Math+Biology

"The pluses and minuses of maths on my bioscience course"
Why do Math I hate?
Scores with bated breath do I wait …
Polynomial monomial factorial,
Why does it sound to me so unreal?
(a+b)2=a2+2ab+b2,
with a blank look on the white board do I stare …
Teachers came teachers went school came to an end,
till now haven’t deciphered why to infinity limits do tend!!!
Then happened biosciences,
With applied Mathematics, biostatistics I made new alliances,
Math was no more unreal
touching cells, life, taking mankind to a top gear !!!

I don’t have strong mathematical intuition – in fact I’ve always found formal Math courses quite difficult. Limits, Derivatives, Integration always seemed like a sci-fi movie, where you see all the action, never understanding why they are doing it. It was one of the reasons I opted for the Bioscience stream. But I guess the Math ghost was not going to leave me alone. I found Math also in my Biosciences course, not on the face but subtly.

My Biosciences Modules were soul-changing. They changed my whole perspective towards Mathematics. I started discovering my own way of learning Math that I need: plotting graphs to help understand equations, running small “trial and error” tests with some sample numbers when developing algorithms. Of course I have a great resource – the Web, where I can browse tutorials for maths courses from universities anywhere in the world, read the manuals of statistical packages and so on.

My Biostatistics made me realize how important Statistics is for a researcher to design his project, sample size, analyze and interpret the data obtained using different tests like ANOVA, t-test, p value…etc. Even understanding cellular events like cell cycle, Na-K channels, ATP metabolism in Biochemical pathways, ligand –receptor interactions, macromolecular interactions…etc. require good physical and mathematical framework in the mind so that anything new/abnormal will get noticed quickly.

Without strong Math base, JDW could not have noticed the thermodynamically stable DNA helix structure, Ramachandran would not be able to make a plot, and Breslauer et al.(1986) would not be able to formulate Tm calculation by nearest neighbor method. Physical chemistry is the subject to make a complete portrait of Biology in mind, to understand each and every aspect of it.

My Biophysics Professor says that Biology is nothing but physical chemistry and I think physical chemistry is explained best in terms of mathematical derivations like PV=nRT, ΔH= ΔG+TΔS, etc. which are so universal and important not only in mechanics but also in Biology. He dramatically changed my view towards Math.

Studying the system like cell, which is under control of many factors, requires mathematics for expressing its thermodynamic behavior. Cell is the most thermodynamically efficient system man would come across which not only functions isothermally but also perpetuates by mitosis and produces variability by meiosis to maintain diversity of life. You understand Math, you understand Life!!!

Math simplifies the complex correlation between different factors such as in enzyme kinetics, fermentation technology, etc. various formulae help us to study complex systems. Maths is required in process management of many upstream and downstream regulation processes at industrial level for production of various vital enzymes, antibiotics, vaccines, and biological products.

Right from agriculture, forestry, botany, zoology, microbiology, biochemistry, pharmacy to medicine each and every branch of biology requires mathematics for expressing theoretical concepts and their applications in real life. Mathematics helps to clarify the underlying mechanisms; this is because the process of modelling makes us concentrate on separating the essential from the inessential. A model can be used to investigate situations that are not easily agreeable to experiment like global warming etc. Mathematics is valuable in testing out ideas. Mathematics is a concise but powerful language that allows the `hidden' similarities between different systems to be discovered.

But, How much math do you really need in Biology?

Even though Math is helpful in every aspect, complicated, multistage derivations and use of horrible roman letters in the formulae removes it charm. Calculus is a real headache sometimes …it comes in the theory without any prior resolution like in bioinformatics writing algorithms for different processes like DNA- protein interaction, protein-protein interaction, etc.

Furthermore, mathematical modelling of cellular processes is quite challenging. Cell, the unit of life, is infinitely complex. There are millions of things going around in a single cell, maintinaining control and order among its molecules as exemplified, for instance, in the DNA-RNA-protein machinery, absorbing nutrients and generating biomass to perform specific functions, such as secreting chemicals or engulfing pathogens, adapting to its microenvironment by moving toward sources of nutrients or by remaining quiescent when resources are scarce, and replicating when conditions are favourable. Besides, the human body has 1013 cells of different types and functions continuously talking to each other, it is quite clear that mathematical models of biological processes are extremely difficult or rather impossible. Even the most successful models can be expected to deal only with limited situations, ignoring all but the most essential variables. What you need is some automated way to model this, probably a simulator, probably a tool. This could remove unnecessary use of Math making the course even more fun. The usage of Math should not make students run away from the course but to make them believe in the course, believe in course’s realism.

There is no obligation to love math any more than grammar, composition, curfew or washing up after dinner. It depends on the individual choice since everyone has different approach towards understanding of biology through math or any other way. Depending on that each one develops different levels of liking or fear for it. Still nothing is stable...we know.. so it’s better keep fingers crossed and have a faith in you that once you overcome the fear of math…it will help you instead of giving headache.

