Aidan I Brown

PEX5 and Ubiquitin Dynamics on Mammalian Peroxisome Membranes

Peroxisomes are membrane-bound organelles within eukaryotic cells that post-translationally import folded proteins into their matrix. Matrix protein import requires a shuttle receptor protein, usually PEX5, that cycles through docking with the peroxisomal membrane, ubiquitination, and export back into the cytosol followed by deubiquitination. Matrix proteins associate with PEX5 in the cytosol and are translocated into the peroxisome lumen during the PEX5 cycle. This cargo translocation step is not well understood, and its energetics remain controversial. We use stochastic computational models to explore different ways the AAA ATPase driven removal of PEX5 may couple with cargo translocation in peroxisomal importers of mammalian cells. The first model considered is uncoupled, in which translocation is spontaneous, and does not immediately depend on PEX5 removal. The second is directly coupled, in which cargo translocation only occurs when its PEX5 is removed from the peroxisomal membrane. The third, novel, model is cooperatively coupled and requires two PEX5 on a given importomer for cargo translocation — one PEX5 with associated cargo and one with ubiquitin. We measure both the PEX5 and the ubiquitin levels on the peroxisomes as we vary the matrix protein cargo addition rate into the cytosol. We find that both uncoupled and directly coupled translocation behave identically with respect to PEX5 and ubiquitin, and the peroxisomal ubiquitin signal increases as the matrix protein traffic increases. In contrast, cooperatively coupled translocation behaves dramatically differently, with a ubiquitin signal that decreases with increasing matrix protein traffic. Recent work has shown that ubiquitin on mammalian peroxisome membranes can lead to selective degradation by autophagy, or ‘pexophagy.’ Therefore, the high ubiquitin level for low matrix cargo traffic with cooperatively coupled protein translocation could be used as a disuse signal to mediate pexophagy. This mechanism may be one way that cells could regulate peroxisome numbers.

A storage-based model of heterocyst commitment and patterning in cyanobacteria

When deprived of fixed nitrogen (fN), certain filamentous cyanobacteria differentiate nitrogen-fixing heterocysts. There is a large and dynamic fraction of stored fN in cyanobacterial cells, but its role in directing heterocyst commitment has not been identified. We present an integrated computational model of fN transport, cellular growth, and heterocyst commitment for filamentous cyanobacteria. By including fN storage proportional to cell length, but without any explicit cell-cycle effect, we are able to recover a broad and late range of heterocyst commitment times and we observe a strong indirect cell-cycle effect. We propose that fN storage is an important component of heterocyst commitment and patterning in filamentous cyanobacteria. The model allows us to explore both initial and steady-state heterocyst patterns. The developmental model is hierarchical after initial commitment: our only source of stochasticity is observed growth rate variability. Explicit lateral inhibition allows us to examine ΔpatS, ΔhetN, and ΔpatN phenotypes. We find that ΔpatS leads to adjacent heterocysts of the same generation, while ΔhetN leads to adjacent heterocysts only of different generations. With a shortened inhibition range, heterocyst spacing distributions are similar to those in experimental ΔpatN systems. Step-down to non-zero external fN concentrations is also investigated.

Reconciling cyanobacterial fixed-nitrogen distributions and transport experiments with quantitative modelling

Filamentous cyanobacteria growing in media with insufficient fixed nitrogen (fN) differentiate some cells into heterocysts, which fix nitrogen for the remaining vegetative cells. Transport studies have shown both periplasmic and cytoplasmic connections between cells that could transport fN along the filament. Two experiments have imaged fN distributions along filaments. In 1974, Wolk et al found a peaked concentration of fN at heterocysts using autoradiographic techniques. In contrast, in 2007, Popa et al used nanoSIMS to show large dips at the location of heterocysts, with a variable but approximately level distribution between them. With an integrated model of fN transport and cell growth, we recover the results of both Wolk et al and of Popa et al using the same model parameters. To do this, we account for immobile incorporated fN and for the differing durations of labelled nitrogen fixation that occurred in the two experiments. The variations seen by Popa et al are consistent with the effects of cell-by-cell variations of growth rates, and mask diffusive gradients. We are unable to rule out a significant amount of periplasmic fN transport.

Heterocyst placement strategies to maximize the growth of cyanobacterial filaments

Under conditions of limited fixed-nitrogen, some filamentous cyanobacteria develop a regular pattern of heterocyst cells that fix nitrogen for the remaining vegetative cells. We examine three different heterocyst placement strategies by quantitatively modelling filament growth while varying both external fixed-nitrogen and leakage from the filament. We find that there is an optimum heterocyst frequency which maximizes the growth rate of the filament; the optimum frequency decreases as the external fixed-nitrogen concentration increases but increases as the leakage increases. In the presence of leakage, filaments implementing a local heterocyst placement strategy grow significantly faster than filaments implementing random heterocyst placement strategies. With no extracellular fixed-nitrogen, consistent with recent experimental studies of Anabaena sp. PCC 7120, the modelled heterocyst spacing distribution using our local heterocyst placement strategy is qualitatively similar to experimentally observed patterns. As external fixed-nitrogen is increased, the spacing distribution for our local placement strategy retains the same shape, while the average spacing between heterocysts continuously increases.

