BIOPHYSICS - THEORY
Biophysics is a sub-discipline of the Biology that studies the physical principles underlying all the processes of the living systems.
Biophysics is a reductionistic science because it determines that all the phenomena observed in nature have a predictable scientific explanation.
If some natural phenomena cannot be explained at present, it would not mean that those phenomena won’t be explained in the future. Our ignorance about those phenomena is because we do not have the adequate tools to study the underlying causes to those phenomena. However, there are problems which scientists think will never have an explanation; for example, the size of the Universe.
The life is a function of state that depends on stochastic processes at microscopic level (microphysical laws) and deterministic processes at macroscopic level (macrophysical laws). The biophysics' subjects of study are both, stochastic and deterministic processes.
A stochastic system is a system whose microscopic states have random underlying causes. A deterministic system is a system whose microscopic states have knowable underlying causes.
Biophysics is not a branch of physics, but of Biology. I make this clarification because in many books of biophysics it is said that biophysics is the study of the biological processes from the point of view of physics, which is erroneous because the physics is not limited to the study of the biological processes but of the processes taking place in the whole nature. Biophysics explains the biological phenomena applying physical principles.
For example, biophysics studies the changes of polarity in the microtubules of Paramecium, or the transference of energy from one to another molecule of the complex molecular engine known as ATP synthase, or the mechanics of a human skeleton, or the dynamics of fluids of a grasshopper, etc.
In general, a system is an amount of matter contained by real or imaginary limits.
In biophysics, the same as in thermodynamics and quantum mechanics, a system is an aggregate of elements integrated into real or imaginary limits.
The difference between the concept of system in thermodynamics and the concept of system in biophysics is that thermodynamics considers a system like a conglomerate of matter, whereas biophysics considers a system as the aggregates of matter with a set of functions that compose a process within structural and space/time limits.
A thermodynamic system is one that can exchange heat and energy with the environment. The living beings are essentially thermodynamic systems. For example, an ant is a system made of diverse kinds of molecules, while the nervous functions of that ant constitute a system formed by autoregulated sequences of microphysical processes.
The systems can be classified into the following types:
Open systems, which interchange matter and energy with the environment.
Closed systems, which only interchange energy with the environment, but not matter.
Isolated systems, which do not interchange energy and matter with the environment. The isolated systems are idealizations which do not exist in the real world.
The living beings are true-open systems because they interchange matter and energy with the environment.
A false concept on the state of the Earth's system has been introduced by some authors saying that the Earth is a “quasi-closed” system; i.e., that the Earth “almost” does not interchange matter with the outer space. This is a conceptual error because the concept does not imply the quantity of matter interchanged, but the interchange of matter between a system and its surroundings. If a system is interchanging few particles with its surroundings, then that system would be an open system. “Quasi-closed" systems do not exist in nature or in mathematical equations.
THERMODYNAMICS IN BIOPHYSICS
In view of the fact that bionts are thermodynamic systems, they are governed by the same physical laws by which the inert matter is governed. The formulas on heat transfer which are applicable to the processes in inert systems also are appropriate for biosystems. Thus, the laws that we have learned in papers like heat transfer and heat stored by greenhouse gases are also functional for biosystems.
The paths of heat transfer in biosystems are exactly the same paths that happen in the abiotic nature (abiotic means lifeless). Consequently, we can apply to biosystems’ thermal processes the same mathematical procedures and physical laws that we use for studying the inert matter.
Let us deal first with the definitions of the laws of thermodynamics and the concepts and formulas used in heat transfer science.
1. LAWS AND GENERAL FORMULAS:
1st Law of Thermodynamics: Energy can be changed from one form to another, but it cannot be created or destroyed.
The mathematical expression of the 1st. law is as follows:
ΔU = ΔQ – ΔW
Where ΔU is the increase of the internal energy of a thermodynamic system, ΔQ is the amount of heat applied to the thermodynamic system, and ΔW is the change of work done by that thermodynamic system.
The formula means that the change in the internal energy of a system is equal to the heat transferred to that system minus the work done by that system in its environment.
2nd Law of Thermodynamics: In all transformations from one form of energy into another form of energy, a quantity of energy is always dispersed towards other states, generally in the form of heat.
The mathematical expression of the 2nd law is as follows:
ΔS/Δt ≥ 0
Where ΔS is the increase of the entropy, and Δt is time.
The formula denotes that the change in the entropy in a thermodynamic system is always higher or equal to zero, and that time is the fundamental dimension in which the system is doing work.
