Entropy and the Second Law of Thermodynamics:
The second law of thermodynamics states that heat flows from hot to cold and never the other way around unless external work is done. This law is considered one of the most fundamental laws of physics and has been extensively studied and experimentally verified. Einstein and Eddington emphasized the significance and universality of the second law.

Carnot’s Idealized Heat Engine and Efficiency:
Sadi Carnot’s work laid the foundation for understanding heat engines and their efficiency. He proposed an idealized frictionless heat engine that transfers heat from a hot reservoir to a cold reservoir. Carnot showed that the efficiency of this heat engine is determined by the temperatures of the hot and cold reservoirs.

Clausius’ Definition of Entropy:
Clausius defined entropy as the integral of heat transfer divided by temperature. For a reversible engine operating between two temperatures, the change in entropy is zero. This definition, however, did not directly correspond to any measurable physical property.

Boltzmann’s Definition of Entropy and Accessible States:
Boltzmann’s definition of entropy states that entropy is proportional to the logarithm of the number of accessible states. This definition provides a statistical interpretation of entropy. It connects entropy to the number of possible arrangements of particles in a system.

Landauer’s Principle and the Energy Cost of Computation:
Landauer explored the relationship between information processing and thermodynamics. He proposed that erasing information (resetting a bit) requires an energy cost due to the increase in entropy. This principle has implications for the energy efficiency of computation and has been studied in the context of quantum computing.

Biological Systems and Molecular Motors:
Biological systems, such as molecular motors, operate in a non-equilibrium state and exhibit remarkable energy efficiency. These systems utilize chemical energy to perform work and transport molecules against concentration gradients. The study of molecular motors provides insights into the relationship between thermodynamics and biological processes.

Landauer’s Limit for Computation Memory:
At a certain temperature T, there is a minimum amount of energy required for a computer to read and reset a memory. This minimum energy is directly related to the entropy of the memory.

Entropy Change During Memory Readout:
The entropy of a memory changes from K log 2 (two accessible states) to K log 1 (one accessible state) when it is read. This change in entropy is irreversible, as the act of reading the memory reveals information that cannot be fully erased.

Experimental Verification of Landauer’s Limit:
Jeff Boker, a professor at Berkeley, conducted experiments to measure the energy required to read and reset a spin. The results showed that the average energy required was within 20% of the Landauer limit, indicating that it is possible to design systems that operate close to the theoretical minimum energy for computation memory.

Conclusion:
The Landauer limit sets a fundamental limit on the energy required for computation memory, regardless of the cleverness of the design. Experiments have demonstrated the feasibility of operating close to this limit, suggesting the possibility of ultra-low-energy computing systems in the future.

Properties of Large Numbers and Statistical Physics:
The second law of thermodynamics is considered sacred because it describes the properties of large numbers. It is based on statistical physics, which deals with the behavior of systems with a large number of particles. Laws of logic and mathematics are experimental and are considered true because they work.

Entropy and Polymers:
Entropy is the measure of disorder in a system. Polymers are long, chain-like molecules. A polymer in a crumpled state has higher entropy than a stretched-out polymer because there are more ways for the polymer to be crumpled than stretched out. When a polymer is stretched out, it will contract like a rubber band due to the increase in entropy.

Molecular Motors:
Molecular motors are proteins that use energy to transport cargo within cells. Kinesin and dynein are two important molecular motors. Kinesin transports cargo towards the ends of cells, while dynein transports cargo towards the cell body. Dynein is a complex motor with a mass of 1.5 megadaltons and consists of an amino acid chain and accessory proteins. Despite being discovered decades ago, the full operation of dynein is still not fully understood.

Cellular Motor Structure and Function:
Steven Chu introduces a cellular motor structure resembling polypeptide chains curled in a helix form, with amino acids represented as little bobs. This structure, comprising six domains, exhibits unique motor properties distinct from kinesin and myosin, and originates from DNA packaging and unwinding motors. The motor’s effectiveness in “backwards” motion remains a mystery.

Cartoon Representation of Motor Mechanism:
A cartoon animation depicts two monomers attached to cargo, exhibiting Brownian motion and deciding to step. The linker arm transitions between a straight state and a bent state, enabling the motor’s movement.

Yogi Berra’s Wisdom and Observation:
Steven Chu emphasizes the value of observation and prolonged monitoring in scientific research. He highlights the importance of attending friends’ memorial services to ensure reciprocity.

