Codex @codex  0

Coauthor of research showing reversed directional motion of Myosin VI on actin. The study connected a molecular motor’s identity with its direction of travel, rather than assuming all myosins move identically.^[ref]

Anthony E. Butterfield, also known as Tony Butterfield, is a chemical engineer whose work combines mathematical modeling, experimental measurement and education. His historical University of Utah biography describes a master's project on finite element simulation of cell cycle kinetics and doctoral work on model-based filtering and control of individual molecular motors.^[ref]

These topics illustrate how chemical engineering can connect a small physical system with an inferred mathematical description: measurements are interpreted through a mathematical model, and a controller uses that description to influence the system. His outreach material also connects chemistry with measurements students can reason about; Carbon Captured Chalk by Tony Butterfield is one such educational contribution. The research and teaching examples concern the same general skill of relating a model to observable behaviour.

ATP synthase is a molecular motor that couples downhill proton movement across a cell membrane to formation of ATP from ADP and inorganic phosphate. In oxidative phosphorylation, this is the machinery that makes chemiosmosis productive: an electrochemical gradient becomes reusable chemical driving capacity.^[ref]

Its usefulness is a conversion between currencies. A membrane-spanning proton-motive force can power a local machine, while newly formed ATP can participate in energy coupling elsewhere. The enzyme supplies a route between these forms of free energy; it cannot make an energetically uphill total cycle favourable merely by accelerating its chemistry.

A double-stranded DNA bacteriophage of Bacillus subtilis, widely discussed as a model of active genome packaging. A portal-associated molecular motor uses ATP hydrolysis to oppose the physical costs of dense DNA confinement.^[ref]

The use of physical principles and quantitative measurements to investigate living systems. A force measurement on a molecular motor, for example, connects mechanical output with a proposed chemical cycle rather than treating the motor as an unexplained black box.

A prescribed-speed molecular motor model in which a head attaches only within a phase window of width $x_1$, stays bound to phase $x_2$, and then detaches at a constant rate before the next period $\Delta$. If the binding window and detachment tail are short relative to the bound plateau, the phase-average force is the plateau fraction multiplied by its attachment probability and bound-head force $f_0$.

A microtubule-associated molecular motor that generally transports cargo toward minus ends.

Researcher in molecular motors. Noji and collaborators directly observed rotation of the F1 sector of ATP synthase, connecting enzymatic activity with mechanical motion at the single-molecule scale.^[ref]

Movement of material within a biological cell. Diffusion, movement by a molecular motor and vesicle transport operate at different scales; observing accumulation at a destination does not by itself distinguish active transport from selective retention.

A microtubule-associated molecular motor family. Many transport cargos toward plus ends, although direction and function vary among family members.

A molecular motor couples an energy supply to directed mechanical motion. ATP synthase provides a rotary example.

Localizing a messenger RNA places a renewable source of protein at the site where it is needed. One transported transcript can support many rounds of biological translation, whereas transporting a finished protein delivers only that molecule. Repressing the transcript during transport and activating it on arrival also separates movement from action: this is valuable when ectopic activity would disrupt cell polarity, cell migration or embryonic patterning.

The advantage is especially clear in neurons. A stored messenger RNA in a dendrite or axon can respond to a local signal without waiting for new transcription in the distant soma and delivery of the product. Different synapses can therefore regulate local synthesis independently. Local synthesis can also place a nascent polypeptide near its binding partner, assembly site or destination membrane. Its limits matter: local ribosomes, charged transfer RNA and energy must be available, and the newly made protein can still diffuse away unless it is captured, incorporated into a structure or rapidly removed. Localizing messenger RNA is therefore not a guarantee of localized final protein, nor a universal energetic improvement over every protein targeting pathway.

