#### Steven Chu (Stanford Professor) – Remarks at U Michigan (Sep 2022)

#### Chapters

#### Abstract

Exploring Entropy, Molecular Motors, and Statistical Physics: Unveiling Insights from Stephen Chu and Beyond

Introduction:

In this article, we delve into the captivating world of entropy, molecular motors, and statistical physics, drawing inspiration from the groundbreaking work of Stephen Chu and other leading scientists. Our journey begins with an exploration of the second law of thermodynamics, a fundamental principle that has shaped our understanding of energy flow and entropy. We then delve into Carnot’s idealized heat engine, Clausius’ definition of entropy, and Boltzmann’s statistical interpretation of entropy, gaining deeper insights into the nature of heat and disorder.

Landauer’s Principle and the Energy Cost of Computation:

Landauer’s principle, a cornerstone of modern thermodynamics, reveals the inherent energy cost associated with information processing and computation. This principle underlines the minimum energy required to read and reset a bit of information and has been supported by experimental evidence, pointing to the future possibility of ultra-low-energy computing systems.

Entropy of Polymers and Molecular Motors:

The second law of thermodynamics, deeply embedded in statistical physics, sheds light on systems with numerous particles. We focus on entropy as a measure of disorder, especially in polymers and molecular motors. Polymers, such as rubber bands, have a natural inclination towards crumpled states due to their higher entropy. Molecular motors, including kinesin and dynein, are integral to cellular cargo transport. While kinesin moves cargo towards cell ends, dynein transports it towards the cell body. However, dynein’s complex behavior still presents scientific enigmas.

Insights from Stephen Chu’s Research:

Stephen Chu, a notable physicist, has significantly advanced our understanding of molecular motors and statistical physics. His studies on monomer motors, which differ from kinesin and myosin motors, provide insights into DNA packaging and unraveling. His work on Brownian motion and stepping deepens our understanding of molecular motors’ behaviors.

Cellular Motor Structure and Function:

Steven Chu introduces a novel cellular motor structure resembling polypeptide chains formed into a helix, with amino acids depicted as small bobs. This structure, composed of six domains, demonstrates unique motor properties separate from those of kinesin and myosin, primarily seen in DNA packaging and unwinding motors. The motor’s capability for “backwards” motion remains a puzzling aspect.

Nanoparticle Development and Imaging Neurons:

Advancements in nanoparticles have significantly transformed cellular imaging. Chu’s collaboration with nanoparticle experts overcame initial challenges, leading to breakthroughs in nanoparticle synthesis. These enhancements have enabled long-term tracking of individual vesicles in neurons, offering new insights into their transport mechanisms.

Data Analysis and Motor Efficiency:

The analysis of data from vesicle tracking experiments revealed interesting patterns. By calculating the mean and dispersion of vesicle positions, researchers could deduce different steady-state velocities among neurons. Chu’s investigation into vesicle transport quantization suggests a link between the number of motors moving a vesicle and its velocity.

Step Size and Dwell Time Distributions:

Advanced techniques for tracking single molecular steps of kinesin have unveiled the distribution of step sizes. The analysis of intervals between steps suggested a rise and fall pattern, leading to a two-rate constant model to explain these findings.

Measuring Single Molecular Steps:

With improved methods, researchers can now track single molecular steps for extended periods, gaining valuable insights into motor protein behavior without harming the cell.

Step Size Distribution:

By analyzing histograms of measured steps, the distribution of step sizes taken by motor proteins can be determined.

Backward Steps:

At body temperature, backward steps by motor proteins are rare, but this is limited by the resolution of the measurement technique. Smaller steps, including zero or negative ones, may go unnoticed within the noise.

Comparison with In Vitro Experiments:

Comparing in vivo (live cells) and in vitro (purified components) experiments shows good agreement in step size distributions, indicating that in vitro systems can replicate aspects of in vivo behavior.

Dwell Time Distribution:

The dwell time distribution of motor proteins, representing the time taken to move from one step to the next, has been observed to have its own distribution.

Two Rate Constants:

The observed rise and fall pattern in the dwell time distribution implies the existence of two rate constants, suggesting distinct conformational changes during the motor protein’s stepping cycle.

Convolution of Rate Constants:

The convolution of two single exponential decays with equal rate constants can recreate the observed dwell time distribution, offering a potential explanation for the rise and fall pattern.

ATP-Powered Dynein Motor:

Dynein, a molecular motor, relies on ATP (adenosine triphosphate) to generate movement.

Two Rate Constants for ATP Burning:

Earlier studies only identified one rate constant for ATP burning in dynein. However, newer findings at higher ATP concentrations reveal two rate constants, challenging the existing model.

Phosphate Release as the Second Rate-Limiting Step:

The traditional model assumed a single ATP-burning event as the rate-limiting step. The discovery of two rate constants at high ATP concentrations suggests that phosphate release is also a rate-limiting step.

Revisiting Earlier Data:

Reanalysis of previous data, using a different approach, corroborated the existence of two rate constants, supporting the revised model.

Implications for Dynein’s Function:

The recognition of two ATP-burning events in dynein has significant implications for understanding its processivity and efficiency. It also questions the Hill coefficient analysis previously used to determine the number of active sites in dynein.

