The Alzheimer's disease risk gene BIN1 regulates activity-dependent gene expression in human-induced glutamatergic neurons.

Bridging Integrator 1 (BIN1) is the second most important Alzheimer's disease (AD) risk gene, but its physiological roles in neurons and its contribution to brain pathology remain largely elusive. In this work, we show that BIN1 plays a critical role in the regulation of calcium homeostasis, electrical activity, and gene expression of glutamatergic neurons. Using single-cell RNA-sequencing on cerebral organoids generated from isogenic BIN1 wild type (WT), heterozygous (HET) and homozygous knockout (KO) human-induced pluripotent stem cells (hiPSCs), we show that BIN1 is mainly expressed by oligodendrocytes and glutamatergic neurons, like in the human brain. Both BIN1 HET and KO cerebral organoids show specific transcriptional alterations, mainly associated with ion transport and synapses in glutamatergic neurons. We then demonstrate that BIN1 cell-autonomously regulates gene expression in glutamatergic neurons by using a novel protocol to generate pure culture of hiPSC-derived induced neurons (hiNs). Using this system, we also show that BIN1 plays a key role in the regulation of neuronal calcium transients and electrical activity via its interaction with the L-type voltage-gated calcium channel Cav1.2. BIN1 KO hiNs show reduced activity-dependent internalization and higher Cav1.2 expression compared to WT hiNs. Pharmacological blocking of this channel with clinically relevant doses of nifedipine, a calcium channel blocker, partly rescues electrical and gene expression alterations in BIN1 KO glutamatergic neurons. Further, we show that transcriptional alterations in BIN1 KO hiNs that affect biological processes related to calcium homeostasis are also present in glutamatergic neurons of the human brain at late stages of AD pathology. Together, these findings suggest that BIN1-dependent alterations in neuronal properties could contribute to AD pathophysiology and that treatment with low doses of clinically approved calcium blockers should be considered as an option to slow disease-onset and progression.

Integration of Microfluidic Devices with Microelectrode Arrays to Functionally Assay Amyloid-ß-Induced Synaptotoxicity.

Alzheimer's disease (AD) is a neurodegenerative disease and the most frequent cause of dementia. It is characterized by the accumulation in the brain of two pathological protein aggregates: amyloid-ß peptides (Aß) and abnormally phosphorylated tau. The progressive cognitive decline observed in patients strongly correlates with the synaptic loss. Many lines of evidence suggest that soluble forms of Aß accumulate into the brain where they cause synapse degeneration. Stopping their spreading and/or targeting the pathophysiological mechanisms leading to synaptic loss would logically be beneficial for the patients. However, we are still far from understanding these processes. Our objective was therefore to develop a versatile model to assay and study Aß-induced synaptotoxicity. We integrated a microfluidic device that physically isolates synapses from presynaptic and postsynaptic neurons with a microelectrode array. We seeded mouse primary cortical cells in the presynaptic and postsynaptic chambers. After functional synapses have formed in the synaptic chamber, we exposed them to concentrated conditioned media from cell lines overexpressing the wild-type or mutated amyloid precursor protein and thus secreting different levels of Aß. We recorded the neuronal activity before and after exposition to Aß and quantified Aß's effects on the connectivity between presynaptic and postsynaptic neurons. We observed that the application of Aß on the synapses for 48 h strongly decreased the interchamber connectivity without significantly affecting the neuronal activity in the presynaptic or postsynaptic chambers. Thus, through this model, we are able to functionally assay the impact of Aß peptides (or other molecules) on synaptic connectivity and to use the latter as a proxy to study Aß-induced synaptotoxicity. Moreover, since the presynaptic, postsynaptic, and synaptic chambers can be individually targeted, our assay provides a powerful tool to evaluate the involvement of candidate genes in synaptic vulnerability and/or test therapeutic strategies for AD.

High-Content Screening of Synaptic Density Modulators in Primary Neuronal Cultures.

