Relaxation in the Nuclear Microcosm

All of us want to give themselves a hard earned ‘rest’ after a “hard day’s night”, don’t we? So do the protons, perturbed by the destabilizing magnetic component of the radio-frequency pulse [which previously ‘happily’ aligned themselves to the externally applied magnetic field; one way (parallel) or the other (antiparallel)] applied at the Larmor frequency. It is like slapping an individual in a “merry go round” each time he came near a person who is paid just for slapping that person. But, when we call ‘spin’, we do not mean ‘spin’ the way we see them in a classical world. [We’ve given various names to the ‘quarks’: up, down, strange, bottom etc. depending on ‘something’ called ‘flavor’; and red, green and blue depending on ‘something’ called ‘color’.However, spin, flavor, color etc.‘in the quantum world’ have ‘no relevance’ to what we usually attribute to them in our everyday life. Things are a bit crazy in the quantum world, but I will take recourse to some ‘classical world’ analogies to make the description lucid.]

Thus, the already aligned nuclei (parallel or anti-parallel to the applied steady external magnetic field B0), has now been perturbed owing to the ‘knocking’ by the ‘magnetic component’ (B1) of the electromagnetic RF pulse. The nuclei gain energy and sway away from the perpendicular to the horizontal (90 degree) depending on how long the RF pulse is applied. So, now the nuclei behave like ‘punch-drunk’( like a person who’s been reeling due to a strong blow to the head!). Remember, that this new angular momentum is also a vector quantity having magnitude and direction. It can be resolved in terms of a horizontal component (Mxy) and a vertical component Mz. Anyway, the proton does recover from this situation, after some time, once the external RF field has stopped. Typically, Mxy component decays faster than the recovery of Mz.

The excited proton recovers in two ways and both forms occur simultaneously: (1) The excited nuclei which now have been ‘forced’ to lie horizontally (90 degree), ‘re-align’ themselves back to their ‘original position’ as they were before the RF pulse (perpendicularly towards the field of externally applied field B0); and (2) the energized protons dissipate their energies to the surrounding nuclei (horizontally) at their level. The first example, obviously, is called the (spin-lattice, or longitudinal) relaxation; while the second one, transverse relaxation (T2). There is little energy loss due to RF emission.

T1 relaxation, also known as, longitudinal relaxation or spin-lattice relaxation can be best understood if you see the following Youtube video. [The spiral trajectory, in this case, reminds me of the laser experiment I did to satisfy my lesser friends. Analogically, the trajectory would be such, if the power supply were switched off.] In T1 relaxation, the proton loses energy to the surrounding lattice, by interacting with nuclei in the lattice which are in vibrational, translational and rotational motion. Clearly, the surrounding nuclei (lattice) having the same (or nearly same) Larmor frequency will efficiently absorb energy of the excited proton, resulting in a tiny rise of temperature.

T2 relaxation (transverse or spin-spin relaxation) on the other hand, does not involve exchange of energy with the lattice.
The magnetic moments of the protons merely changes phase. Here, the nuclei exchange “quantum states” (kind of, what Einstein called ‘spooky action at a distance’): an excited nucleus (proton) will transfer its energy and relax, while the neighboring nucleus in the lower energy state that absorbs it becomes excited. This loss of phase coherence of spins can be clearly seen in this beautiful video.

It can be understood easily that T1 and T2 values would depend on the surrounding molecular environment (tissues, for example). Hence, the values differ in different tissues. Again, since Mxy decays faster, as described, it may be understood why T1 is greater than T2 (usually, T1=5T2). Both T1 and T2 contribute toward contrast in tissues. T1 relaxation time is the time needed for 63% of protons to return to their previous equilibrium state. Likewise, T2 relaxation time is the time needed for 63% of protons to become dephased owing to their interaction with nearby protons. The contrast, naturally depends on the water content of the tissues. Grey matter has about 10% more water than white matter and this creates a contrast. We can also create contrast by varying TR and TE times.

TR (Repetition Time) refers to the time gap at which consecutive RF pulses are applied; while TE (Echo Time) refers to the time delay between the applied RF pulse and its reception (echo). T1 weighted images (T1W) are produced by keeping TR and TE relatively short, while T2 weighted images (T2W) are produced by keeping TR and TE relatively long. Water molecules being relatively light spins much faster than the Larmor frequency, making energy transfer rather tough (exchanging of packets of energy becomes more efficient as the relative angular velocity narrows). Consequently, water has a long T1 time. Proteins and nucleic acids being rather heavy, spin slowly. They also have problem with energy exchanging, and thus have a long T1. Cholesterol, a medium sized molecule, precesses near the Larmor frequency, efficiently absorbing the energy and giving a small T1 value.Thus (fat) liquid cholesterol in craniopharyngiomas, a benign tumor, appears bright on T1W images (T1 being small, the rate at which RF energy is released is fast. Hence, the signal intensity in NMR is high).

