Physics, Muscles and Unbreakable Sticks

   High-school physics tells us that when an object is displaced through ds (an infinitesimal displacement) under the influence of a force F , the infinitesimal work done in the process is given by the “dot product” of the force with the infinitesimal displacement. This statement can be summarized by the well-known relation dW = F.ds   (where vectors are written in bold). The problems that one has to solve as a high-school student usually involve pumps supplying water to a tall building or a lift at a construction site carrying cement to the top floor. All that the students have to do is to multiply the gravitational force of the earth with the height of the building to calculate the work done. I have done this so many times that “W = mgh ” has now become permanently imprinted on my brain. These textbooks rarely talk about problems such as the work done by a human being (or, for that matter by any animal) while lifting objects

   Consider the case when a person holds a heavy dumb-bell stationary in front of his or her face. To keep the dumb-bell stationary, the person, using his or her muscles, has to apply an upward force to counter the downward pull of gravity.  Since the dumb-bell is stationary, or in other words ds = 0 , the work done by the person should be zero. And since no work is done by the person, his or her energy expenditure should be zero; and hence, he or she should not tire at all. This, clearly, is a contradiction!  All human beings (including Arnold Schwarzenegger), while lifting heavy weights, will sooner or later, tire. So where is the catch? 

   If one thinks for a while it is not hard to realise that the answer to this problem must lie in the mechanism with which muscles function. Even though no apparent macroscopic work is being performed, at the microscopic level, the fibres that constitute the muscles must undergo rapid movements for which work in the  sense dW = F.ds is required. Therefore, even when the weight that the person is holding is not displaced, microscopic displacements of the muscle-fibres would require work, consume energy and hence, the person would tire.

   It turns out that the Sliding Filament Model, modern molecular biologists’ explanation to muscle contraction, uses this very idea at its core. Muscles are made up of strands of fibres which are wrapped around each other. The functional unit of a muscle fibre, called a “Sarcomere”, is composed of two characteristically different protein-filaments: the “thin” filaments made up of a protein called Actin and the “thick” filaments made up of another protein called Myosin. Actin molecules have specific regions on them which have a very strong affinity to certain domains on Myosin molecules. Ordinarily, these binding sites on Actin molecules are ‘hidden’ or not accessible. But a signal from a motor-neuron, causes changes in the structure of Actin molecules, ‘unmasking’ those binding sites, to which Myosin molecules can now bind. Such interactions between Actin and Myosin are called “cross-bridges”. 

   Sarcomeres are observed to contract when the muscle which they are a part of contracts. But does that imply that the protein-fibres (Actin and Myosin filaments) which are building blocks of the Sarcomere also contract? Scientists were able to show that contraction of the Sarcomere is caused not by the contraction of its constituent filaments but by increasing the overlap of the thick and thin filaments. In the relaxed state, the two kinds of filaments overlap over a certain region. When the muscle contracts, the thick (Myosin) and thin (Actin) filaments slide against each other in opposite directions, increasing their overlap and as a consequence (see figure 1), decreasing the length of the Sarcomere. This sliding movement is achieved by bringing about a change in the structure Myosin, which causes the Actin filament to be tugged towards the centre of the Sarcomere. This is the step where work in the  sense dW = F.ds is performed and the energy required to change molecular conformations is supplied by ATP molecules- the universal “energy-currency” of life. Therefore, a person holding heavy weights tires as his/her ATP molecules get depleted.

   It is quite remarkable that with the help of molecules such as Actin and Myosin, a trained weightlifter can lift weights in the excess of 200 kg (approximately 10 to the power 25  times heavier than molecules like myosin) above their head. In each thick filament, every second, around 350 of its myosin heads form five cross-bridges. The number of thick and thin filaments in a muscle fibre and the number of muscle fibres in a muscle are so large that, molecules which are insignificant on their own, when acting together, can produce enormous forces.

   Perhaps, a thousand years down the line, children’s story-books will not have stories of sticks that cannot be broken when bunched together, but will talk about how tiny molecules, acting in tandem, can bring about events of simply astronomical relative magnitudes.

United we stand!