Ataxia telangiectasia

How did the condition arise?

Ataxia means no coordination in the simple movements such as walking and Telangiectasias are enlarged blood vessels (spider-like veins) just below the surface of the skin. Ataxia-telangiectasia (A-T) is genetically inherited disease, which means it is passed down from generation to the next.

Every living organism possesses a genome that contains the biological information needed to construct and maintain that organism. The chromosome is a discrete unit of genome carrying many genes. These genes are units of genetic information expressed in the form of proteins. Each of them consisting of a very long molecule of duplex DNA(deoxyribonucleic acid), where DNA is a molecule made up of chains of subunits called nucleotides.

Human Genome is comprised of 23 pairs of Chromosomes, of which 22 pairs are autosomal and 1 pair is sex chromosome. These chromosomes have a long q arm and a short p arm. Each of these pairs has one chromosome from mother and one from father. They carry a copy of a number of duplicate genes known as alleles.

A-T is caused by autosomal recessive mutations in the ATM (Ataxia Telangiectasia Mutated) gene located on chromosome 11 section 11q22-23. Mutation is a change in the nucleotide sequence of the gene. A-T is an autosomal recessive trait,that means mutation is in a gene present on autosomal chromosomes and both parents must provide a defective alleles of the gene to the child to have symptoms of the disorder. More than 500 unique ATM gene mutations are known. Most mutations are null mutations which results in total absence of ATM protein.

For the organism to grow, it’s cells need to divide.For that cells need to undergo sequence of activities called the cell cycle. In the cell cycle, there is multiplication of cell along with its DNA content. There is a control mechanism in this process called Cell cycle checkpoints which ensures whether the processes at each phase of the cell cycle have been accurately completed before progression into the next phase.Few of them are DNA damage checkpoints where the damage in DNA to be replicated is detected and repaired.DNA repair is the process by which a cell identifies and corrects damage to it’s DNA molecules.

The ATM protein is thought to play a role in regulating cell cycle checkpoints and in repair of double stranded DNA. As the result, the mutated ATM gene leads to a high frequency of mutations resulting in various complications and abnormalities seen in A-T patients.

What is the prognosis likely to be?

Ataxia-telangiectasia is a complex genetic disorder. Generally, in all the cases telangiectasia is followed by ataxia, after a gap of few years. A-T patients usually show uncontrolled infection in adolescence which may prove fatal, though some show variability in severity, age of onset, and rate of progression.

The primary features of classic A-T include progressive ataxia with onset between ages one and four years, progressively slurred speech, oculomotor apraxia that is inability to follow an object across visual fields, choreoathetosis which means writhing movements, oculocutaneous telangiectasia that is enlarged blood vessels in skin of nose, ears, and inside of the elbow , knee , whites of the eyes etc. A-T pateints also show hypersensitivity to ionizing radiation with increased susceptibility to cancer and susceptibility to frequent infections due to immunodeficiencies.Immunodeficiency (or immune deficiency) is a state in which the immune system's ability to fight infectious disease is compromised or entirely absent.

Ataxia is progressive and show various other neurological manifestations, including mask-like face, excessive drooling, abnormal eye movements and loss of tendon reflexes. Where tendon reflex are the one elicited by a sharp tap on the appropriate tendon or muscle to induce brief stretch of the muscle, followed by contraction. There are other complications like chromosomal instability,poor development of secondary sexual characteristics, premature aging with strands of gray hair and abnormalities such as diabetes.

A distinct feature of A-T pateints is that they have extreme sensitivity to ionizing radiation. For e.g., X rays used in the therapeutic treament of the pateints with AT often produce devastating death of normal tissues. X ray induced DNA breaks in one or both strands of the double helix may go unrepaired, leading to a vareity of chromosomal breaks and rearrangements.Thus the patients have a high frequency of mutations resulting into a marked increased risk for various types of cancer, particularly Leukaemia (Blood Cancer) and Lymphoma (cancer of cells of Immune systems).

A-T heterozygote is the one who have different alleles of ATM gene, that is one defective and one normal ATM gene on chromosome 11 pair. These heterozygote for ATM gene defects are common and appear to be particularly vulnerable to the induction of cancer by radiations. Female heterozygote for AT mutation have overall two fold increased risk of breast cancer and a five folds higher risk for the breast cancer before the age of 50 years. Epidemiologic studies suggest that A-T carriers are at an increased risk for heart disease. Eventually, it can be seen that the prognosis for individuals with A-T is poor, where death occurs in their teens or early 20s.

What treatments are available?

There is no specific treatment for ataxia-telangiectasia. Treatment is directed at specific symptoms such as Cancer, Diabetes etc. Immunodeficiencies are present in 60% to 80% of individuals with classic A-T.Blood concentration of the immunoglobulin’s like IgA, IgE, and IgG are reduced where immunoglobulins are the protein produced by immune cells which play an essential role in body’s Immune system by fighting infection. IVIG (Intravenous immunoglobulin) replacement therapy is given to the A-T patients were blood product containing immunoglobulin (IgG) is administered intravenously in them.

