Search bioRxiv⌕ Search

Biology subjects

Spill, F.

Publications and source records attributed to Spill, F..

17 recordsLinked to original sources

Mathematical Modelling of the Mitochondrial Dicarboxylate Carrier (SlC25A10)

1The mitochondrial dicarboxylate carrier SLC25A10 mediates reversible exchange among succinate, malate, and phosphate, contributing to mitochondrial metabolic regulation. Structural studies establish a ping-pong mechanism, but most mathematical models still assume sequential binding, lacking mechanistic justification and overlooking the alternation of a single binding site. Here, we present the first mechanistically derived and thermodynamically consistent model of SLC25A10 based on a ping-pong framework. The model incorporates competitive binding of succinate, malate, and phosphate, heteroexchange, reversibility, and electroneutrality, and is calibrated using experimental datasets from intact mitochondria and reconstituted proteoliposomes. To estimate kinetic parameters and quantify their uncertainty, we employed Bayesian inference, enabling statistically rigorous calibration to uptake and competition assays. The model introduces new terms that quantify which substrate and from which side of the membrane is most likely to start the transport cycle. Beyond reproducing experimentally observed exchange kinetics, the model resolves non-equilibrium transport dynamics that are difficult to access directly in classical uptake assays. In particular, the simulations reveal a two-phase response in which an initial phosphate-driven high-flux uptake regime for malate and succinate is followed by a slower redistribution phase in which the two dicarboxylates continue to readjust primarily against each other. The model also predicts that mitochondrial morphology modulates early transport behaviour, with matrix swelling increasing and matrix condensation decreasing the initial SLC25A10 flux magnitude. More broadly, the framework provides a quantitative basis for studying how substrate competition, thermodynamic driving forces, and compartment geometry shape SLC25A10-mediated exchange, and it offers a transferable modelling strategy for other carriers in the SLC25 family.

systems biology↗

The role of contact guidance and ECM remodelling in cancer invasion: a computational study

The extracellular matrix (ECM) is a complex network of fibrous proteins and other macromolecules that provides both structural support and directional cues that regulate cancer cell invasion and tumour progression. Its fibre organisation plays a critical role in directing migration through contact guidance, while cancer cells simultaneously remodel the matrix through biochemical and mechanical interactions. However, the interplay between ECM architecture, chemical gradients, and matrix remodelling remains poorly understood. Mathematical modelling offers a powerful approach to explore how ECM architecture regulates this process. We present a hybrid computational model, implemented in PhysiCell, that integrates a discrete agent-based cell model with a continuous representation of the chemical microenvironment and ECM microstructure. In an advance over previous efforts, we adapt several mechanisms to a fibre-focused representation of the ECM, including "cell-front" ECM sensing reflecting protrusion-driven engagement of the matrix, contact-guided cell movement via ECM fibre orientation integrated with chemotaxis bias, and proliferation regulated by oxygen and mechanical pressure. In addition, we introduce a new mechanical mechanism for ECM density displacement alongside degradation to simulate how cells redistribute matrix fibres. Simulations reveal how the interplay between initial fibre alignment, anisotropy (fibre-fibre alignment correlation), and fibre reorientation capacity affects invasion, and how competing mechanical and chemical cues influence the invasive potential of tumour cells. Furthermore, our results demonstrate that the balance between degradation and displacement strongly affects invasion dynamics, with high displacement promoting the formation of dense ECM rims around tumour spheroids, whereas increased degradation enables greater invasive spread. This work provides mechanistic insights into bidirectional interactions between cancer cells and the surrounding ECM, highlighting how structural remodelling of the ECM influences the invasive potential of cancer cells. Author summaryCancer cells invade surrounding tissue by interacting with the extracellular matrix (ECM), a fibrous network of proteins that provides both mechanical support and directional cues for migration. Experiments have shown that the orientation of ECM fibres can either promote or hinder invasion, but it remains difficult to disentangle the underlying mechanisms because cells both respond to and actively remodel the matrix. To address this challenge, we developed a computational model that simulates how cancer cells migrate through and reshape the ECM. The model combines individual cell behaviour with a representation of ECM structure, including fibre orientation, anisotropy (fibre-fibre alignment correlation), and density. Our simulations show that invasion depends on the initial fibre orientation and on chemical cues. We also introduce a mechanism that allows cells to mechanically displace the matrix, revealing how the balance between matrix degradation and physical pushing can generate either compact tumour growth or sparse invasion. These results help explain how physical interactions between cells and their environment shape tumour invasion. More broadly, the framework provides a tool to explore how mechanical and chemical signals together regulate collective cell migration in cancer and other biological systems.