References:

11.      Life the Science of Biology (8^th Edition), Sadava, Heller, Orians, Purves, Hillis,

22.    www.nature.com/scitable/topicpage/the-sliding-filament-theory-of-muscle-contraction-14567666

A Bad Day

Although shielded from direct impact by the majestic Albizia saman trees lining the street, an umbrella couldn’t prevent her from being thoroughly drenched. It didn’t help that she had an enormous suitcase to take care of and the winds just made matters worse. The rain had bombarded the city ceaselessly since it had begun four hours ago and as was apparent from the intensity of light reaching the surface of Caesar Road, it would continue to do so for the for the next few hours- a period which was of immense importance to her. It was 10:45 am and she had exactly 55 minutes to reach the train terminus and board the northward-bound express.

Despite the distance being less than 7 kilometres, leaving from Amboli for Bandra Terminus just 75 minutes before the train’s scheduled departure time, even on a bright, sunny day in May, is a significant risk, given the city’s unpredictable traffic- unless, of course, you can manage to manoeuvre yourself and your luggage in (and out of) an impossibly crowded commuter train compartment. On a rainy day in July – a time of the year when half of the city’s roads simply disappear – it is nothing short of suicide. Rains can make your travel plans go haywire in ‘n’ different ways. Water-logging can cause traffic-jams, grind some suburban sections to a complete halt. And for some reason (which I have never been able to understand), heavy rains always make it impossibly hard to find vacant auto-rickshaws.

Having stood on the street, in a rather unforgiving spell of rain, for nearly 20 minutes, without encountering a single vacant auto-rickshaw, she was already repenting not heeding her mother’s desperate urges to leave early.

‘Wouldn’t the train be delayed as well?’ It was a reassuring possibility. But with a sinking feeling she realised that many trains from Bandra Terminus would be running, at least till Borivali, on the eastern-most track, which is dedicated for long-distance trains and therefore, immune from any delays on the Western suburban line. Delays on the Western Line, where instances of water-logging are rare, are never quite as severe as the woes of its ‘Central’ counterpart, a line that runs through some of the city’s worst affected areas during rains.      

At ten past eleven, after what seemed like an eternity, a BEST bus turned left (as the Caesar Road, initially running west to east, takes a southward turn towards JP Road), to reveal a single headlamp, gliding very low on the road, trailed by a black and yellow, doorless vehicle- which made her heart miss a beat. As the auto neared, it appeared (you can never be certain, as the possibility of a small individual camouflaged right in the corner of the passenger-seat cannot be discounted) to be empty. The autowallah miraculously managed to hear her scream (“Autooo!”), amid the rain and the traffic and steered his vehicle to the edge of the pavement.

“Bandra Terminus?” she asked, her fingers crossed. The autowalla’s reaction couldn’t have been more annoying. He barely exercised either his vocal chords or any of his facial muscles before speeding away in the rain.

Dismayed, she kicked a small stream of water flowing on the road, grabbed her suitcase and started walking, the umbrella (now folded) tucked under her arm. She reasoned, her only hope of boarding the train was to walk till the junction where Caesar Road meets SV Road, hope to quickly find a vacant auto (and a cooperative autowalla) and also hope that the train would depart at least 10 minutes late.

She was about to step onto the kerb on the other side of the road, when a cry of pain made her turn around. A man was rubbing his right big toe, which was exposed in his sandals. The sharp leg of her suitcase which had been trailing behind her had, clearly, caught him.

“I’m really, really sorry! Are you hurt?” she exclaimed.

The man, who was wearing a funny, yellow poncho, put on a strained smile and said, “I’m fine, I’m fine. It’s alright.”   

And then they parted ways. She made her way towards St. Blaise Church, as fast as she could. The man in the bright, yellow poncho was quickly forgotten.

While she had been walking furiously, the man in the bright, yellow poncho had crossed the street, exhibiting extreme recklessness in his short journey to the other side of the street (prompting three different men to scream out some very precious words in three different languages). He looked to his right and waved his arm. Within seconds, an empty auto stopped near him. He got in and the vehicle pulled away from the kerb.

It was 11:25 by the time she walked past the church and crossed SV Road. Tired, cold and frustrated, she found herself hoping for a miracle. The rain had eased a little. Traffic appeared to be reasonably smooth, at least on the southward bound lane. She felt her prayers were answered when an auto drifted near her and a middle-aged couple got out. Without waiting for the woman to finish settling their fare, she got into the auto and announced her destination (“Bandra Terminus!”). She received no response from the autowalla for the next minute or so, while the woman (whose husband was holding a United Colors of Benetton carrybag) demanded that the autowalla return her change- a sum of Rs. 3/-. The autowalla, quite irritated, gave her a 10 rupee note instead. He shook his head as the woman walked away and said, “Did you say Bandra Terminus?” It was 11:29 am.