Subacute hemorrhage also has shorter T1, due to the presence of paramagnetic iron in methemoglobin present in the tissue, hence high signal intensity. Cerebrospinal fluid (CSF), edema (collection of fluid in tissue space or ECF) having more water content have both long T1 & T2 relaxation time. They give low signal intensity in T1 (dark) but higher signal intensity (bright) in T2W images. T2W images are superior to their T1 counterparts in case of infarction, edema, demyelination etc. Contrast agents like the heavy metal Gadolinium, a paramagnetic substance, has been used to reduce both T1 and T2 times by introducing inhomogeneity in the magnetic field. Gadolinium is complexed (chelated) with a substance called DTPA to prevent toxic build-up inside body tissues. This gives high signal in T1W but a low signal in T2W. It (the complex) does not cross the blood brain barrier (BBB); but disruption in the BBB or parts of the brain where it is deficient (circumventricular organs), take-up the substance and affects relaxation properties.

Below is an MRI showing changes in Subacute Sclerosing Panencephalitis, a complication of measles. Note: Panels A and C are T1-weighted images; B and D are T2-weighted images. The hypointense (darker) signal on the T1-weighted image (arrow in A) and a hyperintense (bright) signal on the T2-weighted image (arrow in B) can be clearly seen.

Given all these, it can be said that relaxation parameters of nuclei have enabled us in visualizing biological tissues nonivasively, identifying chemicals spectroscopically and a lot more as we shall see later.

• References: Magnetic Resonance Imaging: David D. Stark, William. G. Bradley, Jr.

• NMR spectroscopy
• Magnetic Resonance Imaging
• Principles of NMR
• William P. Dillon. Neuroimaging in Neurologic Disorders. In: Harrison's Principles of Internal Medicine, 17th Ed., Volume 2, McGraw Hill; 2008. p. 2491-2497.
• Ian L. Pykett, Ph.D., Jeffrey H. Newhouse, M.D., Ferdinando S. Buonanno, M.D., Thomas J. Brady, M.D., Mark R. Goldman, M.D., J. Philip Kistler, M.D., & Gerald M. Pohost, M.D. (1982). Principles of Nuclear Magnetic Resonance Imaging Radiology
• Time constants

Last Modified: Aug 19, 2010

Quantum Biology: The Spooky NanoWorld of Molecules

We are quite adept in solving numerical problems in our everyday ‘analog world’ using decimal rules developed by us. Digital computers, on the other hand, calculate using binary or Boolean (0, 1) rules, and then convert the result in decimal format with the help of dedicated binary to decimal converter ICs. In the molecular world, calculations ‘happen’ in a strange way.

Take for example the case of Fluorescent Resonant Energy Transfer or FRET. Also known as Forster Resonant Energy Transfer, this phenomenon is characterized by the emission of a photon of one frequency (upon stimulation) which, in turn, activates an acceptor molecule to emit a photon of another wavelength. There’s one clause that says that the first photon (from the donor molecule) will only be emitted when it can definitively be coupled with the ‘acceptor’. But in the first place, how is this ‘virtual photon’ to know whether its bride was waiting or not when it hasn’t even visited her? Yet FRET doesn’t fret, and the process goes on.

All plants use chlorophyll to trap sunlight and convert it to chemical energy in the form of carbohydrates by photosynthesis. The efficiency approximates 100%. The predominant classical approach was that the photons hopped from light capturing pigment biomolecules to the ultimate reaction center where the actual conversion was taking place. But this ‘first choose and then pick’ approach that classical physics suggested would mean considerable loss of energy as heat, as photons wasted time as they hopped down the energy ladder. Quantum mechanics bypassed this by allowing simultaneous sampling of all energy states at one go by its unique properties of ‘superposition’ and ‘entanglement’. Graham Fleming and researchers at Lawrence Berkeley National Laboratory and the University of California at Berkeley showed the existence of a process of ‘quantum beating’, (a phenomenon akin to 'heterodyning’ in radio sets that is used to obtain intermediate frequencies for amplification) occurred which allowed sampling of all energy states by interference of the propagating wave. They used two-dimensional electronic spectroscopy in order to probe the sequence of events that occurred.

