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Roee R.
Biomolecular Scientist and Engineer
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Physics (Heat Transfer)
TutorMe
Question:

Explain, in words, why the temperature profile through a barrier or material is linear if the temperatures on either side of the barriers is constant.

Roee R.

We start with the behavior of the barrier material in terms of heat transfer through the material, along its thickness. We assume that Newton's law of cooling is in effect, meaning that heat will flow from a high-temperature reservoir to a low-temperature reservoir, and that that heat flow is proportional to the termperature difference between reservoirs. We then consider an infinitesimal thickness of the material (a slice cut perpendicular to the thickness axis) and see that, in this case, the rate of heat transfer from one element to its neighboring element is proportional to the temperature difference between the elements. In functional form, we say that the derivative of temperature (across the thickness axis) equals the heat transfer rate times some constant k. Now, we know that in a steady-state case, because of energy conservation, the rate of heat entering the material must equal the rate of heat leaving the material, which then means that the rate of heat transfer is this same rate throughout the material. Because the heat transfer rate is constant, the derivative of temperature through the material thickness (from hot side to cold side) is linear since the derivative of it is a constant. The temperature profile is thus linear and is a line drawn from the hot temperature side to the cold temperature side.

Calculus
TutorMe
Question:

Prove that the limit of sin(x) is x as x approaches zero: $$lim_{x \to 0}\sin(x) = x$$

Roee R.

The derivative of sin(x) is cos(x) and the value of cos(x) at zero is 1. Working backwards, the function with derivative 1 is f(x) = x $$\frac{d}{dx}\sin(x) = cos(x)$$ $$lim_{x \to 0}\cos(x) = 1$$ $$\int_a^b (1) \mathrm{d}x =x$$

Biological Engineering
TutorMe
Question:

Why is it so difficult to change the genes of plants and animals in order to optimize them for agricultural production? Creating the DNA is very simple, so what is difficult in inserting the genes into the desired species?

Roee R.

The major difficulty in adding, or transfecting, foreign DNA into organisms is two-fold: first, the DNA has to actually enter the cells, and, second, most organisms have defense mechanisms that destroy DNA not belonging to the cell's genome. Especially with plants, which typically have a very thick cell wall made of cellulose, the DNA has to be made to cross this border. Many methods have been developed to push DNA through cell membranes and cell walls, using such forces as electrical fields, heat, and physical pressure in the form gold nanoparticles. At the microscopic level, unless the DNA is adsorbed onto a physical particle that can then be phyiscally pushed through the cell membrane, it is rare for a DNA molecule to actually make it into the cell. For this reason, most transfection methods have a low efficiency, meaning that out of all the DNA molecules added to the host cells, very few make it. Because of low transfection efficiency, lots and lots of extra DNA has to be added to the cells and lots of cells have to be specially treated to weaken their cell membranes so that there is a small chance a DNA molecule will pass through. Additionally, most higher-order organisms have enzymes that will chew up foreign DNA the moment it is inside the cell. Typically, an organism needs to be found that has weakened abilities to manage its foreign DNA, and the search for organisms like these (for instance, a banana species that cannot protect itself from foreign DNA) can take decades, even when scientists mutate the organisms themselvs artificially. Another strategy is to put a gene in the DNA to be added which gives the organism something it cannot live without, such as resistance to an antibiotic or poison. Then, after transfection, the poison is added and only those organisms that have been stably transfected remain. This is known as selection pressure.

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