They travelled with surprising swiftness and she found herself praising the municipal authorities for having done a reasonably good job at maintaining the roads. She was relieved to find the perennially crowded section of the road near Andheri Railway Station to be relatively traffic-free. They took the Andheri Flyover to cross over to the eastern side of the railway line. A short wait at a traffic-signal (the 30 seconds at that junction felt like an hour), followed by a smooth ride on the Western Express Highway and an amazingly quick transit through the densely populated neighbourhood of Bandra (East) brought her to one of Bombay’s four main railway termini.

She handed the autowalla a 100 rupee note and without waiting for him to return the change hauled her suitcase out and started running towards the ugly white-washed building. She sprinted (rather awkwardly) past the ticket-booking windows, past the cafeteria, into a corridor that led to the platforms. Halfway towards the pedestrian subway, she realised she had absolutely no clue which of the six platforms the train was departing from. She doubled back to the main hall, narrowly avoiding knocking down an old man and dropping her umbrella in the process. Her eyes desperately searched for an electronic display board. She lost twenty-five more precious seconds before locating one, half obscured by a meshwork of cables and wires. Paschim Express was on Platform 3.

She dashed back towards the subway, oblivious to the curses directed towards her. Thankfully, the subway had sloping ramps in place of stairs. She threw herself down the slope and nearly lost control of her suitcase. Within seconds she was at the bottom of the slope, terribly out of breath. But there was no time to rest. The signboards for Platform 1 and 2 passed her in a blur, as she adjusted her course onto the ramp leading to Platforms 3 and 4. Dragging the suitcase up the slope took much longer. She glanced at her watch as she finally reached the top. It was 11:52.

It took her a few moments to fully comprehend the information collected by her eyes. A train was motionless on Platform 4. Its name-plates suggested it was Vivek Express and judging from the mood of the people around it, the train seemed to have just concluded its 40 hour journey from Jammu. Platform 3 appeared empty. But near the northern end of the platform, a yellow ‘X’, next to a red, blinking light, was just disappearing behind a bend.

                                                                                                                         

                 Inside the WAP-5 locomotive of Paschim Express the two Locopilots (they are never ‘engine-drivers’!) were having a conversation.

                “It was close. You risked your job, you know.” – Man 1

                “I know, I know. They might still suspend me!” – Man 2

                “They asked Patel to cover for you and he wasn’t pleased” – Man 1

                “Of course, he wasn’t! But he shouldn’t worry, now that I am here.” – Man 2

                “I think you must have set some sort of a record today!” – Man 1

                “Possible! But what matters is that I reached sixty seconds before the scheduled departure time. Technically, I wasn’t late.  And the trains are late today, anyway.” – Man 2

                And then he removed his bright, yellow poncho, hung it on a hook and went back to his seat as the train eased into its first scheduled halt at Platform number 8 of Andheri Railway Station.

               

संस्कृतभाषा न कठिना

एकचक्षुर्नकाकोSयं बिलमिच्छन्न पन्नग: |

क्षीयते वर्धते चैव न समुद्रो न चंद्रमा ||

This was, by some distance, the high point of our Class IX Sanskrit textbook. The syllabus had recently changed, which meant fresh (and therefore not so efficiently censored) textbooks. Mistakes were discovered at alarmingly high frequencies. Whether the inclusion of this shloka in a chapter comprising of many other riddles (none of which I can recall) was an honest mistake or there were deeper reasons behind the decision will remain a mystery and it is not my intention to unravel it.

The riddle roughly translates as follows: “I am one-eyed, but not a crow. I seek a hole but I am not a snake. I grow and shrink. I am neither the sea nor the moon.”

If the authors expected students to accept the answer given at the end of the chapter, then they should have thought of one which was at least not as lame as a ‘needle’!          