That the RBCs (erythrocytes), actomyosin complexes use quantum mechanics for system optimization has been established. Cellular respiration in the mitochondria, DNA, and the brain too might exploit quantum computing.

Counting without disturbing the molecule may be achieved by quantum mechanics, for it allows a molecule to know as if ‘intuitively’, the state of another molecule placed at a distance. Erwin Schrödinger, in his book 'What is Life?', opined that biological systems could be using the principles of quantum theory to maintain biological order. Sir Roger Penrose along with Stuart Hamerhoff proposed that the brain could be working as a quantum computer. In reaction to this, Max Tegmark showed that environmentally induced decoherence would foil any quantum interaction taking place. But Tegmark assumed the average kinetic energy (temperature) of the brain as 310 K (273+37). While this is true in a macroscopic world, Koichiro Matsuno has shown, using black body radiation measurements, that actomyosin complexes which are abundant in the axons of nerve cells, can reach local temperatures as low as 1.6*10-3K. It is as if nature has evolved ways to ensure decoherence free subspaces where entanglement and quantum interaction were possible. Stephen Hawking in his book 'A Brief History of Time' observed that quantum mechanics was the basis of modern biology and chemistry and the only area where quantum mechanics was not properly integrated were gravity and the large-scale structure of the universe (page 60).

To quote Ogryzko "Indeed, if it has taken Humankind only few decades to approach the use of entanglement in quantum information technology, one can wonder why Life, in billions of years of evolution, could not also learn to take advantage, finding in entanglement an alternative resource for stabilizing biological order." It seems we need an entirely different approach if we wanted to probe the mysteries of life and quantum theory is poised to help us in this regard.

P.S. I am glad that the prestigious multidisciplinary journal "NeuroQuantology" published this article with the title "The Spooky NanoWorld of Molecules" and archived it in their "arNQ Eprints and Repository". I thought I could share this with you, my readers!

Last modified: Jun 29, 2010
References:
Quantum Biology
Vasily V Ogryzko (2008). Erwin Schroedinger, Francis Crick and epigenetic stability Biology Direct, 3 (1) DOI: 10.1186/1745-6150-3-15

Neurons: Digital or Analog?

Its very hard to stamp neurons solely as either an analog device or a digital device. Actually its both. I'll tell you why it is analog. When an impulse arrives at the cell body of neuron, it creates an EPSP or excitatory post synaptic potential. During an EPSP, the sensitivity of the post synaptic ending to another stimulus is increased, hence the name. At this phase, stimuli add up resulting in spatial or temporal summation. Thus individual stimulation may not elicit a propagating action potential, but together they can cause enough inflow of sodium ions to produce an action potential. So from this point of view, we can see that the neuron is not following an all or none law; and the actions may best be described as analog.

Once an action potential has occurred, it always spreads down the axon to the synaptic knob. Actually, when a neuron is stimulated at any point in its course, the nerve depolarizes in both the directions. Since the cell body of a neuron is devoid of the neurotransmitter machinery of a synapse, the impulse is not chemically forwarded to the adjacent neuron. Thus this part of the neuron is rather like a diode in electronics. On the whole, the axonal and synaptic part of a neuron resembles a Boolean machine, a ‘0 or 1’ response. So this part of the neuron is undoubtedly digital.

The story doesn’t stop here. There’s a quantum touch to a neuron too. Quantum mechanics can be foxy. You can imagine of a cat as either alive or dead. In quantum mechanics, the cat (called the Schrodinger's cat) may have another state: BOTH dead and alive at the same time. Quantum superposition is thought to exist in the brain too and even Bose-Einstein condensate may form among the neural proteins. But how an interaction like this forms in the warm (thermal noise) environment of the brain and how the brain avoids decoherence at this temperature, has been studied by Stuart Hameroff and Roger Penrose. Their proposed the Orch OR (orchestrated objective reduction) hypothesis addresses the issue of ‘binding’ of consciousness and the mechanisms of the thalamocortical circuitry by quantum interactions.