systems biology↗

Curvature-dependent morphological reorganization of the endoplasmic reticulum determines the mode of epithelial migration

From single-cell extrusion to centimeter-sized wounds, epithelial gaps of various sizes and geometries appear in all organisms. For gap closure, epithelial cells invoke two orthogonal modes: lamellipodial crawling at the convex edge and purse-string-like movements at the concave edge. The mechanisms underlying these differential responses to geometric cues remain elusive. Here we perform an intracellular cartography to reveal that in both micropatterned and naturally arising gaps, the endoplasmic reticulum (ER) undergoes edge curvature-dependent morphological reorganizations with convex and concave edges promoting ER tubules and sheets, respectively. This reorganization depends on cytoskeleton-generated protrusive and contractile forces. Additionally, theoretical modeling predicts that the curvature-specific ER morphology leads to a lower strain energy state. ER tubules at the convex edge favor perpendicularly oriented focal adhesions, supporting lamellipodial crawling while ER sheets at the concave edge favor parallelly oriented focal adhesions, supporting purse-string-like movements. Altogether, ER emerges as a central player in cellular mechanotransduction, which orchestrates two orthogonal modes of cell migration by integrating signals from cytoskeletal networks.

cell biology↗

A hybrid computational model of cancer spheroid growth with ribose-induced collagen stiffening

Metastasis, the leading cause of death in cancer patients, arises when cancer cells disseminate from a primary solid tumour to distant organs. Growth and invasion of the solid tumour often involve collective cell migration, which is profoundly influenced by cell-cell interactions and the extracellular matrix (ECM). The ECMs biochemical composition and mechanical properties, such as stiffness, regulate cancer cell behaviour and migration dynamics. Mathematical modelling serves as a pivotal tool for studying and predicting these complex dynamics, with hybrid discrete-continuous models offering a powerful approach by combining agent-based representations of cells with continuum descriptions of the surrounding microenvironment. In this study, we investigate the impact of ECM stiffness, modulated via ribose-induced collagen cross-linking, on cancer spheroid growth and invasion. We employed a hybrid discrete-continuous model implemented in PhysiCell to simulate spheroid dynamics, successfully replicating three-dimensional in vitro experiments. The model incorporates detailed representations of cell-cell and cell-ECM interactions, ECM remodelling, and cell proliferation. Our simulations align with experimental observations of two breast cancer cell lines, non-invasive MCF7 and invasive HCC1954, under varying ECM stiffness conditions. The results demonstrate that increased ECM stiffness due to ribose-induced cross-linking inhibits spheroid invasion in invasive cells, whereas non-invasive cells remain largely unaffected. Furthermore, our simulations show that higher ECM degradation by the cells not only enables spheroid growth and invasion but also facilitates the formation of multicellular protrusions. Conversely, increasing the maximum speed that cells can reach due to cell-ECM interactions enhances spheroid growth while promoting single-cell invasion. This hybrid modelling approach enhances our understanding of the interplay between cancer cell migration, proliferation, and ECM mechanical properties, paving the way for future studies incorporating additional ECM characteristics and microenvironmental conditions.

systems biology↗

Pyruvate from bone marrow mesenchymal stem cells supports myeloma redox homeostasis and anabolism

Multiple myeloma is an incurable cancer of plasma cells that depends on the bone marrow for its survival. Despite its prevalence, the molecular mechanisms underlying this malignancy remain poorly understood. In this study, we aim to bridge this knowledge gap by elucidating the metabolic interplay between myeloma cells and bone marrow mesenchymal stem cells (BMMSCs). BMMSCs are crucial in supporting myeloma cell metabolism, contributing to their proliferation, survival, and resistance to chemotherapy. Through a combination of mathematical modelling and experimental co-cultures, we demonstrate that pyruvate - the end product of glycolysis - plays a key role in myeloma cell metabolism. Our findings reveal that myeloma cells predominantly rely on the uptake of pyruvate produced by neighbouring BMM-SCs via the plasma membrane proton-linked monocarboxylate transporters MCT-1 and MCT-2 encoded by the Slc16a1 and a2 genes, respectively. Furthermore, we show that pharmacological inhibition of the MCT-1/2, with AZD3965, triggers a cascade of compensatory metabolic responses, disrupting redox balance and significantly reducing the proliferation capacity of co-cultured myeloma cells.