The formula permits us to deduce other conceptualizations of the 2nd law which mean the same thing, for example:
1. No system can transform energy into useful forms of energy with an efficiency of 100 percent.
2. Energy cannot spontaneously rearrange from low density states to high density states.
3. Heat is never spontaneously transferred from cold systems to hot systems.
4. The entropy of any thermodynamic system is constantly increasing over time.
2. GENERAL FORMULAS TO CALCULATE THE FLUCTUATIONS OF TEMPERATURE:
CONDUCTION is the flow of heat through solids and liquids by vibration and collision of molecules and free electrons. The molecules of a portion of a system at a higher temperature vibrate faster than the molecules of other regions of the same -or of another- system at lower temperature. The molecules with a higher movement collide with the molecules less energized and transfer part of their energy to the less energized molecules of the colder regions of the structure. For example, the energy transfer by conduction through the bodywork of a car.
Metals are the best thermal conductors; while non-metals are poor thermal conductors. For comparison, the thermal conductivity (k) of the copper is 401 W/m*K, while the thermal conductivity (k) of the air is 0.0263 W/m*K. The thermal conductivity of the carbon dioxide (CO2) is 0.01672 W/m*K, almost the thermal conductivity of an isolator.
Formula to calculate the conductivity gradient for a given system:
q = - kA (Δ T/Δ n)
Where Δ T/Δ n is the temperature gradient in the direction of area A, and k is the thermal conductivity constant obtained by experimentation in W/m.K.
CONVECTION is the heat transfer through currents within a fluid (a liquid or a gas). Convection is a movement of liquid or gaseous volumes. When a mass of a fluid warms because it is in contact with a hot surface, its molecules are expanded and scattered causing that the mass of that fluid becomes less dense. As the hotter volume of the fluid becomes less dense, it will be displaced vertically and/or horizontally, while the less hot but denser volumes of the fluid will sink (the less hot volume is displaced by the hotter volume of fluid). By this mechanism, the hotter volumes transfer energy towards the less hot volumes of that fluid (a liquid or a gas).
For example, when we heat up water on a stove, the volume of water at the bottom of the pot will be warmed up by conduction from the metal of the pot and it will become less dense. Then, because it is less dense, it will shift upward to the surface of the volume of water and will displace to the upper -less hot and denser- mass of water.
Formula of Convection:
q = hA (Ts - T ∞)
Where h is the constant for the convective heat transfer coefficient, A is the area implied, and Ts - T∞ is the difference between the temperature of skin (Ts) and the temperature of the flowing fluid (T∞).
To calculate the convective heat transfer coefficient of the skin we use the next formula:
h = (8.3 W/m^2 K) [(v air (0.6 s/m)]
Where vair is the velocity of air (m/s) and 0.6 s/m is a proportionality constant. For example, if a clothed man is surrounded by air which velocity is 0.5 m/s, the convective heat transfer coefficient (h) of his skin would be:
h = (8.3 W/m^2 K) [0.5 m/s (0.6 s/m)] = 8.3 W/m^2 K (0.3) = 2.49 W/m^2 K
RADIATION is the transfer of heat by electromagnetic radiation. It does not need a propagating medium. Radiated energy moves at the speed of light. The thermal energy radiated by the Sun can be exchanged between the solar surface and the Earth's surface without heating the transitional space.
For example, if I place an object (such as a coin, a car, or myself) under the direct sunbeams, I will note in a little while that the object will be heated. The exchange of energy between the Sun and the object occurs by radiation.
Living beings are good emitters and absorbers of radiant energy. For example, the skin of a white human being has an emissivity of 0.7 - 0.9, depending on the pigmentation of the skin; bronzed skins absorb and emit more energy than white skins.
The formula to know the amount of heat transferred by radiation is:
q = e σ A [(ΔT)^4]
Where q is the heat transferred by radiation, E is the emissivity of the system, σ is the constant of Stephan-Boltzmann (5.6697 x 10^-8 W/m^2.K^4), A is the area involved in the heat transfer by radiation, and T^4 is the the fourth power of the absolute temperature.
EXAMPLES IN THE HUMAN BODY
The rate of thermal energy storage in form of internal energy of the human body is defined by the next formula:
q = M – W – E – Q = W/m^2
Where q is the rate of energy storage of human body, M is the metabolic rate of human body in Mets (58.2 W/m^2 = 1 Met), W is the mechanical work produced by the human body, E is the rate of total evaporative loss due to evaporation of sweat, and Q is the total rate of energy loss from the skin (not including sweat).
For knowing the linear flux of energy (JQc) under the mentioned conditions, we use the next formula:
JQc = - λ (∆T / ∆x)
Where λ is the thermal conductivity (thermal coefficient) in J/m s K, ∆T is the difference of temperature between two systems, and ∆x is the direction of the temperature gradient.
