Non-equilibrium is the new challenge !

Athokpam Langlen Chanu *

A cold rain was drizzling, and I was enjoying a hot 'chai' at the SSS-I canteen. The mulberry tree just outside the window made me wonder, "How beautiful it is that we can learn Nature through Mathematics !" "Hey, Langlen! How's your day going on?" came a familiar voice that drew me back to reality.

"Hi, Laija! It's fine, thank you."
"Laija told me your Complex Dynamics Lab team is working on some interesting problems ," said Mitsna.

"Langlen! Tell us about your research," Laija said, "Let's see if we humanities researchers can understand a bit of it."
"You guys can surely understand. The crux is the science, not the technical details."
"Very true! C'mon! Your research!"

"Ever heard about 'Non-equilibrium systems' or 'Fluctuations'?" I asked. Both Laija and Mitsna shook their heads. I was silent for a moment. "Do you guys ever wonder what makes us alive?"
"Because... because we are breathing?" said Mitsna.
"Since we eat food?" added Laija.

"Yes, these activities produce the very act of living," I continued. "When we breathe, the cells inside our body absorb oxygen from the blood and release carbon dioxide into the same. When the foods we eat or drink are digested, our cells absorb the nutrients. When there is such a kind of exchange of energy or matter with the surrounding, the system is in non-equilibrium.

In the book What is Life ? : The Physical Aspect of the Living Cell (1944), the physicist Erwin Schrödinger said living systems stay alive by avoiding equilibrium.

Most systems, at the microscopic to macroscopic scales, are actually non-equilibrium, for example, enzymatic cycles in living cells, swarming schools of fish, flocking birds, swirling storms, etc. At equilibrium, system-properties don't change with time. Equilibrium is kind of boring, but non-equilibrium corresponding to 'activeness' is interesting!"

"So… we are basically alive because the cells inside us are continuously functioning in non-equilibrium conditions. Langlen, you also mentioned 'Fluctuations'. What are they?"

"Fluctuations are what we commonly know as noise. However, physicists prefer the term 'fluctuations'. Laija, do you think noise is bad?"
"I guess so. We normally don't want noise."

"Noise is unwanted. However, many researchers have found that noise or fluctuation is an interesting entity. Sometimes, noise is good. Cells inside us communicate by signalling process. In such small systems, stochastic or random noise can amplify weak signals and help in signalling, a phenomenon called stochastic resonance. The physics of fluctuations in equilibrium systems is well-established. However, the search for a general theory of non-equilibrium fluctuations is still going on."

"Wow! Noise is interesting!" Mitsna was stunned. "What's your research in this connection ?"

"Our recent work concerns a theoretical and computational study to find the role of stochastic fluctuations in a non-equilibrium model system. We have found that these fluctuations drive the system to non-equilibrium behaviour."

"What's your non-equilibrium model?" asked Laija.

"Think of a toy box consisting of three molecular species A, B and X. The molecules inside are now well-stirred, resulting in three possible chemical reactions due to random collisions among them. This means the system shows stochastic reaction dynamics. Considering the populations or numbers of A and B are quite large as compared to that of X, we now call it an open system. Assume the reactions occur at different rates. It is thus a non- equilibrium system where X constantly reacts with both A and B."

"Is this a realistic model? " asked Laija.
"Yes. This toy box can represent a cell. A, B and X can be the molecules inside, undergoing the three reaction channels, thereby exhibiting non-equilibrium behaviour. "
"How'd your team study stochastic fluctuations in this model ?" asked Mitsna.

"We studied stochastic fluctuations using two different approaches. Firstly, we adopted an approach called stochastic formalism from Physics and Mathematics and secondly, we used computers. In brief, the reactions are converted to a Mathematical equation popularly known as Master Equation (ME)," I said, "Mitsna, what do you think we do with an equation?"

"I think you try to solve it."

"YES! The solution of ME tells us the distributions of the variables A, B, X at any instant of time. This time-evolution of any system is called system-dynamics. Now, to measure fluctuations in the system, we used a quantifier called Fano factor (F). Depending on the value of F, one can study the behaviour of system-dynamics. So, we calculated the F value for our model and found F. This theoretically predicts a noise-enhancement process for our system where increased fluctuations are present. This indicates stochastic fluctuations drive the system to non-equilibrium."

"In science, predictions are not valid until they are proven experimentally," Laija said, "Is that right ?"

"To validate our Mathematical calculations, we performed what is known as numerical experiment or computer simulation," I replied.
"What's a numerical experiment or computer simulation?"

"There exist various natural processes difficult to experiment in real physical conditions, for instance, cascades of chemical reactions happening inside the microscopic cells (called metabolic pathways) or in the outer space (like interstellar or intergalactic). Nonetheless, we need to study their system-dynamics.

"This is when we create mini-labs on our computers, known as computer simulations or numerical experiments. We write algorithms or numerical codes to solve the equations governing these processes in cells to galaxies and give them to computers as inputs. Computers then execute the codes and show us how the system behaves."

"How'd you perform this simulation?"
"The ME is hard to manually solve for systems with multiple variables, but computers can easily solve it," I said, "Physicist Daniel Thomas Gillespie gave the Stochastic Simulation Algorithm (SSA) to numerically solve the ME."

"What's special about SSA?" asked Mitsna.
"In the well-stirred chemical system, two independent stochastic or random processes occur, namely, which reaction and at what time. These ideas are encoded in the SSA. SSA shows the time-evolution of the populations in the system. The SSA simulation of our model showed that X fluctuates about a steady-state value (~7777.78), driving the dynamics to non-equilibrium."

"Computer simulations are cool!"
"Indeed advanced and powerful techniques!" I continued, "Do you guys believe every natural process has some kind of inbuilt memory?"

"Memory as in how we remember things?" asked Laija.

"Memory is nothing but history. Processes with memory are called non-Markov processes, and those memoryless processes are Markov processes. Physicist van Kampen says "Non-Markov is the rule, Markov is an exception."

Practically, the three chemical reactions may not finish instantly once started; say A+X takes 14 seconds, B+X takes 4 seconds, and B+B takes 8 seconds. The reactions thus have inherent delays in time. SSA doesn't consider this time-delay. So, we performed simulations using Delay SSA (DSSA) given by Bratsun et al. Our mathematical analysis of fluctuations predicted that fluctuations vary with time-delay (T).

The DSSA simulation of our model verified this prediction (Fig3). As before, our calculation from DSSA simulation result data shows time-delay produces noise enhancement driving the system to non-equilibrium.

"What's the significance of this work? Does it have any real-life applications?" asked Laija. "Living cells work at non-equilibrium steady-state. Our theoretical and computational study can provide valuable insights into understanding how such systems work.

It also highlights time-delay affects system-dynamics and produces non- equilibrium. Studying non-equilibrium fluctuations is all about understanding life; how life emerges and continues. If we understand the role of these fluctuations, we can manipulate them in useful ways, for example, in the detection of the growth of cancerous cells.

"Research in non- equilibrium science, both theoretically and experimentally, is still in its infancy. Besides non-equilibrium biological systems, we also need to look at other non-equilibrium systems to solve varied issues such as energy crisis, financial crisis or climate control. Understanding non-equilibrium is the biggest challenge for the future."

"Your research on non-equilibrium fluctuations," Laija smiled, "has lots of prospects across many disciplines."
"Very interesting indeed!" Mitsna said in excitement, "Let's catch up again soon for more discussion."
"Sure! See you guys soon. Bye!"
And with that, I smiled back at the mulberry tree.