Allocating dissipation across a molecular machine cycle to maximize flux

Significance Cells use molecular machines to complete many tasks. These machines consume free energy to operate, typically by converting a high-concentration chemical into a low-concentration one. Each step of a machine’s operating cycle consumes some free energy, and different allocations of the available free energy among the machine steps lead to different machine speeds. We show that the speed-maximizing allocation is not even, instead depending on the timescales of the various steps. Models fit to experimental molecular machine dynamics often find similarly uneven free energy use. Deviations from the optimal allocation can drastically slow machine operation, suggesting a significant functional advantage to machines with dissipation allocation that is tuned to improve speed. Biomolecular machines consume free energy to break symmetry and make directed progress. Nonequilibrium ATP concentrations are the typical free energy source, with one cycle of a molecular machine consuming a certain number of ATP, providing a fixed free energy budget. Since evolution is expected to favor rapid-turnover machines that operate efficiently, we investigate how this free energy budget can be allocated to maximize flux. Unconstrained optimization eliminates intermediate metastable states, indicating that flux is enhanced in molecular machines with fewer states. When maintaining a set number of states, we show that—in contrast to previous findings—the flux-maximizing allocation of dissipation is not even. This result is consistent with the coexistence of both “irreversible” and reversible transitions in molecular machine models that successfully describe experimental data, which suggests that, in evolved machines, different transitions differ significantly in their dissipation.

Effective Dissipation: Breaking Time-Reversal Symmetry in Driven Microscopic Energy Transmission

At molecular scales, fluctuations play a significant role and prevent biomolecular processes from always proceeding in a preferred direction, raising the question of how limited amounts of free energy can be dissipated to obtain directed progress. We examine the system and process characteristics that efficiently break time-reversal symmetry at fixed energy loss; in particular for a simple model of a molecular machine, an intermediate energy barrier produces unusually high asymmetry for a given dissipation. We relate the symmetry-breaking factors found in this model to recent observations of biomolecular machines.

Single file diffusion into a semi-infinite tube.

We investigate single file diffusion (SFD) of large particles entering a semi-infinite tube, such as luminal diffusion of proteins into microtubules or flagella. While single-file effects have no impact on the evolution of particle density, we report significant single-file effects for individually tracked tracer particle motion. Both exact and approximate ordering statistics of particles entering semi-infinite tubes agree well with our stochastic simulations. Considering initially empty semi-infinite tubes, with particles entering at one end starting from an initial time t = 0, tracked particles are initially super-diffusive after entering the system, but asymptotically diffusive at later times. For finite time intervals, the ratio of the net displacement of individual single-file particles to the average displacement of untracked particles is reduced at early times and enhanced at later times. When each particle is numbered, from the first to enter (n = 1) to the most recent (n = N), we find good scaling collapse of this distance ratio for all n. Experimental techniques that track individual particles, or local groups of particles, such as photo-activation or photobleaching of fluorescently tagged proteins, should be able to observe these single-file effects. However, biological phenomena that depend on local concentration, such as flagellar extension or luminal enzymatic activity, should not exhibit single-file effects.

Allocating and Splitting Free Energy to Maximize Molecular Machine Flux

Biomolecular machines transduce between different forms of energy. These machines make directed progress and increase their speed by consuming free energy, typically in the form of nonequilibrium chemical concentrations. Machine dynamics are often modeled by transitions between a set of discrete metastable conformational states. In general, the free-energy change associated with each transition can increase the forward rate constant, decrease the reverse rate constant, or both. In contrast to previous optimizations, we find that in general flux is maximized neither by devoting all free-energy changes to increasing forward rate constants nor by solely decreasing reverse rate constants. Instead, the optimal free-energy splitting depends on the detailed dynamics. Extending our analysis to machines with vulnerable states (from which they can break down), in the strong driving corresponding to in vivo cellular conditions, processivity is maximized by reducing the occupation of the vulnerable state.

A Model of Autophagy Size Selectivity by Receptor Clustering on Peroxisomes

Selective autophagy must not only select the correct type of organelle, but also must discriminate between individual organelles of the same kind so that some but not all of the organelles are removed. We propose that physical clustering of autophagy receptor proteins on the organelle surface can provide an appropriate all-or-none signal for organelle degradation. We explore this proposal using a computational model restricted to peroxisomes and the relatively well characterized pexophagy receptor proteins NBR1 and p62. We find that larger peroxisomes nucleate NBR1 clusters first and lose them last through competitive coarsening. This results in significant size-selectivity that favors large peroxisomes, and can explain the increased catalase signal that results from siRNA inhibition of p62. Excess ubiquitin, resulting from damaged organelles, suppresses size-selectivity but not cluster formation. Our proposed selectivity mechanism thus allows all damaged organelles to be degraded, while otherwise selecting only a portion of organelles for degradation.

Uniform spatial distribution of collagen fibril radii within tendon implies local activation of pC-collagen at individual fibrils

Collagen fibril cross-sectional radii show no systematic variation between the interior and the periphery of fibril bundles, indicating an effectively constant rate of collagen incorporation into fibrils throughout the bundle. Such spatially homogeneous incorporation constrains the extracellular diffusion of collagen precursors from sources at the bundle boundary to sinks at the growing fibrils. With a coarse-grained diffusion equation we determine stringent bounds, using parameters extracted from published experimental measurements of tendon development. From the lack of new fibril formation after birth, we further require that the concentration of diffusing precursors stays below the critical concentration for fibril nucleation. We find that the combination of the diffusive bound, which requires larger concentrations to ensure homogeneous fibril radii, and lack of nucleation, which requires lower concentrations, is only marginally consistent with fully processed collagen using conservative bounds. More realistic bounds may leave no consistent concentrations. Therefore, we propose that unprocessed pC-collagen diffuses from the bundle periphery followed by local C-proteinase activity and subsequent collagen incorporation at each fibril. We suggest that C-proteinase is localized within bundles, at fibril surfaces, during radial fibrillar growth. The much greater critical concentration of pC-collagen, as compared to fully processed collagen, then provides broad consistency between homogeneous fibril radii and the lack of fibril nucleation during fibril growth.