Languages are in the public domain. They do not belong to any particular group, especially languages like Sanskrit which have existed mostly on paper and rarely (if not never) in sound waves and therefore are immune to bids of ownership. There have been claims of existence of Sanskrit speaking villages in modern India. But those are results of modern-day Sanskrit revival movements, rather than ancient Sanskrit speaking communities existing in seclusion.  Because no modern Indian linguistic/religious group can claim Sanskrit as their own, I find the controversy stirred up by the CBSE’s decision to celebrate Sanskrit Week rather amusing.  Some supporting this move have argued that most Indian languages are derived from Sanskrit and therefore promoting Sanskrit is equivalent to preserving our culture.  On the other hand, groups opposing this move accuse the government of trying to impose Hindu traditions on the nation by promoting a language which is so closely associated with Hindu religious texts. I think, both stands are equally misinformed.

Sanskrit is certainly a very old language when compared to most modern Indian languages. Kalidasa, the most celebrated Sanskrit poet-playwright, is thought to have been born in the 5^th century CE, when Sanskrit literature was probably at its peak. Marathi, on the other hand, appears only after the 12^th century. Does that mean Marathi descended from Sanskrit in a linear fashion? Not unlike Latin, Sanskrit was mostly a written language, a symbol class and education. Ever since its grammar was codified, it has remained in a permanantly fossilized state with its use being restricted to literature. A vast majority of the population communicated in the vernacular. These vernacular or prakrit languages are more likely to be the ancestors of modern-day languages and Sanskrit could be just another shoot in the tree of languages rather than being the root.

Religious texts in Hinduism, Jainism have been written in Sanskrit. Does that make it a religious language? And does studying Sanskrit imply giving you allegiance to India’s Hindu Right? Nothing could be further away from the truth. Sanskrit is too multifaceted, too versatile to be labelled a religious language. (After all, how could a language which dares to make riddles about  male genitals be just a religious language?) I have had the honour of knowing staunch atheists who have earned PhDs in Sanskrit literature. Their passion for Sanskrit was entirely compatible with their dislike of Hindutva politics. Religious texts in Sanskrit might be well known. But literature that defines the language and grants it worldwide fame is in the form of poems and plays.

उपमा कालिदासस्य भारवेरर्थगौरवम् |

 दंडिन: पदलालित्यम्  माघे सन्ति त्रयो गुणा ||

(Kalidasa’s simile, Bharavi’s depth of meaning, Dandin’s wordplay…Magha has all three of these qualities.)

And that is perhaps why three of the most famous Sanskrit writers have been immortalized in this shloka for their writing ability and not religious philosophy. Therefore, Sanskrit deserves to be delinked from the religious texts it is so often associated with and examined as a language in its own right.

Therefore, the stand taken by the groups opposing the Sanskrit Week Celebrations- by labelling Sanskrit Week Celebrations a Hindu conspiracy- seems ridiculous. A more legitimate mode of opposition would have been to argue that no language (whether it is the mother of all languages or a foreign language) can be forced on students and that the CBSE need not issue advisories on school activities that are cultural in nature. After all, CBSE’s objectives are confined to the realm of conducting examinations and prescribing the syllabus to schools affiliated to itself.

I feel Sanskrit has been defamed by people belonging to both camps. On the right, Sanskrit has been made the ‘mother of all languages’, something which it is not. And on the left, Sanskrit has been tagged a ‘Hindu conspiracy’.

Perhaps we need more riddles about needles (or human genitalia?) until Sanskrit is freed from cheap politics.

References:

1.       http://en.wikipedia.org/wiki/K%C4%81lid%C4%81sa

2.       http://en.wikipedia.org/wiki/Marathi_language

3.       http://www.bbc.com/news/world-asia-28755509

4.       http://en.wikipedia.org/wiki/Sanskrit_language

5.       http://cbse.nic.in/welcome.htm

Away He Walks

Muffled screams and stifled cries

Of pain and grief, unseen by eyes

In the land of truth and peace and gods

Of shattered dreams and blatant lies

Where terror rules and bullets fly

Where uniforms kill and plainclothes die

Where people rule, or so they say

Justice, though, turns a blind eye

Ban the words: ‘human rights’!

Unquestionable, truly, is the nation’s might

Our ‘collective conscience’ swells with pride

When men are hanged in the dead of the night

Where laws are guilty of heinous crimes

Where emerald greens turn into mines

Where villages vanish as waters rise

‘Development, development’, scream out headlines

As smoke spirals and fires rage

‘Eye for an eye’, demands the sage

Keepers of law, unfazed and unmoved

Quietly turn a fresh new page

 

Has, out of our lives, the light gone?

The ‘no ordinary one’ that once here shone?

Six and a half decades have passed

As away he walks, distant and alone