cancer biology↗

A Mathematical Exploration of SDH-b Loss in Chromaffin Cells

The succinate dehydrogenase (SDH) is a four-subunit enzyme complex (SDH-a, SDH-b, SDH-c, and SDH-d) central to cell carbon metabolism. The SDH bridges the tricarboxylic acid cycle to the electron transport chain. A pathological loss of the SDH-b subunit leads to a cell-wide signalling cascade that shifts the cells metabolism into a pseudo-hypoxic state akin to the so-called Warburg effect (or aerobic glycolysis). This trait is a hallmark of phaeochromocytomas, a rare tumour arising from chromaffin cells; a type of cell that lies in the medulla of the adrenal gland. In this study, we leverage the insights from a mathematical model constructed to underpin the metabolic implications of SDH-b dysfunction in phaeochromocytomas. We specifically investigate why chromaffin cells seemingly have the ability to maintain electron transport chains (ETC) Complex I function when confronted with the loss of the SDH-b subunit while other cells do not. Our simulations indicate that retention of Complex I is associated with cofactor oxidation, which enables cells to manage mitochondrial swelling and limit the reversal of the adenosine triphosphate (ATP) synthase, supporting cell fitness, without undergoing lysis. These results support previous hypotheses that point at mitochondrial proton leaks as a critical factor of future research. Moreover, the model asserts that control of the proton gradient across the mitochondrial inner membrane is rate-limiting upon fitness management of SDH-b deficient cells.

bioengineering↗

P53 Orchestrates Cancer Metabolism: Unveiling Strategies to Reverse the Warburg Effect

Cancer cells exhibit significant alterations in their metabolism, characterised by a reduction in oxidative phosphorylation (OXPHOS) and an increased reliance on glycolysis, even in the presence of oxygen. This metabolic shift, known as the Warburg effect, is pivotal in fuelling cancers uncontrolled growth, invasion, and therapeutic resistance. While dysregulation of many genes contributes to this metabolic shift, the tumour suppressor gene p53 emerges as a master player. Yet, the molecular mechanisms remain elusive. This study introduces a comprehensive mathematical model, integrating essential p53 targets, offering insights into how p53 orchestrates its targets to redirect cancer metabolism towards an OXPHOS-dominant state. Simulation outcomes align closely with experimental data comparing glucose metabolism in colon cancer cells with wild-type and mutated p53. Additionally, our findings reveal the dynamic capability of elevated p53 activation to fully reverse the Warburg effect, highlighting the significance of its activity levels not just in triggering apoptosis (programmed cell death) post-chemotherapy but also in modifying the metabolic pathways implicated in treatment resistance. In scenarios of p53 mutations, our analysis suggests targeting glycolysis-instigating signalling pathways as an alternative strategy, whereas targeting solely synthesis of cytochrome c oxidase 2 (SCO2) does support mitochondrial respiration but may not effectively suppress the glycolysis pathway, potentially boosting the energy production and cancer cell viability.

cancer biology↗

Discretised flux balance analysis for reaction-diffusion simulation of single-cell metabolism

Metabolites have to diffuse within the sub-cellular compartments they occupy to specific locations where enzymes are, so reactions could occur. Conventional flux balance analysis (FBA), a method based on linear programming that is commonly used to model metabolism, implicitly assumes that all enzymatic reactions are not diffusion-limited though that may not always be the case. In this work, we have developed a spatial method that implements FBA on a grid-based system, to enable the exploration of diffusion effects on metabolism. Specifically, the method discretises a living cell into a two-dimensional grid, represents the metabolic reactions in each grid element as well as the diffusion of metabolites to and from neighbouring elements, and simulates the system as a single linear programming problem. We varied the number of rows and columns in the grid to simulate different cell shapes, and the method was able to capture diffusion effects at different shapes. We then used the method to simulate heterogeneous enzyme distribution, which suggested a theoretical effect on variability at the population level. We propose the use of this method, and its future extensions, to explore how spatiotemporal organisation of sub-cellular compartments and the molecules within could affect cell behaviour.

