Five weeks in the Loyola University Chicago ,I come here for learning the applications of math in other subjects ,in this article we talk about some basically application of math in biochemistry.

AN INTRODCTION FOR THE PROTEIN X-RAY CRYSTALLOGRAPHY

For one of the mathematical applications in the biochemistry I have learned in the laboratory is calculating the protein structure .In the laboratory ,the basically work is to get much protein by culturing microorganism and destroying the cellsand get the protein crystal in some special conditions ,then go to the national laboratory to get the x-ray pattern. This pattern contains the information about the crystal and we need to get the structure of the unit cell ,by the nature of the wave diffraction we can define a mathematical representation for the changing of the vector .Then we can define scattering factor

. Then we can define the scattering for the whole unit cell

with scattering of all the atoms in the unit cell add together .And we can change the formula in another mode

for the real unit cell scattering .This is a Fourier transform ,then we can calculate the electron density

by the scatteringdataF which we can get from the x-ray pattern .That is the principle of the software and on the computer it will get a blue three-dimensional picture and the next part is construct the chemistry structure in the pattern. For each point is an atom you have built in the picture ,then the computer will calculate the electron density

and by the transform to get the calculate F ,then compare it with the initial F from the original x-ray pattern we can get the error ,then we do this work again and again till the error is the minimum .The final goal is to get the solution of the protein structure

.

(For the three pictures above 1.protein crystal 2. chemistry structure 3. x-ray pattern , from left to right )

PERSONAL FEELING FOR THE LAOCAL RESEARCH CUKTURE

During the exchange programme ,with the help of doctoral candidates ,I understand the basic work in the laboratory ,usually a research programme is begin with the idea of professor and doctoral candidates then it will be implemented by each doctoral candidates ,undergraduate students only do some simple work in the lab such as culture the microbe and manufacture the solution .Each Thursday all the people in the lab will have a meeting to talk about the results recently and the plan for the future ,compare with LZU ,in the lab ,it has a good atmosphere to communicate work ,each person will ask others for help when they face some problems they can not deal with ,so for the whole lab can work in a efficient way ,it showed me that how the research really like for the biochemistry ,the most popular application is the medicine ,knowing the structure we can find the feature of the proteins then we can know the principle of the disease and we will design the special compound to act on the protein to solve the problem .It’s all for the human’s health .

(the meeting of the lab on Thursday)

PERSONAL UNDERSTANDING FOR THE APPLICATIONS OF MATH IN OTHER BASIC SUBJECTS

For the application in other subjects ,for example ,in the crystallography ,most valuable things are the suitable definition and the translation for the realistic problem and the abstract theorem ,for idea witch build a connection between two sets and solve the problem in the set we are familiar with ,so that’s the Fourier transform witch connects the three-dimensional space and the reciprocal space then we can built the structure by deal with elements in the reciprocal space ,so for the reality is already there ,if we want to solve the problem ,maybe understand the phenomenon in another way is better than built a new theorem by finding the unknown .So the mathematics is the tool to translate the facts in the nature into the logical language that human can understand and change something .

PERSONAL UNDERSTANDING FOR THE FUDAMENTAL KNOWLODGE WITH APPLICATION

For example ,in the protein x-ray crystallography and many other subjects build on experiment ,it’s hard to avoid experimental error and calculating error ,for the knowledge of physics and chemistry ,crystal can have the scattering but it depends on the details of the protein ,first it needs to get a lot of protein by break the cells ,temperature and PH should be suitable for the protein structure during the crystallizing .Even on this conditions ,it also needs high-intensity x-ray to get the patterns ,these patterns contains the information about the structure of the crystal ,it’s not convenient to deal with the patterns directly ,we need to calculate it and change the data into the normal pictures ,it’s not a real space which displayed on the screen ,we can only deal with the elements in visual spaces and we use the visual model to get the calculate data to compare with the original data in the experiment Fourier transform guarantees t,that’s the reaction persons can do with the experiment .Analysis, statistics ,geometry ,statistics and so on. All these branches are useful in biochemistry ,statistics can have a qualitative analysis for the new phenomenon ,it has a prediction for the future results .But for the real product ,it needs to control the details of the structure and to design the special protein which we cannot do with the technology now .So the applications of math in other subjects can use computer as a medium to achieve the other subjects’ demand ,it needs to prove the feasibility with the basic math theorem and the other subjects’ knowledge ,under the help of the computer language ,the final result may be a software as a tool to help others to solve the problems ,so it needs other subjects’ knowledge make sure the application of the math.