There are several channels of heat transfer between the human body and its environment. Some channels end in the corium, internal with respect to the epidermis; other channels “cross” muscles, fat layer, epidermis and hair, until reaching the interface or viscous boundary layer, which connects the body system with the environment and where the thermal energy is transferred to the surrounds by conduction, convection, radiation and evaporation, if the body is within air, or by conduction, convection and radiation, if it is submerged in water.
For example, the energy transferred by conduction can reach directly to the interface or viscous boundary layer. The energy transferred by convection can diffuse only to the layer of fat; however, the heat insulated by the layer of fat is transferred through conduction out to the interface (viscous boundary layer) where it will start again the channel of convection and radiation for being diffused to the surrounds. On the other hand, the energy transferred by radiation begins in the epidermis, not in the inner tissues, and it is radiated directly towards the environment.
For calculating changes of the internal energy of a biosystem we use the fundamental Gibbs' formula. Gibbs’ formula permits the calculation of the differential of the internal energy (dU) of a biosystem (any living being), which is determined by several differentials that are translated into work:
dU = T dS – p dV + Fdl + Σ μi dni + ψ dq
Where T is the temperature of the system, dS is the local entropy of the system, -p is the compression pressure, dV is the differential of volume caused by the compression, F is a given force exerted on the system, dl is the differential of elongation or size change, m is a determined number of molecules, i is a unit vector in a given direction, μi is the chemical potential of the unit vector, dni is a certain number of atoms or molecules, ψ is an electrodynamic potential and dq is any amount of electrical charge.
We could say that the Gibbs’ fundamental equation is the equation of life, of such form that we could determine whether a system is biotic or not by simply trying to apply the formula on the work (W) done by that biosystem and on the amount of heat used by that system for doing work. Any of the Gibbs’ fundamental equation parameters can be adjusted by expanding or reducing them according to the studied bioprocess or to the biosystem’s physiology.
HEAT FLUX DUE TO CONDUCTION BETWEEN THE HUMAN BODY AND ITS ENVIRONMENT.
As we have learned in the previous section, the formula to know the linear flux of energy due to conduction is as follows:
JQc = - λ (∆T / ∆x)
λ (thermal coefficient) of human epidermis and corium = 0.34 J/m s K
T of surrounds = 315.65 K (42.5 °C)
T of the human body = 306.15 K (33 °C)
∆T = 9.5 K
∆x = 0.01 m (averaged thickness from bone to the viscous boundary layer)
JQc = - 0.34 J/m s K (9.5 K / 0.01 m) = - 323 J/s
Then the load of heat flux by conduction between the human body and the surroundings is - 323 J/s. The negative sign means that the energy flux is from higher to lower temperature, in this case from the surroundings (warmer) to the human body (colder).
When we investigate the human body, we use the value 0.7 like the absorptivity-emissivity of the human body because it is a gray body.
In 14 September 2008 at 11:00 UT , the ambient temperature was 20 °C. The temperature of my left forearm skin was 31.4 °C. What is the heat flux between my body and the environment?
If the environmental temperature is lower than the temperature of the human body, the last would tend to lose more energy. If Met = 1, cooling or heating of the human body would not occur. If Met > 1, the human body would heat up and it would have to “force” the excess of energy towards the environment; first by convection (almost 80% of the thermal energy stored) into the human body, by conduction out to the epidermis, and through conduction, radiation, evaporation and convection from the epidermis to the environment. If Met is less than 1, the human body would cool, and the mechanisms to stop losing energy would be triggered.
HEAT FLUX DUE TO RADIATION BETWEEN THE HUMAN BODY AND ITS ENVIRONMENT.
To know the flux of energy transferred from the body to the environment due to radiation we would use the next formula:
q = 0.7 (A) (σ) (Tsur^4 - Thb^4)
Where 0.7 is the absorptivity- emissivity of the real human body (because it is a gray body. The value changes depending on the pigmentation of the skin), A is the area of exchange of heat, σ is the Stephan-Boltzmann constant (or proportionality constant = 5.6697 x 10^-8 W/m^2 K^4), Tsur is the temperature of the environment surrounding the body, and Thb is the temperature of the human body.
For example, let’s suppose an adult (body surface = 1.9 m^2) in an environment at 20 °C and with a skin temperature of 31.5 °C. First of all we should convert Centigrades to Kelvin:
Absolute temperature of environment = 20 °C + 273.15 = 293.15 K
Absolute temperature of the human skin = 31.5 °C + 273.15 = 304.65 K
A = 1.9 m^2
q = 0.7 (1.9 m^2) (5.6697 x 10^-8 W/m^2 K^4) ([293.15 K]^4 - [304.65 K] ^4) = - 92.66 J/s (-93 J/s, rounding up the cipher). - 93 J/s is Power, equivalent to - 93 W.
