Physical aspects of epithelial cell-cell interactions: hidden system complexities
The maintenance of homeostasis and the retention of ordered epithelial cell self-organization are essential for morphogenesis, wound healing, and the spread of cancer across the epithelium. However, cell-cell interactions in an overcrowded environment introduce a diversity of complications. Such interactions arise from an interplay between the cell compressive and shear stress components that accompany increased cell packing density. They can lead to various kinds of cell rearrangement such as: the epithelial-to-mesenchymal cell state transition; live cell extrusion; and cell jamming. All of these scenarios of cell rearrangement under mechanical stress relate to changes in the strengths of the cell-cell and cell-matrix adhesion contacts. The objective of this review study is twofold: first, to provide a comprehensive summary of the biological and physical factors influencing the effects of cell mechanical stress on cell-cell interactions, and the consequences of these interactions for the status of cell-cell and cell-matrix adhesion contacts; and secondly, to offer a bio-physical/mathematical analysis of the aforementioned biological aspects. By presenting these two approaches in conjunction, we seek to highlight the intricate nature of biological systems, which manifests in the form of complex bio-physical/mathematical equations. Furthermore, the juxtaposition of these apparently disparate approaches underscores the importance of conducting experiments to determine the multitude of parameters that contribute to the development of these intricate bio-physical/mathematical models.
Exploring characteristic features for effective HCN1 channel inhibition using integrated analytical approaches: 3D QSAR, molecular docking, homology modelling, ADME and molecular dynamics
Neuropathic pain (NP) is characterized by hyperalgesia, allodynia, and spontaneous pain. Hyperpolarization-activated cyclic nucleotide-gated (HCN) channel involved in neuronal hyperexcitability, has emerged as an important target for the drug development of NP. HCN channels exist in four different isoforms, where HCN1 is majorly expressed in dorsal root ganglion having an imperative role in NP pathophysiology. A specific HCN1 channel inhibitor will hold the better potential to treat NP without disturbing the physiological roles of other HCN isoforms. The main objective is to identify and analyze the chemical properties of scaffolds with higher HCN1 channel specificity. The 3D-QSAR studies highlight the hydrophobic & hydrogen bond donor groups enhance specificity towards the HCN1 channel. Further, the molecular interaction of the scaffolds with the HCN1 pore was studied by generating an open-pore model of the HCN1 channel using homology modelling and then docking the molecules with it. In addition, the important residues involved in the interaction between HCN1 pore and scaffolds were also identified. Moreover, ADME predictions revealed that compounds had good oral bioavailability and solubility characteristics. Subsequently, molecular dynamics simulation studies revealed the better stability of the lead molecules A7 and A9 during interactions and ascertained them as potential drug candidates. Cumulative studies provided the important structural features for enhancing HCN1 channel-specific inhibition, paving the way to design and develop novel specific HCN1 channel inhibitors.
Structural investigation, computational analysis, and theoretical cryoprotectant approach of antifreeze protein type IV mutants
Antifreeze proteins (AFPs) have unique features to sustain life in sub-zero environments due to ice recrystallization inhibition (IRI) and thermal hysteresis (TH). AFPs are in demand as agents in cryopreservation, but some antifreeze proteins have low levels of activity. This research aims to improve the cryopreservation activity of an AFPIV. In this in silico study, the helical peptide afp1m from an Antarctic yeast AFP was modeled into a sculpin AFPIV, to replace each of its four α-helices in turn, using various computational tools. Additionally, a new linker between the first two helices of AFPIV was designed, based on a flounder AFPI, to boost the ice interaction activity of the mutants. Bioinformatics tools such as ExPASy Prot-Param, Pep-Wheel, SOPMA, GOR IV, Swiss-Model, Phyre2, MODFOLD, MolPropity, and ProQ were used to validate and analyze the structural and functional properties of the model proteins. Furthermore, to evaluate the AFP/ice interaction, molecular dynamics (MD) simulations were executed for 20, 100, and 500 ns at various temperatures using GROMACS software. The primary, secondary, and 3D modeling analysis showed the best model for a redesigned antifreeze protein (AFP1mb, with afp1m in place of the fourth AFPIV helix) with a QMEAN (Swiss-Model) Z score value of 0.36, a confidence of 99.5%, a coverage score of 22%, and a p value of 0.01. The results of the MD simulations illustrated that AFP1mb had more rigidity and better ice interactions as a potential cryoprotectant than the other models; it also displayed enhanced activity in limiting ice growth at different temperatures.