The neuron thus seems to behave in analog, Boolean and quantal ways, so far, until string theory comes up with another!
Last modified: never
Reference: hyper-links, unless specifically mentioned

Master Of Puppets Im Pulling Your Strings

How big is the universe or what is a universe after all? Well, a web search on the definition did not say much about these. One site described it as all matter and energy in space. Then we must ask ourselves which method we should adopt to detect these ALL matter and energy/energies. For example, a bat can not see. To this creature, the universe would appear as its tactile senses and the ultrasound echoes (bats use echolocation) would allow it to perceive. It thus appears that our observation is not only limited to the gadgets we build, but also the degrees of freedom (dimensions) in which we are accustomed to. We can't visualize 7 or say 14 dimensions, can we? What if the universe consisted of many sub-universes containing as many or as few of these dimensions? We may try to conjecture the infiniteness of the universe in our own familiar dimensions in the form of the 'recursive' Klein bottle (picture on the left), or the Moebius strip.

Take the case of those working at the Chandra observatory. They can see through X-ray vision and see the universe at a completely different perspective. The picture of one x-ray galaxy is given here, for your reference. Thus you have infra-red, ultra-violet, radio-wave astronomy and many more. If you are bit observing, you'd note that all those modalities cited above used the electromagnetic spectrum; perhaps because light's (and all other electromagnetic waves) speed were the highest and possibly also because that we can not imagine any other type of constructs of the universe(s), since we are slave to our senses and the dimensions they restrict ourselves in. We have seen how quantum theory can wreck havoc with our classical thinking, by its killer 'superposition'; its time we greet the new kid on the block: String Theory. If you thought quantum theory was too much, then this one is for you. Watch this fabulous video. Do read the text and ponder over them. It suggests that we are floating in a three dimensional space, surrounded by membranes. Even if there is 'another universe' nearby, we could not reach out of our 'braneworld' and see or touch them. So check out this video. Enjoy the possible proximity with another universe (may be God's own) with in your own reach but don't try to reach out; for they can't see you!

By the way, I think, gravity waves are a good contender in this regard. They are supposed to travel at the speed of thought. Secondly, they pass through all matter unchanged, beating even light in this regard. When we develop better SQUID devices, we may be better able to explore the cosmos.

BTW, the title of this post has been taken from the Master of Puppets song by Metallica. Here 'Master of Puppets' refers to God, and Strings to String theory. Nothing serious!

Last modified: April 1, 2009
Reference: hyper-links, unless specifically mentioned

The Cat is Out of The Box Now

How would you react if I told you that a cat were both alive and dead, that too at the same time? or for that matter, about a solitary electron in the famous double-slit experiment, that "it goes through both slits and it goes through neither, and it goes through just one and it goes through just the other"? You'd say I had gone out of my head, wouldn't you? Then you are in for surprise.

Strange things happen in the strange strange quantum world. The cat in question is the famous (or infamous) Schrodinger's cat. This feline creature resides in a box where a radioactive substance is kept. As the radioactive atoms decay, they emit alpha particles, which in turn is sensed by a Geiger counter, kept inside the same enclosure. If the counter detects a decay, it will activate a relay which will then break a container containing the deadly hydrocyanic acid (HCN) and the cat dies.
Before an observer opens the box the cat's life is a superposition of states: dead and alive. But when an observer opens the box, the wave function collapses: into one of these two states.

Likewise, an electron collapses its own wavefunction (changes its mind) , as the following video will show, when an observer is spying on its intention(s):



The above instances are quite in tune with Heisenberg's uncertainty principle, which says that you either calculated the position of an electron precisely or its momentum at a time. For when you measured one with precision, the value of the other will be more uncertain.

Does it mean we will never get to the bottom of the quantum world with our classical mind? Only time will tell.

Last modified: never
Reference: hyper-links, unless specifically mentioned

Electronic versus Biological Clock: A Comparative Analysis

Electronic clocks rely on oscillators to derive its clock signals. Modern day clocks employ crystals made of quartz, instead of employing CR (Capacitor-Resistor) or LC (Inductor(L)-Capacitor) networks, transistors or 'flip flop' integrated circuits, for the production of clock signals. In a typical electronic device, such as a computer or mobile phones, there is the need for not one but many different clock signals, for its different sub-systems. This is achieved by using decade counters (such as the TTL IC 7490, TTL stands for transistor transistor logic), which divide the clock frequencies by 10, or by using dividing by 12 IC 7492. By using such devices and others, in cascading manners, many different frequencies can be synthesized which may then be fed to the corresponding sub-systems.