The synapse, which represents the structural and functional basis of neuronal communication, is one of the first elements affected in several neurodegenerative diseases. To better understand the potential role of gene expression in synapse loss, we developed an original high-content screening (HCS) model capable of quantitatively assessing the impact of gene silencing on synaptic density. Our approach is based on a model of primary neuronal cultures (PNCs) from the neonatal rat hippocampus, whose mature synapses are visualized by the relative localization of the presynaptic protein Synaptophysin with the postsynaptic protein Homer1. The heterogeneity of PNCs and the small sizes of the synaptic structures pose technical challenges associated with the level of automation necessary for HCS studies. We overcame these technical challenges, automated the processes of image analysis and data analysis, and carried out tests under real-world conditions to demonstrate the robustness of the model developed. In this article, we describe the screening of a custom library of 198 shRNAs in PNCs in the 384-well plate format. © 2023 The Authors. Current Protocols published by Wiley Periodicals LLC. Basic Protocol 1: Culture of primary hippocampal rat neurons in 384-well plates Basic Protocol 2: Lentiviral shRNA transduction of primary neuronal culture in 384-well plates Basic Protocol 3: Immunostaining of the neuronal network and synaptic markers in 384-well plates Basic Protocol 4: Image acquisition using a high-throughput reader Basic Protocol 5: Image segmentation and analysis Basic Protocol 6: Synaptic density analysis.

Alzheimer's genetic risk factor FERMT2 (Kindlin-2) controls axonal growth and synaptic plasticity in an APP-dependent manner.

Although APP metabolism is being intensively investigated, a large fraction of its modulators is yet to be characterized. In this context, we combined two genome-wide high-content screenings to assess the functional impact of miRNAs and genes on APP metabolism and the signaling pathways involved. This approach highlighted the involvement of FERMT2 (or Kindlin-2), a genetic risk factor of Alzheimer's disease (AD), as a potential key modulator of axon guidance, a neuronal process that depends on the regulation of APP metabolism. We found that FERMT2 directly interacts with APP to modulate its metabolism, and that FERMT2 underexpression impacts axonal growth, synaptic connectivity, and long-term potentiation in an APP-dependent manner. Last, the rs7143400-T allele, which is associated with an increased AD risk and localized within the 3'UTR of FERMT2, induced a downregulation of FERMT2 expression through binding of miR-4504 among others. This miRNA is mainly expressed in neurons and significantly overexpressed in AD brains compared to controls. Altogether, our data provide strong evidence for a detrimental effect of FERMT2 underexpression in neurons and insight into how this may influence AD pathogenesis.

Pyk2 overexpression in postsynaptic neurons blocks amyloid ß1-42-induced synaptotoxicity in microfluidic co-cultures.

Recent meta-analyses of genome-wide association studies identified a number of genetic risk factors of Alzheimer's disease; however, little is known about the mechanisms by which they contribute to the pathological process. As synapse loss is observed at the earliest stage of Alzheimer's disease, deciphering the impact of Alzheimer's risk genes on synapse formation and maintenance is of great interest. In this article, we report a microfluidic co-culture device that physically isolates synapses from pre- and postsynaptic neurons and chronically exposes them to toxic amyloid ß peptides secreted by model cell lines overexpressing wild-type or mutated (V717I) amyloid precursor protein. Co-culture with cells overexpressing mutated amyloid precursor protein exposed the synapses of primary hippocampal neurons to amyloid ß1-42 molecules at nanomolar concentrations and induced a significant decrease in synaptic connectivity, as evidenced by distance-based assignment of postsynaptic puncta to presynaptic puncta. Treating the cells with antibodies that target different forms of amyloid ß suggested that low molecular weight oligomers are the likely culprit. As proof of concept, we demonstrate that overexpression of protein tyrosine kinase 2 beta-an Alzheimer's disease genetic risk factor involved in synaptic plasticity and shown to decrease in Alzheimer's disease brains at gene expression and protein levels-selectively in postsynaptic neurons is protective against amyloid ß1-42-induced synaptotoxicity. In summary, our lab-on-a-chip device provides a physiologically relevant model of Alzheimer's disease-related synaptotoxicity, optimal for assessing the impact of risk genes in pre- and postsynaptic compartments.

High-Content Screening for Protein-Protein Interaction Modulators Using Proximity Ligation Assay in Primary Neurons.