Introduction of Up-converting Nanoparticles:
Up-converting nanoparticles are introduced as new optical probes for studying cellular processes. These nanoparticles utilize a two-step excitation mechanism, where infrared light is converted into visible light. Infrared light is advantageous as it does not damage cells, and the nanoparticles have extended longevity.

Quantum Dot Behavior and Photobleaching:
Quantum dots, represented in gray, exhibit blinking and various behaviors before undergoing photobleaching at high intensities.

Challenges and Improvements in Nanoparticle Development:
Initial nanoparticles had low brightness and clustered together, affecting their optical properties. Scientists overcame these issues by growing their own crystals and optimizing the nanoparticle composition. The resulting nanoparticles were brighter and more stable, making them suitable for long-term imaging.

Enhanced Properties of the Optimized Nanoparticles:
Nanoparticles exhibited 150-200 times higher brightness at animal imaging intensities. At high intensities used for high-resolution studies, they were still 6-10 times brighter. The nanoparticles could be made very small (down to 10 nanometers) while maintaining high brightness.

Experimental Setup for Tracking Vesicles:
Immature neurons were placed in a flow cell with a 900-micron gap. Nanoparticles coated with a chemical signal were introduced into the flow cell. Neurons grabbed the chemical signal and transported it back to their cell bodies via motor molecules. The nanoparticles were excited with infrared light, eliminating reactive ion species and photophysics issues.

Data Analysis and Results:
Raw data consisted of tens of minutes of a single vesicle moving over a millimeter. Segments of constant velocity were identified and concatenated to represent the same vesicle’s journey. The mean and dispersion of the vesicle’s position over time were calculated. The ratio of twice the mean to the dispersion (mean over dispersion) was plotted for each vesicle. For many vesicles, this ratio reached a steady-state value, representing the vesicle’s constant velocity. Different neurons exhibited different steady-state values, with some reaching two, three, or five distinct values.

Conclusion:
The optimized nanoparticles enabled long-term, high-resolution tracking of vesicles in neurons. The analysis of vesicle motion provided insights into the dynamics of intracellular transport and the behavior of motor molecules.

Quantization of Vesicle Motion:
Observed quantization in the asymptotic values of vesicle motion, despite variations in vesicle sizes and quantization numbers. Suspicion that the quantization might be related to the number of motors moving the vesicle.

Independent Motors and Mathematical Modeling:
Hypothesized that if motors are independent and not communicating, the combined effect would result in the product of individual motor probability functions. The product of two Gaussians (representing independent motors) is also a Gaussian. In the limit of many small steps (large number of motors), the displacement remains the same, but the dispersion decreases.

Experimental Verification:
In vitro experiment with DNA origami confirmed the mathematical model, showing that velocity remains constant with increasing numbers of motors (up to three motors). In live cell experiments, the number of motors influences the motion of vesicles, with a 5% change observed when motors are attached to the same vessel.

Calculating Motor Efficiency:
Calculated the free energy release from ATP hydrolysis at 37 degrees Celsius to be 12 kT. Measured the viscosity of the medium using particles of different sizes, finding that the viscosity depends on the size of the molecule. Efficiency of the motor was estimated to be at least 50% if burning two ATPs and 90% if burning one ATP.

Measuring Vesicle Movement at Different Temperatures:
By tracking vesicle movement at different temperatures (37 degrees, 30 degrees, and 22 degrees), individual single steps could be observed.

Measuring Single Molecular Steps:
Researchers can now track single molecular steps for extended periods without damaging the cell, revealing valuable insights into motor protein behavior.

Step Size Distribution:
The distribution of step sizes taken by motor proteins can be determined by analyzing the histograms generated from the measured steps.

Backward Steps:
At body temperature, motor proteins rarely take backward steps, but this observation is limited by the resolution of the measurement technique. Smaller steps, including zero or negative steps, may be hidden within the noise.

Comparison with In Vitro Experiments:
When comparing data from in vivo experiments (using live cells) and in vitro experiments (using purified components), there is good agreement between the step size distributions, suggesting that the in vitro system captures some aspects of the behavior observed in living cells.

Dwell Time Distribution:
The time taken by motor proteins to move from one step to the next, known as the dwell time, also exhibits a distribution.