In both plant and animal kingdoms, including humans, there are many 'clock generating' cells that functions as biological clocks. For example, there is one such clock in the hypothalamus (a part of our brain), which goes by the name of 'circadian clock'. This clock, also called the master clock, is actually a conglomeration of neurones at suprachiasmatic nucleus (SCN) of the hypothalamus, which produces its clock cycles in more or less the same manner as an electronic oscillator does. Circadian means about (circa) days (dies), in Latin, and as the name suggests, this clock enables important tasks, those have some relevance with the time of the day, to be executed in time. Activities such as release of some hormones (ACTH or adrenocorticotrophic hormone, cortisol etc), regulation of body temperature, sleep-wake cycle, behavior, growth and many other activities are controlled by the circadian clock and hence these activities comprise what we call circadian or diurnal rhythms. Like electronic clocks, they are also fed by reset signals, so that the clock may be synchronized with external stimuli, called 'zeitgebers', German for time givers. During daylight, light falls on the retina, the ganglion cells there are stimulated via their melanopsin photoreceptors, which then send this information to the SCN ('master clock') through the retino-hypothalamic tract. This way the clock remains up to date. This story of relay doesn't end here. The hypothalamus again relays this cue to pass on to the pineal gland, which produces 'melatonin' that plays important role in sleep wake cycle.
There other clocks in the brain too. For example, in the arcuate nucleus of the hypothalamus, a pulsatile clock, controls GnRH (gonadotrophin releasing hormone) secretion. This hormone, in turn, regulates the secretion of gonadotrophins: Leutinizing and Follicle stimulating hormone (LH & FSH), which are instrumental in reproduction. Then there are 'peripheral clocks' in areas such as the heart (cardiac pacemaker), intestinal smooth muscles, liver and other organs. In addition, each individual nucleated cell has its own in-built telomere operated clock, that counts 50 times after which the cell self apoptoses (Hayflick limit). This clock is DNA operated. It is likewise speculated that the circadian clock may also be DNA operated, and DNA transcription/translation feedback mechanism, may be the one that does the counting trick. Barring some exceptions, the ultimate effector is change in ionic fluxes in the neurones.

Whatever may be the mechanism of genesis of the clock pulses, it is to be borne in mind that these numerous clocks have to be coordinated, to be of relevance in physiology. This coordination is done sometimes through neuroendocrine mechanisms and sometimes through other means. Since ionic fluxes are involved, it may be possible that in the brain, where electrical circuits abound, electromagnetic coupling might play some role. Also, if the distance between the transmitting and receiving units is negligible and the chances of 'decoherence' is small, coupling through quantum mechanism by entanglement is also not an untenable option. Therefore we need to be open minded and logical if we were to come to a meaningful and universally accepted theory, before the sands of time run out.

Of Lightning, Photosynthesis and Electron Transport Chain

We all know that plants use solar energy to form chemical energy in the form of carbohydrates. The suns rays (photons) impinge on the chlorophyll of the green leaves. This excites them and raises them to a higher energy level. These electrons in turn, transfer their energies to another electron nearby and this process goes on till the energy is transferred to the reaction center, where actual conversion of energy is occurring. This energy transfer occurs at a phenomenal efficiency of about 95%. In order to achieve such unprecedented (compared to about 40% in the most efficient solar cells) efficiency, the electrons should 'change hands' in an efficient way and not merely by a random walk.

The electrons do this by 'sensing' and sorting of the energy levels of different electrons (without ever actually having to go to these places for sensing: what Einstein called spooky action at a distance). How the electrons found the right path so as to reach the destination (to electrons with a lower energy level) quickly and efficiently remained elusive. Now scientists perhaps know the reason. These electrons do some kind of quantum computing to arrive at their destinations with unprecedented efficiency.

This premonition of 'unsorted databases' is characteristic of the quantum computing algorithm. Like gamma synchrony, regular patterns of signals lasting several femtoseconds were found, when the chlorophyll molecules were mapped by using electronic spectroscopy. As in dendritic networks, these 'quantum beats' 'bind' (synchronize) all the energy levels of electrons together. Thus these quantum beats help electrons find out the 'path of least resistance' in such an astonishing efficiency. It is as if the energy status of the electrons were indexed as in a computer search algorithm, so that they could be found out faster.

A similar mechanism may be involved in our mitochondria where electron transport chain occurs. Electrons are transported in the mitochondria along a series of electron acceptors to end up ultimately in cytochrome c, where they combine with oxygen, the ultimate electron acceptor, to form water. This chain is very important as it generates ATP, our own energy currency. Quantum entanglement may explain the subject in a new light.

Just a thought in passing, it is said that lightning follows the path of least resistance. I always wondered how it would know where to advance to next, since it had no prior information about what lied ahead. Now, this quantum computational algorithm may be the suitable one to address this issue.