The proximity ligation assay (PLA) allows the detection and subcellular localization of protein-protein interactions with high specificity. We recently developed a high-content screening model based on primary hippocampal neurons cultured in 384-well plates and screened a library of ∼1100 compounds using a PLA between tau and bridging integrator 1, a genetic risk factor for Alzheimer's disease. We developed image-segmentation and spot-detection algorithms to delineate PLA signals in the axonal network, but not in cell bodies, from confocal images acquired via a high-throughput microscope. To compare data generated from different plates and through different experiments, we developed a computational routine to optimize the image analysis parameters for each plate and devised a range of quality-control measures to ultimately identify compounds that consistently increase or decrease our read-out. We provide the following protocols. © 2019 by John Wiley & Sons, Inc. Basic Protocol 1: Routine culture of rat postnatal hippocampal neurons in 384-well plates Basic Protocol 2: Compound incubation using the high-content screening platform Support Protocol 1: Preparation of intermediate plates for compound screening Support Protocol 2: Preparation of intermediate plates for hit validation (dose-response curves) Basic Protocol 3: Proximity ligation assay in 384-well plates Basic Protocol 4: Image acquisition and analysis Support Protocol 3: Optimization of analysis parameters Basic Protocol 5: Identification of hits Basic Protocol 6: Validation of hits based on dose-response curves.

BIN1 recovers tauopathy-induced long-term memory deficits in mice and interacts with Tau through Thr348 phosphorylation.

The bridging integrator 1 gene (BIN1) is a major genetic risk factor for Alzheimer's disease (AD). In this report, we investigated how BIN1-dependent pathophysiological processes might be associated with Tau. We first generated a cohort of control and transgenic mice either overexpressing human MAPT (TgMAPT) or both human MAPT and BIN1 (TgMAPT;TgBIN1), which we followed-up from 3 to 15 months. In TgMAPT;TgBIN1 mice short-term memory deficits appeared earlier than in TgMAPT mice; however-unlike TgMAPT mice-TgMAPT;TgBIN1 mice did not exhibit any long-term or spatial memory deficits for at least 15 months. After killing the cohort at 18 months, immunohistochemistry revealed that BIN1 overexpression prevents both Tau mislocalization and somatic inclusion in the hippocampus, where an increase in BIN1-Tau interaction was also observed. We then sought mechanisms controlling the BIN1-Tau interaction. We developed a high-content screening approach to characterize modulators of the BIN1-Tau interaction in an agnostic way (1,126 compounds targeting multiple pathways), and we identified-among others-an inhibitor of calcineurin, a Ser/Thr phosphatase. We determined that calcineurin dephosphorylates BIN1 on a cyclin-dependent kinase phosphorylation site at T348, promoting the open conformation of the neuronal BIN1 isoform. Phosphorylation of this site increases the availability of the BIN1 SH3 domain for Tau interaction, as demonstrated by nuclear magnetic resonance experiments and in primary neurons. Finally, we observed that although the levels of the neuronal BIN1 isoform were unchanged in AD brains, phospho-BIN1(T348):BIN1 ratio was increased, suggesting a compensatory mechanism. In conclusion, our data support the idea that BIN1 modulates the AD risk through an intricate regulation of its interaction with Tau. Alteration in BIN1 expression or activity may disrupt this regulatory balance with Tau and have direct effects on learning and memory.

The new genetic landscape of Alzheimer's disease: from amyloid cascade to genetically driven synaptic failure hypothesis?

A strong genetic predisposition (60-80% of attributable risk) is present in Alzheimer's disease (AD). In view of this major genetic component, identification of the genetic risk factors has been a major objective in the AD field with the ultimate aim to better understand the pathological processes. In this review, we present how the genetic risk factors are involved in APP metabolism, ß-amyloid peptide production, degradation, aggregation and toxicity, innate immunity, and Tau toxicity. In addition, on the basis of the new genetic landscape, resulting from the recent high-throughput genomic approaches and emerging neurobiological information, we propose an over-arching model in which the focal adhesion pathway and the related cell signalling are key elements in AD pathogenesis. The core of the focal adhesion pathway links the physiological functions of amyloid precursor protein and Tau with the pathophysiological processes they are involved in. This model includes several entry points, fitting with the different origins for the disease, and supports the notion that dysregulation of synaptic plasticity is a central node in AD. Notably, our interpretation of the latest data from genome wide association studies complements other hypotheses already developed in the AD field, i.e., amyloid cascade, cellular phase or propagation hypotheses. Genetically driven synaptic failure hypothesis will need to be further tested experimentally within the general AD framework.

Rapid Growth Cone Uptake and Dynein-Mediated Axonal Retrograde Transport of Negatively Charged Nanoparticles in Neurons Is Dependent on Size and Cell Type.

Nanoparticles (NPs) are now used in numerous technologies and serve as carriers for several new classes of therapeutics. Studies of the distribution of NPs in vivo demonstrate that they can be transported through biological barriers and are concentrated in specific tissues. Here, transport behavior, and final destination of polystyrene NPs are reported in primary mouse cortical neurons and SH-SY5Y cells, cultured in two-compartmental microfluidic devices. In both cell types, negative polystyrene NPs (PS(-)) smaller than 100 nm are taken up by the axons, undergo axonal retrograde transport, and accumulate in the somata. Examination of NP transport reveals different transport mechanisms depending on the cell type, particle charge, and particle internalization by the lysosomes. In cortical neurons, PS(-) inside lysosomes and 40 nm positive polystyrene NPs undergo slow axonal transport, whereas PS(-) outside lysosomes undergo fast axonal transport. Inhibition of dynein in cortical neurons decreases the transport velocity and cause a dose-dependent reduction in the number of accumulated PS(-), suggesting that the fast axonal transport is dynein mediated. These results show that the axonal retrograde transport of NPs depends on the endosomal pathway taken and establishes a means for screening nanoparticle-based therapeutics for diseases that involve neurons.

The Emerging Role of Mechanics in Synapse Formation and Plasticity.

The regulation of synaptic strength forms the basis of learning and memory, and is a key factor in understanding neuropathological processes that lead to cognitive decline and dementia. While the mechanical aspects of neuronal development, particularly during axon growth and guidance, have been extensively studied, relatively little is known about the mechanical aspects of synapse formation and plasticity. It is established that a filamentous actin network with complex spatiotemporal behavior controls the dendritic spine shape and size, which is thought to be crucial for activity-dependent synapse plasticity. Accordingly, a number of actin binding proteins have been identified as regulators of synapse plasticity. On the other hand, a number of cell adhesion molecules (CAMs) are found in synapses, some of which form transsynaptic bonds to align the presynaptic active zone (PAZ) with the postsynaptic density (PSD). Considering that these CAMs are key components of cellular mechanotransduction, two critical questions emerge: (i) are synapses mechanically regulated? and (ii) does disrupting the transsynaptic force balance lead to (or exacerbate) synaptic failure? In this mini review article, I will highlight the mechanical aspects of synaptic structures-focusing mainly on cytoskeletal dynamics and CAMs-and discuss potential mechanoregulation of synapses and its relevance to neurodegenerative diseases.

Bio-Nano-Magnetic Materials for Localized Mechanochemical Stimulation of Cell Growth and Death.

Magnetic nanoparticles are promising new tools for therapeutic applications, such as magnetic nanoparticle hyperthermia therapy and targeted drug delivery. Recent in vitro studies have demonstrated that a force application with magnetic tweezers can also affect cell fate, suggesting a therapeutic potential for magnetically modulated mechanical stimulation. The magnetic properties of nanoparticles that induce physical responses and the subtle responses that result from mechanically induced membrane damage and/or intracellular signaling are evaluated. Magnetic particles with various physical, geometric, and magnetic properties and specific functionalization can now be used to apply mechanical force to specific regions of cells, which permit the modulation of cellular behavior through the use of spatially and time controlled magnetic fields. On one hand, mechanochemical stimulation has been used to direct the outgrowth on neuronal growth cones, indicating a therapeutic potential for neural repair. On the other hand, it has been used to kill cancer cells that preferentially express specific receptors. Advances made in the synthesis and characterization of magnetic nanomaterials and a better understanding of cellular mechanotransduction mechanisms may support the translation of mechanochemical stimulation into the clinic as an emerging therapeutic approach.

Neuronal Cell Bodies Remotely Regulate Axonal Growth Response to Localized Netrin-1 Treatment via Second Messenger and DCC Dynamics.

Netrin-1 modulates axonal growth direction and speed. Its best characterized receptor, Deleted in Colorectal Cancer (DCC), is localized to growth cones, but also observed in the cell bodies. We hypothesized that cell bodies sense Netrin-1 and contribute to axon growth rate modulation, mediated by the second messenger system. We cultured mouse cortical neurons in microfluidic devices to isolate distal axon and cell body microenvironments. Compared to isolated axonal treatment, global Netrin-1 treatment decreased the axon elongation rate and affected the dynamics of total and membranous DCC, calcium, and cyclic nucleotides. Signals induced by locally applied Netrin-1 propagated in both anterograde and retrograde directions, demonstrated by the long-range increase in DCC and by the increased frequency of calcium transients in cell bodies, evoked by axonal Netrin-1. Blocking the calcium efflux from endoplasmic reticulum suppressed the membranous DCC response. Our findings support the notion that neurons sense Netrin-1 along their entire lengths in making axonal growth decisions.

A microfluidic dual gradient generator for conducting cell-based drug combination assays.

We present a microfluidic chip that generates linear concentration gradients of multiple solutes that are orthogonally-aligned to each other. The kinetics of gradient formation was characterized using a fluorescent tracer matching the molecular weight of small inhibitory drugs. Live-cell signalling and motility experiments were conducted to demonstrate the potential uses and advantages of the device. A431 epidermoid carcinoma cells, where EGF induces apoptosis in a concentration-dependent manner, were simultaneously exposed to gradients of MEK inhibitor and EGF receptor (EGFR) inhibitor. By monitoring live caspase activation in the entire chip, we were able to quickly assess the combinatorial interaction between MEK and EGFR pathways, which otherwise would require costly and time consuming titration experiments. We also characterized the motility and morphology of MDA-MB-231 breast cancer cells exposed to orthogonal gradients of EGF and EGFR inhibitor. The microfluidic chip not only permitted the quantitative analysis of a population of cells exposed to drug combinations, but also enabled the morphological characterization of individual cells. In summary, our microfluidic device, capable of establishing concentration gradients of multiple compounds over a group of cells, facilitates and accelerates in vitro cell biology experiments, such as those required for cell-based drug combination assays.

Microtechnologies for studying the role of mechanics in axon growth and guidance.

The guidance of axons to their proper targets is not only a crucial event in neurodevelopment, but also a potential therapeutic target for neural repair. Axon guidance is mediated by various chemo- and haptotactic cues, as well as the mechanical interactions between the cytoskeleton and the extracellular matrix (ECM). Axonal growth cones, dynamic ends of growing axons, convert external stimuli to biochemical signals, which, in turn, are translated into behavior, e.g., turning or retraction, via cytoskeleton-matrix linkages. Despite the inherent mechanical nature of the problem, the role of mechanics in axon guidance is poorly understood. Recent years has witnessed the application of a range of microtechnologies in neurobiology, from microfluidic circuits to single molecule force spectroscopy. In this mini-review, we describe microtechnologies geared towards dissecting the mechanical aspects of axon guidance, divided into three categories: controlling the growth cone microenvironment, stimulating growth cones with externally applied forces, and measuring forces exerted by the growth cones. A particular emphasis is given to those studies that combine multiple techniques, as dictated by the complexity of the problem.

Neuron Subpopulations with Different Elongation Rates and DCC Dynamics Exhibit Distinct Responses to Isolated Netrin-1 Treatment.

Correct wiring of the nervous system requires guidance cues, diffusible or substrate-bound proteins that steer elongating axons to their target tissues. Netrin-1, the best characterized member of the Netrins family of guidance molecules, is known to induce axon turning and modulate axon elongation rate; however, the factors regulating the axonal response to Netrin-1 are not fully understood. Using microfluidics, we treated fluidically isolated axons of mouse primary cortical neurons with Netrin-1 and characterized axon elongation rates, as well as the membrane localization of deleted in colorectal cancer (DCC), a well-established receptor of Netrin-1. The capacity to stimulate and observe a large number of individual axons allowed us to conduct distribution analyses, through which we identified two distinct neuron subpopulations based on different elongation behavior and different DCC membrane dynamics. Netrin-1 reduced the elongation rates in both subpopulations, where the effect was more pronounced in the slow growing subpopulation. Both the source of Ca(2+) influx and the basal cytosolic Ca(2+) levels regulated the effect of Netrin-1, for example, Ca(2+) efflux from the endoplasmic reticulum due to the activation of Ryanodine channels blocked Netrin-1-induced axon slowdown. Netrin-1 treatment resulted in a rapid membrane insertion of DCC, followed by a gradual internalization. DCC membrane dynamics were different in the central regions of the growth cones compared to filopodia and axon shafts, highlighting the temporal and spatial heterogeneity in the signaling events downstream of Netrin-1. Cumulatively, these results demonstrate the power of microfluidic compartmentalization and distribution analysis in describing the complex axonal Netrin-1 response.