Two Rate Constants:
The rise and fall pattern observed in the dwell time distribution suggests the presence of two rate constants, indicating that the motor protein may undergo distinct conformational changes during its stepping cycle.

Convolution of Rate Constants:
The convolution of two single exponential decays, with equal rate constants, can produce the observed dwell time distribution, providing a potential explanation for the rise and fall pattern.

ATP-Powered Dynein Motor:
Dynein, a molecular motor, utilizes ATP (adenosine triphosphate) as its fuel source to generate movement. ATP binds to the active site of dynein, triggering a series of rapid chemical reactions. Electron transfer occurs, breaking the phosphate bond of ATP, releasing energy for the motor’s operation.

Two Rate Constants for ATP Burning:
Previous studies identified only one rate constant associated with ATP burning in dynein. However, at significantly higher ATP concentrations, two rate constants emerge, challenging the prevailing model.

Phosphate Release as the Second Rate-Limiting Step:
The prevailing model assumes a single ATP-burning event as the rate-limiting step. The two rate constants observed at high ATP concentrations suggest that phosphate release is the second rate-limiting step.

Revisiting Earlier Data:
Reanalysis of earlier data, using a different approach, revealed evidence of two rate constants, supporting the new model.

Implications for Dynein’s Function:
The discovery of two ATP-burning events has implications for understanding dynein’s processivity and efficiency. It also challenges the Hill coefficient analysis used to determine the number of active sites in dynein.

Predicting N = 4 in the Dispersion Plot:
Adjusting ATP concentration to balance the on and off rates of ATP binding could reveal a peak at N = 4 in the dispersion plot.

Future Experiments:
Ongoing collaborations aim to verify the two-ATP-burning model through further experiments. Researchers plan to measure the dwell time between steps in dynein’s movement under different ATP concentrations.

Conclusion:
This chapter presents a significant shift in understanding dynein’s ATPase cycle, moving from a single ATP-burning event to two, opening up new avenues for research into the motor’s mechanism and function.

Simple Model of Dining Monomer:
Dining monomers have two legs and two steps. They wiggle around due to diffusion and spend most of their time in the down state. When PI leaves, the monomer does a power stroke.

Measurements and Calculations:
The linker arm has two structures and known angles. The size of the molecule and the distances between different parts are known. Using these parameters, a simple model can be created to describe the monomer’s behavior.

The Model’s Findings:
The model fits the experimental data at three different temperatures. It shows that the monomer spends most of its time in the down state and goes up and down randomly.

Is Life Based on the Laws of Physics?:
Irving Schrodinger questioned whether life can be explained by the laws of physics. He argued that the construction of living matter is different from anything tested in the physical laboratory.

Newton’s Laws in a Bacterial World:
If Newton were the size of a bacterium, his laws would be different. Inertia would not exist, and objects would come to a halt as soon as force is removed. Brownian motion would be significant, and F would not equal MA.

The Beauty of How It Works:
Living organisms operate in an overdamped, viscous, jiggling environment. The beauty of how it works lies in its functionality.

entropy:
Entropy increases when blue molecules are dropped into a beaker of clear water molecules because the blue molecules can go anywhere in the beaker, increasing the number of accessible states.

Fluctuation Theorem:
The fluctuation theorem quantifies the probability of entropy increasing over time. It states that the probability of the movie going forward in time divided by the probability of moving going backward in time is not infinity, but rather e to the change in entropy over Boltzmann’s constant. For very short amounts of time, entropy can increase, and this is not a violation of the second law of thermodynamics.

Non-Equilibrium Thermodynamics:
Lars Hansager’s fluctuation-dissipation theorem relates fluctuations about equilibrium to the dissipation of energy. The Onsager regression hypothesis states that a system’s approach back to equilibrium after being put out of equilibrium should be related to fluctuations about equilibrium. Non-equilibrium thermodynamics is used to understand systems that are not in thermal equilibrium, such as the motion of a vesicle driven by a molecular motor.

Vesicle Motion and Temperature:
In the experiment, the vesicle’s motion could not be explained by equilibrium thermodynamics using the cell’s temperature. However, when a temperature 5.7 times higher than the cell’s temperature was used, the data matched the predictions of non-equilibrium thermodynamics. This suggests that the vesicle’s motion is driven by fluctuations in the motor protein, which can be described by a higher effective temperature.