Balance of energy:
To know the balance of the energy (I) we use the next formula:
I = P/A
Where I is the energy balance, P is the flux of energy by radiation and A is the area.
I = - 93 W/1.9 m^2 = - 48.77 W/m^2 (-49 W/m^2, rounding up the cipher).
The negative sign means that the energy is being diffused from higher to lower temperature. The energy balance is 49 W/m^2.
The loss of energy is – 93 J/s and the intensity of the energy radiated is -49 W/m^2; something that does not coincide with reality.
Considering only the area of exposed skin where an active exchange of energy with the environment occurs, the flux of energy by radiation is –13.17 J/s; however, the energy balance is also -49 W/m^2 (As a rule of thumb, for biological heat transfer calculi of the areas exposed to the environment, we consider 14% of the total body surface).
HEAT FLUX DUE TO CONVECTION BETWEEN THE HUMAN BODY AND ITS ENVIRONMENT
To know the flux of energy transferred from the body to the environment due to convection we would use the next formula (described in section 2):
q = hA (Ts - T ∞)
The convective heat transfer coefficient is calculated considering the fluid into which the human body is immersed, for example air or water, and the velocity of that fluid.
For a particular condition under which a naked body, whose exposed skin is 1.6 m^2 which is at a temperature of 31.2 °C, is surrounded by air for which the currents acquire a velocity of 0.5 m/s and is at a temperature of 35 °C, we obtained a value for h equal to 2.49 W/m^2 K. Let us calculate the heat flux from that person due to convection. Please, remember that we should convert the temperature from degrees Celsius to Kelvin, although we can develop the formula using degrees Celsius:
h = 2.49 W/m^2 K
A = 1.6 m^2
Ts = 31.2 + 273.15 = 304.35 K
T ∞ = 35 + 273.15 = 308.15 K
Ts - T ∞ = -3.8 K
q = 2.49 W/m^2 K (1.6 m^2) (-3.8 K) = -15.14 W
The intensity of diffusion of energy due to convection out from a nude human body is:
I = P/A = -15.14 W/1.6 m^2 = -9.5 W/m^2
Now let's consider the skin at 33 °C in an ambient at 42.5 °C. Air velocity is 0.5 m/s:
q = 2.49 W/m^2 K (1.6 m^2) (-9.5 K) = -38 W
And the balance is:
I = P/A = -38 W/1.6 m^2 = -23.7 W/m^2
Fortunately, our bodies count on a precise system of thermorregulation which maintains an internal steady temperature. When the air is warmer than the organism the trajectory of the flux of energy is towards the organism. However, if healthy, when it is under those conditions, the body losses energy through evaporation (sweat).
Heat stroke occurs precisely because the organism cannot discard the absorbed thermal energy from the environment. It has nothing to do with global warming or other extreme climatic conditions, but with the state of healthiness of the organism, which, at some point, cannot respond adequately to high ambient temperatures.
THERMOREGULATION IN PLANTS
Plants, like many other organisms like bacteria, fungi, fish, amphibians and reptiles, are poikilothermic organisms. Poikilotherm is a term referring to living beings which body’s temperature depends on the environmental temperature; hence, they experience fluctuations of their internal temperature, into permissible margins of survival, along with fluctuations of the ambient temperature.
It is not correct to say that poikilotherms cannot control their corporal temperature because they resort to various biophysical and biochemical mechanisms which protect them from severe changes of the environmental temperature. Of course, I am referring to extreme changes which do not exceed the survival restrictions of individuals.
The metabolism of living beings takes place within ideal boundaries of temperature. Many proteins become denaturalized with excessive absorbed energy or inhibited with freezing. Therefore, any organism, so homothermous (organisms which corporal temperature undergoes minimal fluctuations) as poikilothermous (organisms which corporal temperature depends on the environmental temperature) must avoid extreme changes of their internal temperature.
When we talk about plants, we could think that they are organisms unprotected before the oscillations of the environmental temperature, i.e. if the atmosphere is warm, the plant would be warmed up, whereas if the environmental temperature is cold, the plant would be frozen irremediably. It is not true; the vegetables also counts with a complex system of control of their internal temperature. This system consists of diverse elements which work in cascade; for example, transpiration, modification of the vascular system to facilitate the dissipation of the excess of absorbed energy or the storage of the absorbed energy, the regulation of the absorption of energy transferred from the environment by means of biochemical mechanisms, etc.
We are conducting a short investigation for knowing the thermal response of melon plants facing the normal variations of the environmental temperature. The preliminary results are summarized in the following graph: