Statistical Laws of Protein Motion in Neuronal Dendritic Trees

How energy determines spatial localisation and copy number of molecules in neurons

In neurons, the quantities of mRNAs and proteins are traditionally assumed to be determined by functional, electrical or genetic factors. Yet, there may also be global, currently unknown computational rules that are valid across different molecular species inside a cell. Surprisingly, our results show that the energy for molecular turnover is a significant cellular expense, en par with spiking cost, and which requires energy-saving strategies. We show that the drive to save energy determines transcript quantities and their location while acting differently on each molecular species depending on the length, longevity and other features of the respective molecule. We combined our own data and experimental reports from five other large-scale mRNA and proteomics screens, comprising more than ten thousand molecular species to reveal the underlying computational principles of molecular localisation. We found that energy minimisation principles explain experimentally-reported exponential rank distributions of mRNA and protein copy numbers. Our results further reveal robust energy benefits when certain mRNA classes are moved into dendrites, for example mRNAs of proteins with long amino acid chains or mRNAs with large non-coding regions and long half-lives proving surprising insights at the level of molecular populations.

Dendrite architecture determines mitochondrial distribution patterns in vivo

Neuronal morphology influences synaptic connectivity and neuronal signal processing. However, it remains unclear how neuronal shape affects steady-state distributions of organelles like mitochondria. In this work, we investigated the link between mitochondrial transport and dendrite branching patterns by combining mathematical modeling with in vivo measurements of dendrite architecture, mitochondrial motility, and mitochondrial localization patterns in Drosophila HS (horizontal system) neurons. In our model, different forms of morphological and transport scaling rules-which set the relative thicknesses of parent and daughter branches at each junction in the dendritic arbor and link mitochondrial motility to branch thickness-predict dramatically different global mitochondrial localization patterns. We show that HS dendrites obey the specific subset of scaling rules that, in our model, lead to realistic mitochondrial distributions. Moreover, we demonstrate that neuronal activity does not affect mitochondrial transport or localization, indicating that steady-state mitochondrial distributions are hard-wired by the architecture of the neuron.

Endoplasmic reticulum network heterogeneity guides diffusive transport and kinetics

The endoplasmic reticulum (ER) is a dynamic network of interconnected sheets and tubules that orchestrates the distribution of lipids, ions, and proteins throughout the cell. The impact of its complex, dynamic morphology on its function as an intracellular transport hub remains poorly understood. To elucidate the functional consequences of ER network structure and dynamics, we quantify how the heterogeneity of the peripheral ER in COS7 cells affects diffusive protein transport. In vivo imaging of photoactivated ER membrane proteins demonstrates their nonuniform spreading to adjacent regions, in a manner consistent with simulations of diffusing particles on extracted network structures. Using a minimal network model to represent tubule rearrangements, we demonstrate that ER network dynamics are sufficiently slow to have little effect on diffusive protein transport. Furthermore, stochastic simulations reveal a novel consequence of ER network heterogeneity: the existence of "hot spots" where sparse diffusive reactants are more likely to find one another. ER exit sites, specialized domains regulating cargo export from the ER, are shown to be disproportionately located in highly accessible regions, further from the outer boundary of the cell. Combining in vivo experiments with analytic calculations, quantitative image analysis, and computational modeling, we demonstrate how structure guides diffusive protein transport and reactions in the ER.

Computational insights into mRNA and protein dynamics underlying synaptic plasticity rules

Recent advances in experimental techniques provide an unprecedented peek into the intricate molecular dynamics inside synapses and dendrites. The experimental insights into the molecular turnover revealed that such processes as diffusion, active transport, spine uptake, and local protein synthesis could dynamically modulate the copy numbers of plasticity-related molecules in synapses. Subsequently, theoretical models were designed to understand the interaction of these processes better and to explain how local synaptic plasticity cues can up or down-regulate the molecular copy numbers across synapses. In this review, we discuss the recent advances in experimental techniques and computational models to highlight how these complementary approaches can provide insight into molecular cross-talk across synapses, ultimately allowing us to develop biologically-inspired neural network models to understand brain function.

Transport between im/mobile fractions shapes the speed and profile of cargo distribution in neurons

Neuronal function requires continuous distribution of ion channels and other proteins throughout large cell morphologies. Protein distribution is complicated by immobilization of freely diffusing subunits such as on lipid rafts or in postsynaptic densities. Here, we infer rates of immobilization for the voltage-gated potassium channel Kv4.2. Fluorescence recovery after photobleaching quantifies protein diffusion kinetics, typically reported as a recovery rate and mobile fraction. We show that, implicit in the fluorescence recovery, are rates of particle transfer between mobile and immobile fractions (im/mobilization). We performed photobleaching of fluorescein-tagged ion channel Kv4.2-sGFP2 in over 450 dendrites of rat hippocampal cells. Using mass-action models, we infer rates of Kv4.2-sGFP2 im/mobilization. Using a realistic neuron morphology, we show how these rates shape the speed and profile of subunit distribution. The experimental protocol and model inference introduced here is widely applicable to other cargo and experimental systems.

