing the difference in intensity and the minimal difference in time of arrival at the ears, increasing these differences by turning the head.

Localization of a stimulus on the skin depends upon the arrangement of nerve fibres in the skin and in the deep tissues beneath the skin, as well as upon the overlap of receptive fields. Most mechanical stimuli indent the skin, stimulating nerve fibres in the connective tissue below the skin. Any point on the skin is supplied by at least 3, and sometimes up to 40, nerve fibres, and no two points are supplied by precisely the same pattern of fibres.

Finer localization is achieved by what is called surround inhibition. In the retina, for example, there is an inhibitory area around the excited area. This mechanism accentuates the excited area. Surround excitation, on the other hand, is characterized by an excitatory area around an inhibitory area. In both cases contrast is enhanced and discrimination sharpened.

In seeking information about the environment, the nervous system presents the most-sensitive receptors to a stimulating object. At its simplest, this action is reflex. In the retina a small region about the size of a pinhead, called the fovea, is particularly sensitive to colour. When a part of the periphery of the visual field is excited, a reflex movement of the head and eyes focuses the light rays upon that part of the fovea. A similar reflex turns the head and eyes in the direction of a noise. As the English physiologist Charles Sherrington said in 1900, “In the limbs and mobile parts, when a spot of less discriminative sensitivity is touched, instinct moves the member, so that it brings to the object the part where its own sensitivity is delicate.”

Reviewing the Strategy and Determining Success

Another important part of laboratory temperature monitoring is tracking historical data and fluctuations. The right monitor collects data and compiles reports for you. With these reports in hand, it’s easy to see patterns and trends.

From there, you can determine if you’re meeting your goals. You might think your current system is working well, only to see lab temperatures change many times a day. This kind of information can help as you review and revise your strategy.

The system can also give insight into how often the temperature exceeds thresholds. It can even provide data about when fluctuations occur, so you can link those changes back to causes.

With so much information at your fingertips, it’s easy to decide your next steps. Revising your strategy has never been easier.


The suggestion that most amino acid substitutions are slightly deleterious was originally offered to resolve contradictions between the predictions of neutral theory and empirical observations (15). In exploring how this novel premise might realign predictions and data, a number of theoretical studies simulated molecular evolution under predefined distributions of mutant selection coefficients (see, for example, ref. 32). The results presented here suggest that a priori assumption of a particular distribution of mutant selection coefficients is inappropriate for steady-state models of nearly neutral evolution. The distribution of mutant selection coefficients is determined by the operation of the evolutionary dynamic on the landscape of all possible genotypes and therefore cannot be assumed a priori. In fact, the distribution determined by the evolutionary dynamic will differ in important ways from distributions assumed a priori. For instance, we found that the steady-state distribution of mutant selection coefficients will take a form that causes the number of fixations involving an additive fitness change Δx to equal the number of fixations involving an additive fitness change -Δx. This property will not, in general, be exhibited by distributions of mutant selection coefficients assumed a priori.

Although we find that the premise that most substitutions are slightly deleterious may be incorrect, many of the deductions that rely on this premise remain in tact. For example, steady-state nearly neutral evolution may still provide an explanation for the constancy of the rate of molecular evolution across organisms with very different generation times. According to detailed balance, on average, for one adaptive substitution with a given selection coefficient to occur, a corresponding deleterious substitution must also take place. Because deleterious mutations are much less likely to fix than adaptive ones, fixation of deleterious mutations remains the rate-limiting step in molecular evolution, and Ohta's (16) rationale for the molecular clock may still hold. Other classical arguments, such as Ohta's explanation for the surprisingly weak relationship between polymorphism and population size, can be rephrased along similar lines.

An important simplifying assumption in our analysis was that mutations are sufficiently rare that the fixation probability of a mutation is not affected by other segregating alleles. Although future work may determine whether the methods presented here can be generalized to incorporate interactions among segregating sites, we must presently address the applicability of theory that omits such important processes as hitchhiking (15, 33) and background selection (12). Most straightforwardly, the results presented here can be viewed as an approximation that becomes acceptably accurate under certain population parameters. For example, in small populations, mutations are rare, and therefore our simplified evolutionary dynamics and the results we have derived from them become decent approximations of reality (4). More generally, however, the theory considered here may allow us to more adequately understand the behavior of models that frequently serve either as null models or as theoretically tractable heuristics in studies of more complicated molecular evolutionary dynamics. For instance, revising the premise that slightly deleterious substitutions predominate may affect how the null hypothesis of steady-state nearly neutral evolution is simulated in studies measuring rates and effects of adaptation in the genome. Or, to offer another example, closed-form expressions for the effect of population size on key population genetic statistics may facilitate evaluation of the suggestion that the effects of hitchhiking or background selection can be approximated theoretically by a rescaling of population size in neutral theory (12, 34).

Besides adopting important simplifying assumptions, the theory treated here reduces the complexity of dynamics by treating the averages of large numbers of degrees of freedom. Although such averages are clearly meaningful in the classical systems of statistical physics, in which the number of degrees of freedom is generally on the order of Avogadro's number, one may reasonably ask whether averages are actually useful in genetic systems, in which the number of degrees of freedom is so much smaller. Although population genetics initially concerned itself with the dynamics at one or a few sites of interest, the recent flood of genomic data has allowed measurement of averages over many sites. For instance, it is now common to compare average evolutionary rates or average levels of codon bias across many genes in the genome (35, 36). Such studies encounter tremendous noise, and predictions are far from precise (especially by the standards of statistical physics), but averaging across sites within genes and comparing large numbers of genes often allow detection of important trends.

The applicability of the theory treated here should also be discussed in light of Eq. 9 , which gives the probability that any given genotype is fixed in the population. The time scales of evolution do not allow exhaustive exploration of large and rugged fitness landscapes instead, populations are often confined to exploration of a local fitness peak. Such metastable states do not reflect an equilibrium in the strict sense because, given sufficient time, the system would eventually leave each local peak. Nonetheless, under the approximation that the local landscape is bounded by valleys that cannot be traversed, Eq. 9 and the results that follow from it would apply.

A number of authors (3, 37–39) have noted parallels between statistical physics and evolution. In 1930, R. A. Fisher wrote that “. the fundamental theorem [of natural selection] bears some remarkable resemblance to the second law of thermodynamics. It is possible that both may ultimately be absorbed by some more general principle” (3). In accordance with this suggestion, we have shown that the mathematical description of evolution of a finite population in a constant environment is analogous to that of a thermodynamic system. Our treatment does not address how evolutionary systems, which are themselves physical systems, are subject to the laws of statistical physics [as, for example, Schrödinger suggests (40)]. The analogy we have developed does, however, show that the methods used to describe systems in statistical physics can be applied to evolutionary systems in a useful way. This analogy leads to a general analytical form for the steady-state distribution of fixed genotypes, thus reducing the solution of a large family of evolutionary models, including Fisher's geometric model, to several straightforward substitutions. The close parallels between statistical physics and evolutionary dynamics also prove useful in elucidating basic evolutionary relationships, such as that between genetic load and effective population size, and in revealing new generalizations about dynamic behavior at steady state, such as the equality of the number of adaptive and deleterious substitutions. Finally, the analogy permits derivation of an energy function for evolutionary dynamics of a finite population. The form of this energy function is precisely that of free energy, and the maximization of free fitness is precisely analogous to the second law of thermodynamics.


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