The Convolution of Stepping Functions and the Central Limit Theorem:
Steven Chu explains that when you convolute many stepping functions, you get a Gaussian distribution. This is because of the central limit theorem, which states that the convolution of many functions always results in a Gaussian distribution.

The Relationship between Order and Entropy:
Chu shows that the product of the dispersion of a molecular motor system (how orderly the motion is) and the minimum entropy needed to get this order is greater than or equal to 2KT. This is an uncertainty principle, similar to the Heisenberg uncertainty principle for quantum mechanics.

Two Motors Are More Ordered Than One:
Chu demonstrates that two motors are more ordered than one. This is because the dispersion of two motors is less than one, meaning the motion is more tightly distributed.

The Trade-Off between Order and Energy:
Chu explains that as you increase the number of steps in a molecular motor system, the dispersion decreases, meaning the motion becomes more ordered. However, this comes at the cost of increased energy consumption, as more ATP molecules are burned.

Chu’s Pride and Disappointment:
Chu expresses pride in discovering this uncertainty principle for molecular motors. He mentions that two other theorists independently discovered the same principle around the same time and published it six months later. Chu acknowledges that he is more of an experimentalist than a theorist.

Landauer’s Limit and the Minimum Entropy for Precision:
Landauer’s limit sets a minimum entropy requirement for performing operations with a certain level of precision. This limit applies to both biological systems and artificial systems, such as quartz watches. Precision is distinct from accuracy, as precision refers to the level of detail or reproducibility of a measurement, while accuracy refers to the absolute correctness of a measurement.

Criticism of Landauer’s Work:
Landauer’s work initially faced criticism for potentially using circular reasoning. However, subsequent research has validated the results and demonstrated that Landauer’s limit does not violate the second law of thermodynamics.

Relevance to Computation, Biology, and Non-Equilibrium Thermodynamics:
Landauer’s limit has implications for computation, biology, and other fields where order and precision are essential. Non-equilibrium thermodynamics provides a framework for understanding systems that are out of equilibrium, which is often the case in biological and computational processes.

Practical Applications:
The development of high-quality nanoparticles has significantly improved the sensitivity and tracking capabilities of experimental methods. These improved nanoparticles enable tracking of biological processes for extended periods, potentially leading to new insights and discoveries.

ATP and Effective Temperature:
The value of 12 kBT associated with ATP is not directly related to the effective temperature of the system.

Free Energy and ATP Concentration:
Free energy increases when chemical bonds are broken, resulting in a concentration-dependent net free energy determined by the balance of ATP, ADP, and PI in a cell. At higher ADP concentrations, the reaction can reverse, as demonstrated by experiments using a proton pump motor.

Entropy Production by Humans:
Humans are highly efficient entropy generators, producing vast amounts of carbon dioxide and other greenhouse gases, as well as altering the world’s ecosystem through bioengineering and engineering.

Limitations of Optical Tweezers in Studying Motor Efficiency:
Optical tweezers experiments on motor proteins can provide misleading results due to the difference between the motor’s behavior when it has both feet on the ground compared to when it is lifted. The efficiency of a motor increases as it goes faster, similar to a car engine’s efficiency increasing at higher speeds.

Determining the Upper Limit of Motor Efficiency:
The true upper limit of motor efficiency is unknown, as previous studies using optical tweezers did not accurately measure the motor’s behavior under load. A more accurate experiment would involve increasing the viscosity in vitro until the motor stops, imitating the crowded environment of a cell.

Molecular Structures:
There is a high level of consistency between the predicted detailed molecular structures and the structures found in protein databanks, supporting Steven Chu’s model. Ongoing collaborations with structural biologists, including Angel Carter at Cambridge, aim to further validate and refine the model through additional experiments and controls.

Entropy and Uncertainty Principle:
Similar to Heisenberg’s uncertainty principle, there is a fundamental relationship between the minimum entropy cost energy and the orderliness of a system. The minimum entropy cost energy multiplied by the orderliness must be greater than or equal to 2 kT, where k is Boltzmann’s constant and T is temperature. This principle applies to molecular motors operating at kT, representing the minimum energy required for their operation.

Quantization of Time:
Chu does not delve into the question of whether time is quantized, focusing instead on the statistical average behavior of systems over long periods of time. The quantization of time, if it exists, would be imperceptible at the timescales relevant to their research.

Conclusion:
The discussion ends with a request for feedback from the audience on the understandability of the presented concepts.