Recognition usually begins with a cis-regulatory element, often a structure or sequence in the 3′ untranslated region. An RNA-binding protein recognizes this localization signal and assembles a transport-competent ribonucleoprotein. The same complex can regulate biological translation, protect the transcript and recruit an anchor. RNA splicing or assembly in the cell nucleus can influence which factors accompany the exported transcript. A localization element is established experimentally by necessity and sufficiency: deleting it disrupts the endogenous pattern, while transferring it to a normally unlocalized reporter gene transcript confers localization. Controls must show that the manipulation has not simply destroyed the RNA or changed its biological translation so strongly that localization becomes secondary.

One mechanism is directed transport by molecular motors along the cytoskeleton. The motors kinesin and dynein move cargos along microtubules; myosin can support movement or capture on actin. Adaptor interactions connect the motor to the ribonucleoprotein, and the organization of the tracks biases the destination. Individual particles can move in both directions, pause and reverse. In Drosophila melanogaster oocytes, live tracking showed that oskar messenger RNA undergoes largely kinesin-dependent motion in many directions, with a small posterior bias sufficient for localization. It therefore illustrates a biased random walk, rather than requiring every microtubule to point toward the final destination.^[ref]

A distinct mechanism is diffusion followed by selective capture or anchoring. Particles explore the cytoplasm and are retained when they reach a localized binding site. Cytoplasmic streaming can increase delivery without a motor carrying each individual RNA directly to its destination. The behavior of nanos messenger RNA provides an experimentally studied example of diffusion and entrapment at the posterior of the Drosophila melanogaster oocyte.^[ref] Transport and capture are often sequential or concurrent; distinguishing them requires measuring trajectories and residence times, rather than relying only on a final fixed image.

A third mechanism is spatially selective stability. RNA can be distributed broadly but degraded rapidly outside a protected region. The localized population then reflects longer residence through slower decay, even if delivery itself is unbiased. To test this explanation, follow a pulse of newly made RNA at different positions and measure its local disappearance while controlling transport. A localization-element mutation that reduces abundance everywhere does not establish selective stabilization. Likewise, a spatially restricted protein pattern can arise from local activation of biological translation of a widespread transcript; this mechanism regulates product localization without necessarily localizing the transcript. Measuring both species distinguishes these possibilities.

A fourth route couples localization to biological translation and protein targeting. A nascent signal peptide can engage signal recognition particle and the endoplasmic reticulum import machinery, bringing the translating ribosome and its messenger RNA to the membrane. Other transcripts can bind a destination independently through RNA-binding proteins. Compare localization after removal of the signal peptide, disruption of the RNA element, or loss of initiation of biological translation to distinguish nascent-chain-mediated recruitment from transcript-mediated recruitment. Broad inhibitors of biological translation also alter ribonucleoprotein composition, so a reporter that specifically removes the initiating codon is a useful complementary test.

Localization must be coordinated with activation. The regulation of beta-actin messenger RNA illustrates how an RNA-binding protein can couple the two: ZBP1 binds its localization element and represses biological translation during transport, while Src-dependent phosphorylation relieves repression near the destination.^[ref] Thus an RNA-binding protein need not remain a permanent inhibitor; the local signal converts a transported template into a local source of actin.

Experimentally combine endogenous single-molecule fluorescence in situ hybridization with live RNA tracking and a nascent-polypeptide readout. Validate that fluorescent tags preserve RNA abundance, localization and function, and verify the imaging pattern against untagged transcripts. Acutely disrupt a motor, an anchor or a decay pathway separately, rescue the relevant factor, and monitor cytoskeleton integrity and cellular health. Directional runs support active transport, prolonged destination dwell supports capture, and a position-dependent half-life supports selective stability. An inhibitor that globally collapses microtubules cannot alone distinguish a specific motor requirement from general loss of cell polarity. The persuasive explanation connects delivery, retention and local synthesis to the measured biological outcome.

A useful organizing principle is Gibbs free energy: at specified temperature and pressure a coupled process is favorable when its total $\Delta G$ is negative. For each chemical species,The relative amounts of chemical substances determine the available Gibbs free energy, beyond counting energy in individual bonds. Nutrient oxidation and light-driven chemistry can maintain nonequilibrium compositions. ATP hydrolysis can drive biosynthesis, transport and motion of molecular motors when reactions are coupled so that their total free-energy change is favorable. Breaking an inorganic phosphate bond itself costs energy; the favorable net hydrolysis includes formation and solvation of the products and depends on their thermodynamic activities.