Brain atrophies (shrinkage) are observed early in the course of classic A-T, leading to neurological symptoms. Although steroids can temporarily improve in condition of A-T in children, the neurological symptoms reappear within days of their discontinuation.

Speech therapy may also be needed. It can significantly improve diction, especially in the second decade of the disorder. Early and continued physical therapy is helpful to minimize contractures (continuous muscle contraction) and scoliosis (curved spine) which appear in almost all A-T patients with time. Orthopaedic assessment like corrective procedures can be helpful for joint or postural problems, particularly in the lower limbs or spine. Supportive therapy involving usage of drugs, surgeries, and retraining of movements are tried out but individual responses to such therapies vary.

What are common complications and how are they managed?

The infections observed in classic A-T does not include common opportunistic infections, but lung infections are frequent. These patients require aggressive pulmonary hygiene.In A-T patients the frequency and severity of infections correlates more with general nutritional status than with the immune status. So, good health and hygiene should be observed by the patients and their family.

The cells from A-T patients are 30% more sensitive to ionizing radiation than cells from normal .They should avoid exposure to excessive ionizing radiation including those from diagnostic procedures such as CT scans and some chemotherapeutic agents used in treatments.

Parents should regularly monitor their children for early signs of malignancy (e.g., weight loss, bruising, localized pain or swelling) and report it to the Physician. Monitoring of immune status should also be done of the children with severe recurrent infections or undergoing IVIG therapy .They should look out for the more subtle beginnings in their young children for early recognition of A-T. This would also encourage more vigorous treatment for the respiratory infections to which the A-T affected children are prone.

Would gene therapy be appropriate to treat this condition?

Researchers are exploring therapeutic strategies that target the underlying causes of A-T, rather than just the symptoms. Gene Therapy is one of the strategies, in which there is an attempt to replace the defective ATM gene with the normal one. Gene therapy by definition involves the direct genetic modification of cells of the patient to achieve a therapeutic goal.

In one of the approach of gene therapy, gene addition is carried out, where aim is to supply a functioning gene copy that will supplement defective gene. It is generally carried out to treat diseases that are the result of a gene not functioning (Strachan and Read, 2004).It was carried out by transfection of full-length DNA of ATM gene where transfection is the process of deliberately introducing DNA into cells. It was observed that ,expression of ATM DNA in A-T cells enhanced the survival of these cells in response to radiation exposure, decreased radiation-induced chromosome breakage and partially corrected defective cell cycle checkpoints. This correction of the defects in A-T cells suggested future possible approaches in gene therapy against A-T. It is seen that gene augmentation would not be suitable for loss-of-function conditions in which irreversible damage has already been done but still it can be used to mitigate the symptoms of the disease as seen in above example.

The efficiency of various gene therapy protocols are being tested by the scientist in mice and simultaneously new gene therapy protocols are being formulated for A-T which would hopefully allow for stable, long-term production of the ATM protein in the body. However, gene therapy faces many challenges from ensuring that the therapeutic gene inserts safely into the genome to regulating when, where, and how much it is expressed.

Will future children be similarly affected?

A-T occurs at a frequency of about 1 in 40,000 children in the world population but note that the disease may be much more common, since some children with A-T are misdiagnosed or die before they are accurately diagnosed. It is inherited in an autosomal recessive manner. Parents of a A-T patient are both obligate heterozygote carriers of an ATM gene mutation. The carrier is an individual that carries one gene for a particular recessive trait, such that he does not express the trait but, when mated with another carrier, can produce offspring that do. The risk of each sibling of an affected individual being affected is ¼, risk of being an asymptomatic carrier is 1/2, and risk of being unaffected and not a carrier is ¼. Once an at-risk sibling is known to be unaffected, the risk of his or her being a carrier is 2/3.Each sibling of the patient’s parents is at a 50% risk of being a carrier. Most individuals with A-T do not reproduce. So there are very few chances of inheritance of the disease from the patients to his or her future generation.

Genetic counselling and genetic testing are particularly useful in patients with recessive diseases. In case of A-T, if one parent has ataxia and the status of the other parent is not known, genetic testing will determine if the unaffected parent is a carrier of the mutated gene. If the unaffected parent is not a carrier, then there is no chance of transmitting the disease to his or her children. Since results of the genetic tests may affect important life decisions such as whether to have children, Genetic counselling should always be done before the testing.

There are list of mutations that are routinely tested and which help to known which mutations are present in the person. But, genetic tests are available for only few types of hereditary ataxia. For example, in North African Jews, a direct test can be performed to identify the mutation in the ATM gene - C103T - by testing for this mutation alone.

In short, genetic testing can be helpful for people who do not yet have ataxia but are at risk due to family history.