cell biology↗

A mechanical modelling framework to study endothelial permeability

The inner lining of blood vessels, the endothelium, is made up of endothelial cells. Vascular endothelial (VE)-cadherin protein forms a bond with VE-cadherin from neighbouring cells (homophilic bond) to determine the size of gaps between the cells and thereby regulate the size of particles that can cross the endothelium. Chemical cues such as Thrombin, along with mechanical properties of the cell and extracellular matrix (ECM) are known to affect the permeability of endothelial cells. Abnormal permeability is found in patients suffering from diseases including cardiovascular diseases, cancer, and COVID-19. Even though some of the regulatory mechanisms affecting endothelial permeability are well studied, details of how several mechanical and chemical stimuli acting simultaneously affect endothelial permeability are not yet understood. In this article, we present a continuum-level mechanical modelling framework to study the highly dynamic nature of the VE-cadherin bonds. Taking inspiration from the catch-slip behaviour that VE-cadherin complexes are known to exhibit, we model VE-cadherin homophilic bond as cohesive contact with damage following a traction-separation law. We explicitly model the actin-cytoskeleton, and substrate to study their role in permeability. Our studies show that mechano-chemical coupling is necessary to simulate the influence of the mechanical properties of the substrate on permeability. Simulations show that shear between cells is responsible for the variation in permeability between bi-cellular and tri-cellular junctions, explaining the phenotypic differences observed in experiments. An increase in the magnitude of traction force that endothelial cells experience results in increased permeability, and it is found that the effect is higher on stiffer ECM. Finally, we show that the cylindrical monolayer exhibits higher permeability than the planar monolayer under unconstrained cases. Thus, we present a contact mechanics-based mechano-chemical model to investigate the variation in permeability of endothelial monolayer due to multiple loads acting simultaneously.

cell biology↗

Interplay of p53 and XIAP protein dynamics orchestrates cell fate in response to chemotherapy

Chemotherapeutic drugs are used to treat almost all types of cancer, but the intended response, i.e., elimination, is often incomplete, with a subset of cancer cells resisting treatment. Two critical factors play a role in chemoresistance: the p53 tumour suppressor gene and the X-linked inhibitor of apoptosis (XIAP). These proteins have been shown to act synergistically to elicit cellular responses upon DNA damage induced by chemotherapy, yet, the mechanism is poorly understood. This study introduces a mathematical model characterising the apoptosis pathway activation by p53 before and after mitochondrial outer membrane permeabilisation upon treatment with the chemotherapy Doxorubicin (Dox). "In-silico" simulations show that the p53 dynamics change dose-dependently. Under medium to high doses of Dox, p53 concentration ultimately stabilises to a high level regardless of XIAP concentrations. However, caspase-3 activation may be triggered or not depending on the XIAP induction rate, ultimately determining whether the cell will perish or resist. Consequently, the model predicts that failure to activate apoptosis in some cancer cells expressing wild-type p53 might be due to heterogeneity between cells in upregulating the XIAP protein, rather than due to the p53 protein concentration. Our model suggests that the interplay of the p53 dynamics and the XIAP induction rate is critical to determine the cancer cells therapeutic response.

cancer biology↗

Mathematical reconstruction of the metabolic network in an in-vitro multiple myeloma model.

It is increasingly apparent that cancer cells, in addition to remodelling their metabolism to survive and proliferate, adapt and manipulate the metabolism of other cells. This property may be a telling sign that pre-clinical tumour metabolism studies that exclusively utilise in-vitro mono-culture models could prove to be limited for uncovering novel metabolic targets that can translate into clinical therapies. Although this is increasingly recognised, and work addressing this is becoming routinary in a rapidly emerging field, much remains unknown. This study employs an interdisciplinary approach that leverages the predictive power of mathematical modelling to enrich experimental findings. We develop a functional multicellular in-silico model that facilitates the qualitative and quantitative analysis of the metabolic network spawned by an in-vitro co-culture model of bone marrow mesenchymal stem- and myeloma cell lines. To procure this model, we devised a bespoke human genome constraint-based reconstruction workflow that combines aspects from the legacy mCADRE & Metabotools algorithms, the novel redHuman algorithm, along with 13C-metabolic flux analysis. Our workflow transforms the latest human metabolic network matrix (Recon3D) into two cell-specific models coupled with a metabolic network spanning a shared growth medium. When cross-validating our in-silico model against the in-vitro model, we found that the in-silico model successfully reproduces vital metabolic behaviours of its in-vitro counterpart; results include cell growth predictions, respiration rates, as well as support for observations which suggest cross-shuttling of redox-active metabolites between cells. Together, our methodology and its results provide yet another step toward the relevance of studies of this type in the field.