Predicting N = 4 in the Dispersion Plot:

Adjusting ATP concentration to balance ATP binding rates could expose a peak at N = 4 in the dispersion plot.

Future Experiments:

Ongoing research aims to confirm the two-ATP-burning model through additional experiments. Plans include measuring dynein’s dwell time between steps at varying ATP concentrations.

Simple Model of Dining Monomer:

Dining monomers, characterized by two legs and two steps, mainly reside in the down state due to diffusion. Upon PI leaving, the monomer performs a power stroke.

Measurements and Calculations:

With known structures and angles of the linker arm, and known sizes and distances within the molecule, a straightforward model can describe the monomer’s actions.

The Model’s Findings:

The model aligns with experimental data across three temperatures, showing the monomer’s tendency to remain mostly in the down state, moving up and down randomly.

New Insights into Entropy, Fluctuation Theorem, and Non-Equilibrium Thermodynamics:

Entropy:

Entropy increases when blue molecules are mixed with clear water molecules, as the blue molecules disperse throughout the beaker, increasing the number of accessible states.

Fluctuation Theorem:

The fluctuation theorem quantifies the probability of entropy’s temporal increase. It states that the ratio of forward to backward movement probability is not infinite but is e raised to the entropy change over Boltzmann’s constant. Entropy can increase over short periods without violating the second law of thermodynamics.

Non-Equilibrium Thermodynamics:

Lars Hansager’s fluctuation-dissipation theorem connects equilibrium fluctuations to energy dissipation. The Onsager regression hypothesis relates a system’s return to equilibrium after disturbance

to equilibrium fluctuations. Non-equilibrium thermodynamics is crucial for understanding non-thermally balanced systems, like vesicle motion driven by molecular motors.

Vesicle Motion and Temperature:

In experiments, vesicle motion could not be explained by equilibrium thermodynamics at the cell’s temperature. However, using a temperature 5.7 times higher matched non-equilibrium thermodynamics predictions, indicating that motor protein fluctuations drive the vesicle’s motion at a higher effective temperature.

Steven Chu’s Uncertainty Principle for Molecular Motors:

The Convolution of Stepping Functions and the Central Limit Theorem:

Steven Chu explains that convoluting multiple stepping functions results in a Gaussian distribution, as per the central limit theorem.

The Relationship between Order and Entropy:

Chu demonstrates that the product of a molecular motor system’s dispersion (orderliness) and the minimum entropy needed for this order is always greater than or equal to 2KT, forming an uncertainty principle akin to quantum mechanics’ Heisenberg principle.

Two Motors Are More Ordered Than One:

Chu shows that a system with two motors is more ordered than one with a single motor, as evidenced by reduced dispersion in the dual-motor system.

The Trade-Off between Order and Energy:

Chu notes that increasing the number of steps in a molecular motor system reduces dispersion, thus increasing order, but this comes at the cost of higher energy consumption due to increased ATP usage.

Chu’s Pride and Disappointment:

Chu takes pride in discovering this molecular motor uncertainty principle but acknowledges that two other theorists independently arrived at the same principle and published it six months later. Chu self-identifies more as an experimentalist than a theorist.

Entropy, Precision, and the Minimum Energy Requirements for Computation:

Landauer’s Limit and the Minimum Entropy for Precision:

Landauer’s limit sets a baseline entropy requirement for operations with specific precision levels, applicable to both biological and artificial systems like quartz watches. Precision, distinct from accuracy, refers to measurement reproducibility.

Criticism of Landauer’s Work:

Landauer’s work, initially criticized for possible circular reasoning, has since been validated and shown not to violate the second law of thermodynamics.

Relevance to Computation, Biology, and Non-Equilibrium Thermodynamics:

Landauer’s limit is significant for fields requiring precision and order, such as computation and biology. It highlights the role of non-equilibrium thermodynamics in understanding systems outside equilibrium.

Practical Applications:

Advancements in nanoparticles have enhanced experimental sensitivity and tracking capabilities, aiding in the extended tracking of biological processes and potentially leading to new discoveries.

ATP and Effective Temperature:

The 12 kBT value linked to ATP does not directly correspond to the system’s effective temperature.

Is Life Based on the Laws of Physics?:

Irving Schrodinger pondered if life’s mechanisms could be explained by physical laws, noting the distinct nature of living matter construction compared to that in physical laboratories.

Newton’s Laws in a Bacterial World:

In a bacterial-scale world, Newton’s laws would differ significantly. Inertia would be absent, and objects would stop once force is removed. Brownian motion would play a substantial role, altering the F=MA equation.

The Beauty of How It Works:

Life thrives in an environment characterized by viscosity, jiggling, and overdamping, with its beauty lying in its functional mechanisms.

This comprehensive exploration of entropy, molecular motors, and statistical physics, guided by the insights of Stephen Chu and other prominent scientists, underscores the profound implications of these concepts for various fields, ranging from computation to cellular biology. The second law of thermodynamics, Landauer’s principle, and the study of molecular motors provide a deeper understanding of energy flow, information processing, and the intricate workings of living systems. As research continues to unravel the mysteries of these phenomena, we can expect further breakthroughs that will redefine our understanding of the universe and its intricate mechanisms.

Notes by: Rogue_Atom