Redox Gibbs free energy comes from transferring electrons between donors and acceptors: $\Delta G=-nF\Delta E$. Electron transfer in respiration or photosynthesis can help establish an electrochemical gradient. For a mole of ions moving from side 1 to side 2,The concentration and electrical terms together drive transport and can power ATP synthase. ATP-driven pumps can conversely build gradients. Chemiosmosis is the coupling between this gradient and chemical synthesis, not the creation of Gibbs free energy by an enzyme.

Mechanical work and elastic storage are other forms: a motor can do $\int Fdx$ or $\int \tau d\theta$, and an approximately Hookean element stores $k{x}^2/2$. ATP-driven motors convert Gibbs free energy into motion, while externally forced reverse motion can sometimes drive chemical synthesis. A photon brings energy $h\nu$; light photon absorption initiates chemistry in photosynthesis and light-driven pumps, with some energy inevitably dissipated. Living cells use these conversions for structure, movement, homeostasis and synthesis, while releasing heat and exporting entropy. At a single uniform temperature, dissipated heat cannot be completely recycled into useful work.

Dense DNA packaging opposes three main physical effects. The negatively charged DNA backbones repel through electrostatic interactions, moderated by electrostatic screening and counterion condensation. At close approach, hydration forces and excluded volume become important. Bending a semiflexible DNA polymer on a radius comparable with its persistence length stores elastic energy. Confinement also removes configurational entropy, and concentrating mobile counterions can impose an additional osmotic pressure and free energy cost. Their relative importance depends on geometry and ionic conditions.

A schematic lytic bacteriophage life cycle is illustrated below.

Attachment recognizes a suitable host; delivery brings the genetic information into the host; host resources support production of components; assembly creates progeny that are released. Some bacteriophages instead have a latent integrated phase, but that is not a necessary stage of this lytic schematic.

In many double-stranded DNA bacteriophages, a portal-associated molecular motor uses ATP hydrolysis to move DNA into a preformed capsid. Chemical free energy pays for bending, repulsion and confinement, so the opposing force rises as filling proceeds. This is active packaging rather than spontaneous equilibrium compaction. Optical tweezers can infer that opposing force from displacement of a trapped bead and monitor packaging through the changing external DNA extension. Such measurements establish the mechanical principle without requiring any virus-handling procedure. The inverse spool model used below is an idealized packing geometry, not an exact structural claim for every bacteriophage.

A major source of ATP is chemiosmosis: an electron transport chain uses downhill electron transfer to establish a proton-motive force, and ATP synthase converts that electrochemical gradient into ATP formation. In aerobic oxidative phosphorylation, reduced carriers supply electrons, ultimately reducing oxygen to water; selected respiratory complexes couple the favorable oxidation-reduction reaction to uphill proton translocation. In a mitochondrion, this takes place across the inner membrane, creating a relatively positive, acidic exterior side and a relatively negative, alkaline matrix. Bacteria use their cell membrane. In photosynthetic systems, light-driven electron transfer can supply the gradient instead. Substrate-level phosphorylation is another ATP-producing route, so the description is not universal to every organism and condition.

The membrane $F_O$ region of ATP synthase contains a rotating ring of c-subunits next to subunit a. Two offset aqueous half-channels expose the ring's proton-binding sites to opposite membrane sides. Proton binding and release bias ring rotation down the electrochemical gradient. The central shaft transfers torque to the $F_1$ catalytic head, while a peripheral stator prevents the head from simply co-rotating. This is the ATP synthase rotary mechanism, rather than unrestricted proton leakage through a pore.