bioengineering↗

Effects of altered cellular ultrastructure on energy metabolism in diabetic cardiomyopathy - an in-silico study

Diabetic cardiomyopathy is a leading cause of heart failure in diabetes. At the cellular level, diabetic cardiomyopathy leads to altered mitochondrial energy metabolism and cardiomyocyte ultrastructure. We combined electron microscopy and computational modelling to understand the impact of diabetes induced ultrastructural changes on cardiac bioenergetics. We collected transverse micrographs of multiple control and type I diabetic rat cardiomyocytes using electron microscopy. Micrographs were converted to finite element meshes, and bioenergetics was simulated over them using a biophysical model. The simulations also incorporated depressed mitochondrial capacity for oxidative phosphorylation and creatine kinase reactions to simulate diabetes induced mitochondrial dysfunction. Analysis of micrographs revealed a 14% decline in mitochondrial area fraction in diabetic cardiomyocytes, and an irregular arrangement of mitochondria and myofibrils. Simulations predicted that this irregular arrangement, coupled with depressed activity of mitochondrial creatine kinase enzymes, leads to large spatial variation in ADP/ATP profile of diabetic cardiomyocytes. However, when spatially averaged, myofibrillar ADP/ATP ratios of a cardiomyocyte do not change with diabetes. Instead, average concentration of inorganic phosphate rises by 40% due to lower mitochondrial area fraction and dysfunction in oxidative phosphorylation. These simulations indicate that a disorganized cellular ultrastructure negatively impacts metabolite transport in diabetic cardiomyopathy.

cell biology↗

Modeling the three-way feedback between cellular contractility, actin polymerization, and adhesion turnover resolves the contradictory effects of RhoA and Rac1 on endothelial junction dynamics

The formation and recovery of gaps in the vascular endothelium governs a wide range of physiological and pathological phenomena, from angiogenesis to atherosclerosis and tumor cell extravasation. However, the interplay between the mechanical and signaling processes that drive dynamic behavior in vascular endothelial cells is not well understood. In this study, we propose a chemo-mechanical model to investigate the maintenance of endothelial junctions as dependent on the crosstalk between actomyosin contractility, VE-cadherin bond turnover, and actin polymerization, which mediate the forces exerted on the cell-cell interface. Our theoretical model reveals that active cell tension can stabilize cadherin bonds within an adhesion, but excessive RhoA signaling can drive bond dissociation and junction failure. While Rac1-mediated actin polymerization aids gap closure, high levels of Rac1 may also facilitate junction weakening. Combining the modeling framework with novel experiments, we identify how dynamic rupture and heal cycles emerge and, further, describe why gaps tend to localize at multi-cell contacts. Beyond, our analysis also indicates that a critical balance between RhoA and Rac1 expression is required to maintain junction stability and limit endothelial dysfunction. The model predicts how pharmacological modulation of actin polymerization and cell contractility impacts junction stability, with predictions subsequently validated experimentally. Our proposed framework can help guide the development of therapeutics that target the Rho family of GTPases and downstream active mechanical processes.

biophysics↗

CASTLE: Cell Adhesion with Supervised Training and Learning Environment

Different types of microscopy are used to uncover signatures of cell adhesion and mechanics. Automating the identification and analysis often involve sacrificial routines of cell manipulation such as in vitro staining. Phase-contrast microscopy (PCM) is rarely used in automation due to the difficulties with poor quality images. However, it is the least intrusive method to provide insights into the dynamics of cells, where other types of microscopy are too destructive to monitor. In this study, we propose an efficient workflow to automate cell counting and morphology in PCM images. We introduce Cell Adhesion with Supervised Training and Learning Environment (CASTLE), available as a series of additional plugins to ImageJ. CASTLE combines effective techniques for phase-contrast image processing with statistical analysis and machine learning algorithms to interpret the results. The proposed workflow was validated by comparing the results to a manual count and manual segmentation of cells in images investigating different adherent cell types, including monocytes, neutrophils and platelets. In addition, the effect of different molecules on cell adhesion was characterised using CASTLE. For example, we demonstate that Galectin-9 leads to differences in adhesion of leukocytes. CASTLE also provides information using machine learning techniques, namely principal component analysis and k-means clustering, to distinguish morphology currently inaccessible with manual methods. All scripts and documentation is open-source and available at the corresponding GitLab project.