Computational study on the impact of linkage sequence on the structure and dynamics of lignin
Lignin, one of the most abundant biopolymers on Earth, is of great research interest due to its industrial applications including biofuel production and materials science. The structural composition of lignin plays an important role in shaping its properties and functionalities. Notably, lignin exhibits substantial compositional diversity, which varies not only between different plant species but even within the same plant. Currently, it is unclear to what extent this compositional diversity plays on the overall structure and dynamics of lignin. To address this question, this paper reports on the development of two models of lignin containing all guaiacyl (G) subunits with varied linkage sequences and makes use of all-atom molecular dynamics simulations to examine the impact of linkage sequence alone on the lignin's structure and dynamics. This work demonstrates that the structure of the lignin polymer depends on its linkage sequence at temperatures above and below the glass transition temperature ( ), but the polymers exhibit similar structural properties as it is approaching the viscous flow state (480 K). At low temperatures, both of lignin models have a local dynamics confined in a cage, but the size of cages varies depending on structural differences. Interestingly, at temperatures higher than , the different linkage sequence leads to the subtle dynamical difference which diminishes at 480 K.
Extreme enthalpy‒entropy compensation in the dimerization of small solutes in aqueous solution
This communication summarizes findings from the earliest encounters with extreme enthalpy‒entropy compensation, a phenomenon first detected in the 1950s by a reappraisal of isopiestic and calorimetric measurements on aqueous urea solutions in terms of solute self-association. Because concurrent studies of carboxylic acid association were confined to measurement of the equilibrium constant by conductance, IR spectrophotometry or potentiometric titration measurements, temperature-independence of the dimerization constant was mistakenly taken to signify a value of zero for Δ instead of (Δ ‒ TΔ ). In those studies of small-solute self-association the extreme enthalpy‒entropy compensation was reflecting the action of water as a reactant whose hydroxyl groups were competing for the solute carbonyl involved in self-association. Such action gives rise to a positive temperature dependence of Δ that could well be operating in concert with that responsible for the commonly observed negative dependence for protein‒ligand interactions exhibiting extreme enthalpy‒entropy compensation, where the solvent contribution to the energetics reflects changes in the extent of ordered water structure in hydrophobic environments.
Application of artificial neural network for the mechano-bactericidal effect of bioinspired nanopatterned surfaces
This study aimed to calculate the effect of nanopatterns' peak sharpness, width, and spacing parameters on P. aeruginosa and S. aureus cell walls by artificial neural network and finite element analysis. Elastic and creep deformation models of bacteria were developed in silico. Maximum deformation, maximum stress, and maximum strain values of the cell walls were calculated. According to the results, while the spacing of the nanopatterns is constant, it was determined that when their peaks were sharpened and their width decreased, maximum deformation, maximum stress, and maximum strain affecting the cell walls of both bacteria increased. When sharpness and width of the nano-patterns are kept constant and the spacing is increased, maximum deformation, maximum stress, and maximum strain in P. aeruginosa cell walls increase, but a decrease in S. aureus was observed. This study proves that changes in the geometric structures of nanopatterned surfaces can show different effects on different bacteria.
Time-dependent simulation of blood flow through an abdominal aorta with iliac arteries
Atherosclerosis is one of the important diseases of the circulatory system because atherosclerotic plaques cause significant disruption of blood flow. Therefore, it is very important to properly understand these processes and skillfully simulate blood flow. In our work, we consider blood flow through an abdominal aorta with iliac arteries, assuming that the right iliac artery is narrowed by an atherosclerotic lesion. Blood flow is simulated using the laminar, standard and standard models. The obtained results show that despite the use of identical initial conditions, the distribution of velocity flow and wall shear stress depends on the choice of flow simulation model. For the model, we obtain higher values of speed and wall shear stress on atherosclerotic plaque than in the other two models. The laminar and models predict larger areas where reverse blood flow occurs in the area behind the atherosclerotic lesion. This effect is associated with negative wall shear stress. These two models give very similar results. The results obtained by us, and those reported in the literature, indicate that model is the most suitable for blood flow analysis.
The origin of mutational epistasis
The interconnected processes of protein folding, mutations, epistasis, and evolution have all been the subject of extensive analysis throughout the years due to their significance for structural and evolutionary biology. The origin (molecular basis) of epistasis-the non-additive interactions between mutations-is still, nonetheless, unknown. The existence of a new perspective on protein folding, a problem that needs to be conceived as an 'analytic whole', will enable us to shed light on the origin of mutational epistasis at the simplest level-within proteins-while also uncovering the reasons why the genetic background in which they occur, a key component of molecular evolution, could foster changes in epistasis effects. Additionally, because mutations are the source of epistasis, more research is needed to determine the impact of post-translational modifications, which can potentially increase the proteome's diversity by several orders of magnitude, on mutational epistasis and protein evolvability. Finally, a protein evolution thermodynamic-based analysis that does not consider specific mutational steps or epistasis effects will be briefly discussed. Our study explores the complex processes behind the evolution of proteins upon mutations, clearing up some previously unresolved issues, and providing direction for further research.