Morphology and Transport in Eukaryotic Cells

Transport of intracellular components relies on a variety of active and passive mechanisms, ranging from the diffusive spreading of small molecules over short distances to motor-driven motion across long distances. The cell-scale behavior of these mechanisms is fundamentally dependent on the morphology of the underlying cellular structures. Diffusion-limited reaction times can be qualitatively altered by the presence of occluding barriers or by confinement in complex architectures, such as those of reticulated organelles. Motor-driven transport is modulated by the architecture of cytoskeletal filaments that serve as transport highways. In this review, we discuss the impact of geometry on intracellular transport processes that fulfill a broad range of functional objectives, including delivery, distribution, and sorting of cellular components. By unraveling the interplay between morphology and transport efficiency, we aim to elucidate key structure-function relationships that govern the architecture of transport systems at the cellular scale. Expected final online publication date for the Annual Review of Biophysics, Volume 51 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

The prevalence and specificity of local protein synthesis during neuronal synaptic plasticity

To supply proteins to their vast volume, neurons localize mRNAs and ribosomes in dendrites and axons. While local protein synthesis is required for synaptic plasticity, the abundance and distribution of ribosomes and nascent proteins near synapses remain elusive. Here, we quantified the occurrence of local translation and visualized the range of synapses supplied by nascent proteins during basal and plastic conditions. We detected dendritic ribosomes and nascent proteins at single-molecule resolution using DNA-PAINT and metabolic labeling. Both ribosomes and nascent proteins positively correlated with synapse density. Ribosomes were detected at ~85% of synapses with ~2 translational sites per synapse; ~50% of the nascent protein was detected near synapses. The amount of locally synthesized protein detected at a synapse correlated with its spontaneous Ca²⁺ activity. A multifold increase in synaptic nascent protein was evident following both local and global plasticity at respective scales, albeit with substantial heterogeneity between neighboring synapses.

Diffusive search and trajectories on tubular networks: a propagator approach

Several organelles in eukaryotic cells, including mitochondria and the endoplasmic reticulum, form interconnected tubule networks extending throughout the cell. These tubular networks host many biochemical pathways that rely on proteins diffusively searching through the network to encounter binding partners or localized target regions. Predicting the behavior of such pathways requires a quantitative understanding of how confinement to a reticulated structure modulates reaction kinetics. In this work, we develop both exact analytical methods to compute mean first passage times and efficient kinetic Monte Carlo algorithms to simulate trajectories of particles diffusing in a tubular network. Our approach leverages exact propagator functions for the distribution of transition times between network nodes and allows large simulation time steps determined by the network structure. The methodology is applied to both synthetic planar networks and organelle network structures, demonstrating key general features such as the heterogeneity of search times in different network regions and the functional advantage of broadly distributing target sites throughout the network. The proposed algorithms pave the way for future exploration of the interrelationship between tubular network structure and biomolecular reaction kinetics.

Paradoxical relationships between active transport and global protein distributions in neurons

Neural function depends on continual synthesis and targeted trafficking of intracellular components, including ion channel proteins. Many kinds of ion channels are trafficked over long distances to specific cellular compartments. This raises the question of whether cargo is directed with high specificity during transit or whether cargo is distributed widely and sequestered at specific sites. We addressed this question by experimentally measuring transport and expression densities of Kv4.2, a voltage-gated transient potassium channel that exhibits a specific dendritic expression that increases with distance from the soma and little or no functional expression in axons. In over 500 h of quantitative live imaging, we found substantially higher densities of actively transported Kv4.2 subunits in axons as opposed to dendrites. This paradoxical relationship between functional expression and traffic density supports a model—commonly known as the sushi belt model—in which trafficking specificity is relatively low and active sequestration occurs in compartments where cargo is expressed. In further support of this model, we find that kinetics of active transport differs qualitatively between axons and dendrites, with axons exhibiting strong superdiffusivity, whereas dendritic transport resembles a weakly directed random walk, promoting mixing and opportunity for sequestration. Finally, we use our data to constrain a compartmental reaction-diffusion model that can recapitulate the known Kv4.2 density profile. Together, our results show how nontrivial expression patterns can be maintained over long distances with a relatively simple trafficking mechanism and how the hallmarks of a global trafficking mechanism can be revealed in the kinetics and density of cargo.