immunology↗

Integrated in silico and 3D in vitro model of macrophage migration in response to physical and chemical factors in the tumor microenvironment

Macrophages are abundant in the tumor microenvironment (TME), serving as accomplices to cancer cells for their invasion. Studies have explored the biochemical mechanisms that drive pro-tumor macrophage functions, however the role of TME interstitial flow (IF) is often disregarded. Therefore, we developed a three-dimensional microfluidic-based model with tumor cells and macrophages to study how IF affects macrophage migration and its potential contribution to cancer invasion. The presence of either tumor cells or IF individually increased macrophage migration directedness and speed. Interestingly, there was no additive effect on macrophage migration directedness and speed under the simultaneous presence of tumor cells and IF. Further, we present an in silico model that couples chemokine-mediated signaling with mechanosensing networks to explain our in vitro observations. The model proposes IL-8, CCL2 and {beta}-integrin as key pathways that commonly regulate various Rho GTPases. In agreement, in vitro macrophage migration remained elevated when exposed to a saturating concentration of recombinant IL-8 or CCL2, or to the co-addition of a sub-optimal concentration of both cytokines. Moreover, antibody blockade against IL-8 and/or CCL2 inhibited migration that could be restored by IF, indicating cytokine-independent mechanisms of migration induction. Importantly, we demonstrate the utility of an integrated in silico and 3D in vitro approach to aid the design of tumor-associated macrophage-based immunotherapeutic strategies.

systems biology↗

The impact of tumor stromal architecture on therapy response and clinical progression

-- Advances in molecular oncology research culminated in the development of targeted therapies that act on defined molecular targets either on tumor cells directly (such as inhibitors of oncogenic kinases), or indirectly by targeting the tumor microenvironment (such as anti-angiogenesis drugs). These therapies can induce strong clinical responses, when properly matched to patients. Unfortunately, most targeted therapies ultimately fail as tumors evolve resistance. Tumors consist not only of neoplastic cells, but also of stroma, whereby \"stroma\" is the umbrella term for non-tumor cells and extracellular matrix (ECM) within the tumor microenvironment, possibly excluding immune cells1. We know that tumor stroma is an important player in the development of resistance. We also know that stromal architecture is spatially complex, differs from patient to patient and changes with therapy. However, to this date we do not understand the link between spatial and temporal changes in stromal architecture and response of tumors to therapy, in space and time. In this project we sought to address this gap of knowledge using a combination of mathematical and statistical modeling, experimental in vivo studies, and analysis of clinical samples in therapies that target tumor cells directly (in lung and breast cancers) and indirectly (in kidney cancer). This knowledge will inform therapy choices and offer new angles for therapeutic interventions. Our main question is: how does spatial architecture of stroma impact the emergence or evolution of resistance to targeted therapies, and how can we use this knowledge clinically?

cancer biology↗

Balance of Mechanical Forces Drives Endothelial Gap Formation and May Facilitate Cancer and Immune-Cell Extravasation

The formation of gaps in the endothelium is a crucial process underlying both cancer and immune cell extravasation, contributing to the functioning of the immune system during infection, the unfavorable development of chronic inflammation and tumor metastasis. Here, we present a stochastic-mechanical multiscale model of an endothelial cell monolayer and show that the dynamic nature of the endothelium leads to spontaneous gap formation, even without intervention from the transmigrating cells. These gaps preferentially appear at the vertices between three endothelial cells, as opposed to the border between two cells. We quantify the frequency and lifetime of these gaps, and validate our predictions experimentally. Interestingly, we find experimentally that cancer cells also preferentially extravasate at vertices, even when they first arrest on borders. This suggests that extravasating cells, rather than initially signaling to the endothelium, might exploit the autonomously forming gaps in the endothelium to initiate transmigration.

bioengineering↗