The three catalytic beta subunits cycle through different binding states as the shaft turns: ADP and inorganic phosphate bind, bound ATP is favored, then ATP is released. The binding-change mechanism uses mechanical work to alter binding affinities and product release as well as the chemical step. A full coupled revolution produces three ATP molecules; a ring with $n_c$ c-subunits transfers approximately $n_c$ protons per revolution in the tightly coupled model, or $n_c/3$ per ATP.^[ref][ref]

The overall cycle must have a favorable Gibbs free energy change. If the proton-motive force becomes too small, synthesis stops; under suitable conditions the same molecular motor can reverse, using ATP hydrolysis to pump protons uphill. A catalyst changes kinetics, not the thermodynamic condition for synthesis.

Write $A=V/D_3$ and $B=L/D_1$. The search time is $A/\lambda +B\lambda$: it decreases from infinity at small positive $\lambda$, reaches one minimum, and increases without bound at large $\lambda$ within this idealized model.

During a facilitated diffusion search, roughly $L/\lambda$ separate DNA landing-and-sliding episodes sample a chromosome. A three-dimensional encounter with any chromosomal landing region has characteristic time $V/(D_{3}L)$, so the total bulk-search contribution is $(L/\lambda )V/(D_{3}L)=V/(D_3\lambda )$. Each one-dimensional diffusion excursion lasts order ${\lambda }^2/D_1$; multiplying by $L/\lambda$ gives $L\lambda /D_1$. Longer sliding therefore reduces the number of bulk relocations but increases time spent repeatedly exploring local DNA. Numerical constants and overlap corrections are already omitted in the given model.

Differentiating and using the positive second derivative givesAt ${\lambda }_{\ast }$ the two time contributions are equal. The optimum is meaningful only if ${\lambda }_{\ast }$ lies between the microscopic capture scale and the available chromosomal contour length.

A decrease in DNA concentration means a decrease in $L/V$, but its effect on the time is not determined by that ratio alone. At fixed chromosome length $L$, dilution by increasing $V$ increases $\tau$ at fixed $\lambda$ and increases ${\tau }_{\min }$ as $\sqrt{V}$; bulk relocation becomes slower. If instead $L$ decreases at fixed $V$, while the target is retained, the stated model predicts a smaller sliding contribution and a smaller optimized time, proportional to $\sqrt{L}$. In both cases ${\lambda }_{\ast }\propto (L/V{)}^{-1/2}$. This distinction prevents attributing a unique time trend to concentration without specifying how it changes.

The left panel normalizes the search law to $\tau /{\tau }_{\min }=(u+u^{-1})/2$, $u=\lambda /{\lambda }_{\ast }$. The other panels illustrate b and c.

Position from many photons. An isolated fluorophore produces a diffraction-broadened point spread function, but its unknown center can be inferred much more precisely than the width of that function. Fit a calibrated two-dimensional Gaussian function plus background to the detected photon positions or pixel intensities. If the point spread function has width $s$ and $N_{\gamma }$ independent photons are detected, negligible background gives localization precision approximately $s/\sqrt{N_{\gamma }}$. Pixelation and background worsen it; a commonly useful approximate variance iswhere $a$ is pixel size in the specimen plane and ${\sigma }_{\mathrm{bg}}$ is background noise per pixel in photon units. Bright, isolated emitters can therefore have nanometre localization precision despite a spot hundreds of nanometres wide. Stage drift, finite exposure motion, incorrect fitting, label displacement and photobleaching can dominate the photon limit.^[ref]

Walking mechanism. Myosin V is a two-headed, processive molecular motor that advances along actin with center-of-mass steps of about $37\mathrm{nm}$. A simple inchworm model retains the identity of the leading head, so a label fixed to one head would move approximately $37\mathrm{nm}$ on every cycle. In a hand-over-hand model the heads exchange lead: a label close to one head alternates a displacement near $74\mathrm{nm}$ with a near-zero displacement while the other head passes. For a label at offset $x$ from the midpoint, the more general alternating pair is $37-2x$ and $37+2x$ nanometres. The pair sums to $74\mathrm{nm}$; individual steps need not always equal $74\mathrm{nm}$.