Mechanochemical stimulation of MCF7 cells with rod-shaped Fe-Au Janus particles induces cell death through paradoxical hyperactivation of ERK.

Multifunctional nanoparticles that actively target-specific tissues are studied for cancer diagnosis and treatment. Magnetically and optically active particles are of particular interest because they enable multiple imaging modalities and physically modulated therapies, such as magnetic hyperthermia. Fe-Au nanorods are synthesized that have a long iron segment, coated with polyethylene glycol, and a short gold tip functionalized with heregulin (HRG), a known ligand of ErbB family of receptors. HRG-nanorods preferentially target MCF7 cells relative to MDA-MB-231 cells, as demonstrated in a novel microfluidics device. Targeting rates of these classical breast cancer cells correlate with their differential expression of ErbB2/3 receptors. HRG-nanorod binding stimulates the extracellular signal-regulated kinase 1/2 (ERK) phosphorylation in MCF7 cells. The increase in ERK phosphorylation is linked to "active zones," dynamic regions in the cell periphery, which exhibit higher rates of particle binding than the rest of the cell. Periodically stretching cells using magnetic tweezers further activates ERK, which leads to cell death in cells co-treated with B-Raf inhibitors, through ERK hyperactivation. Although to a lesser extent, cell death is also achieved through magnetic hyperthermia. These results demonstrate nanoscale targeting and localized mechanochemical treatment of specific cancer cell lines based on their receptor expression using multifunctional nanoparticles.

Low piconewton towing of CNS axons against diffusing and surface-bound repellents requires the inhibition of motor protein-associated pathways.

Growth cones, dynamic structures at axon tips, integrate chemical and physical stimuli and translate them into coordinated axon behaviour, e.g., elongation or turning. External force application to growth cones directs and enhances axon elongation in vitro; however, direct mechanical stimulation is rarely combined with chemotactic stimulation. We describe a microfluidic device that exposes isolated cortical axons to gradients of diffusing and substrate-bound molecules, and permits the simultaneous application of piconewton (pN) forces to multiple individual growth cones via magnetic tweezers. Axons treated with Y-27632, a RhoA kinase inhibitor, were successfully towed against Semaphorin 3A gradients, which repel untreated axons, with less than 12 pN acting on a small number of neural cell adhesion molecules. Treatment with Y-27632 or monastrol, a kinesin-5 inhibitor, promoted axon towing on substrates coated with chondroitin sulfate proteoglycans, potent axon repellents. Thus, modulating key molecular pathways that regulate contractile stress generation in axons counteracts the effects of repellent molecules and promotes tension-induced growth. The demonstration of parallel towing of axons towards inhibitory environments with minute forces suggests that mechanochemical stimulation may be a promising therapeutic approach for the repair of the damaged central nervous system, where regenerating axons face repellent factors over-expressed in the glial scar.

Advances in magnetic tweezers for single molecule and cell biophysics.

Magnetic tweezers (MTW) enable highly accurate forces to be transduced to molecules to study mechanotransduction at the molecular or cellular level. We review recent MTW studies in single molecule and cell biophysics that demonstrate the flexibility of this technique. We also discuss technical advances in the method on several fronts, i.e., from novel approaches for the measurement of torque to multiplexed biophysical assays. Finally, we describe multi-component nanorods with enhanced optical and magnetic properties and discuss their potential as future MTW probes.

Flow enhanced non-linear magnetophoretic separation of beads based on magnetic susceptibility.

Magnetic separation provides a rapid and efficient means of isolating biomaterials from complex mixtures based on their adsorption on superparamagnetic (SPM) beads. Flow enhanced non-linear magnetophoresis (FNLM) is a high-resolution mode of separation in which hydrodynamic and magnetic fields are controlled with micron resolution to isolate SPM beads with specific physical properties. In this article we demonstrate that a change in the critical frequency of FNLM can be used to identify beads with magnetic susceptibilities between 0.01 and 1.0 with a sensitivity of 0.01 Hz(-1). We derived an analytical expression for the critical frequency that explicitly incorporates the magnetic and non-magnetic composition of a complex to be separated. This expression was then applied to two cases involving the detection and separation of biological targets. This study defines the operating principles of FNLM and highlights the potential for using this technique for multiplexing diagnostic assays and isolating rare cell types.