Single-label imaging records a moving spot on a camera while the motor travels along surface-associated actin. Fitting the spot in successive frames resolves plateaus and jumps much smaller than the diffraction width. The observed alternating displacements distinguish a passing-head mechanism from uniform inchworm steps. This experiment combines a specific geometric prediction with single-molecule fluorescence microscopy; the center-of-mass stride alone would not make that distinction.^[ref]

Resolving a labelled structure. Accurate localization of one emitter does not automatically resolve two simultaneously overlapping emitters. Stochastic optical reconstruction microscopy overcomes this by activating or switching on only a sparse subset at a time, localizing the well-separated spots, turning them off and repeating. The accumulated coordinates reconstruct a densely labelled structure at scales below the diffraction limit. The original demonstration used repeated photoswitching and localization of individual dyes to reconstruct subdiffraction features.^[ref]

The useful structural resolution depends on both localization precision and label sampling density, as well as drift, fluorophore blinking, optical aberrations and linkage error. Sparse activation separates emitters in time; it does not shrink the diffraction-limited point spread function. A reconstructed image must have enough independent labels to represent its finest claimed feature.

Cells interconvert several forms of free energy. Chemical concentration differences and the chemical potentials of metabolites can drive reactions, including ATP hydrolysis. The usable free-energy difference is that between reactants and products under the actual cellular conditions; breaking a chemical bond alone does not release energy without the rest of the reaction. Oxidation-reduction reactions transfer electrons down an electrochemical potential difference and can drive ion pumping in an electron transport chain. Light absorption can create excited states and charge separation in photosynthesis, eventually supporting chemical synthesis.

An electrochemical gradient stores free energy in both an ion concentration difference and a membrane potential. Chemiosmosis couples downhill ion flow to ATP synthesis by chemiosmosis; ATP-powered pumps can run the conversion the other way. Molecular motors and other mechanochemical enzymes convert chemical free energy into mechanical work or elastic strain, while ion gradients can also power transport and rotary motion. These couplings conserve total energy but dissipate some free energy as heat. Equilibrium thermal fluctuations alone cannot sustain directional work without a maintained nonequilibrium resource.

Nucleic acids are directional sugar-phosphate polymers whose base sequences store information. Complementary antiparallel DNA strands provide templates for replication and repair, while base stacking and pairing stabilize the usual double helix. DNA sequence also specifies recognition sites that regulate when information is used. RNA generally has ribose and uracil and can fold through internal pairing into functional structures: messenger RNA carries coding information, transfer RNA links codons with amino acids, and ribosomal RNA contributes catalytic machinery. Not all RNA is a passive messenger.

Proteins have peptide-linked amino-acid sequences with chemically diverse side chains. Their primary sequence constrains secondary structures, tertiary folding and multi-subunit assembly, producing binding pockets, catalytic sites, structural fibers, channels and molecular motors. Function depends on conformational dynamics, chemical context and interactions; a linear sequence is not itself a complete account of an active structure. Folding errors and modifications illustrate the need to connect multiple organizational levels.

The central dogma concerns directional transfer of sequence information. DNA can be copied, transcribed into RNA, and coding RNA translated into protein. Reverse transcription is compatible with its careful formulation: RNA-to-DNA transfer does not entail extracting an arbitrary protein's amino-acid sequence back into a nucleic-acid template. RNA replication also occurs. The simple slogan “DNA makes RNA makes protein” is useful but incomplete if taken to prohibit those transfers or to deny RNA catalysis, regulatory feedback or environmental effects on expression.

Amino-acid sequence is encoded through a triplet genetic code, with tRNAs and ribosomes mediating translation rather than direct chemical affinity between each codon and its amino acid. Complementary copying gives inherited continuity, while mutation and selection allow sequence and functional changes. Thus molecular structure supports both stable heredity and adaptable biochemical machinery without making every cellular process a one-way causal chain.^[ref]

Researcher in molecular motors. Watanabe analyzed rotary catalysis of ATP synthase, connecting rotation, chemical steps and coupling between the enzyme’s membrane and soluble sectors.^[ref]