Quantitative characterization of non-specific interaction of two globular proteins with Dextran T70 in a binary mixture
In a bid to quantify the contribution of molecular structure to non-specific interactions leading to functionally important structural changes in cellular processes, the self-interaction of dextran-T70 (DT70) and its interaction with each of bovine serum albumin (BSA) and ovomucoid trypsin inhibitor (OVO) were studied at pH 7.4 between 5 and 37 °C. The dependences of the apparent molecular weight of each of BSA, OVO and DT70 on the concentration of DT70 were independent of temperature. The activity coefficient of the interaction of each species on DT70 concentration was also independent of temperature. The change in activity coefficient was however dependent on the molecular structure and size of the interacting species. The energy of insertion of each macromolecule in DT70 increased in the order DT70 > BSA > OVO. These findings show that although the enthalpic contribution is negligible, the extent of the entropic contribution to the macromolecular activity coefficient of interaction is chiefly the consequence of the exclusion volume of the interacting macromolecules.
Rational design of potent phosphopeptide binders to endocrine Snk PBD domain by integrating machine learning optimization, molecular dynamics simulation, binding energetics rescoring, and in vitro affinity assay
Human Snk is an evolutionarily conserved serine/threonine kinase essential for the maintenance of endocrine stability. The protein consists of a N-terminal catalytic domain and a C-terminal polo-box domain (PBD) that determines subcellular localization and substrate specificity. Here, an integrated strategy is described to explore the vast structural diversity space of Snk PBD-binding phosphopeptides at a molecular level using machine learning modeling, annealing optimization, dynamics simulation, and energetics rescoring, focusing on the recognition specificity and motif preference of the Snk PBD domain. We further performed a systematic rational design of potent phosphopeptide ligands for the domain based on the harvested knowledge, from which a few potent binders were also confirmed by fluorescence-based assays. A phosphopeptide PP17 was designed as a good binder with affinity improvement by 6.7-fold relative to the control PP0, while the other three designed phosphopeptides PP7, PP13, and PP15 exhibit a comparable potency with PP0. In addition, a basic recognition motif that divides potent Snk PBD-binding sequences into four residue blocks was defined, namely [ΧΧ-]-[ΩΩΩ]-[pS/pT]-[Ψ], where the X represents any amino acid, Ω indicates polar amino acid, Ψ denotes hydrophobic amino acid, and pS/pT is the anchor phosphoserine/phosphothreonine at reference residue position 0.
Computational discovery of dual potential inhibitors of SARS-CoV-2 spike/ACE2 and M: 3D-pharmacophore, docking-based virtual screening, quantum mechanics and molecular dynamics
To find drugs against COVID-19, caused by the SARS-CoV-2, promising targets include the fusion of the viral spike with the human angiotensin-converting enzyme 2 (ACE2) as well as the main protease (M). These proteins are responsible for viral entry and replication, respectively. We combined several state-of-the-art computational methods, including, protein-ligand interaction fingerprint, 3D-pharmacophores, molecular-docking, MM-GBSA, DFT, and MD simulations to explore two databases: ChEMBL and NANPDB to identify molecules that could both block spike/ACE2 fusion and inhibit M. A total of 1,690,649 compounds from the two databases were screened using the pharmacophore model obtained from PLIF analysis. Five recent complexes of M co-crystallized with different ligands were used to generate the pharmacophore model, allowing 4,829 compounds that passed this prefilter. These were then submitted to molecular docking against M. The 5% top-ranked docking hits from docking result having scores -8.32 kcal mol were selected and then docked against spike/ACE2. Only four compounds: ChEMBL244958, ChEMBL266531, ChEMBL3680003, and 1-methoxy-3-indolymethyl glucosinolate (4) displayed binding energies 8.21 kcal mol (for the native ligand) were considered as putative dual-target inhibitors. Furthermore, predictive ADMET, MM-GBSA and DFT/6-311G(d,p) were performed on these compounds and compared with those of well-known antivirals. DFT calculations showed that ChEMBL244958 and compound 4 had significant predicted reactivity values. Molecular dynamics simulations of the docked complexes were run for 100 ns and used to validate the stability docked poses and to confirm that these hits are putative dual binders of the spike/ACE2 and the M.
Analysis of proteins in the light of mutations
Proteins have evolved through mutations-amino acid substitutions-since life appeared on Earth, some 10 years ago. The study of these phenomena has been of particular significance because of their impact on protein stability, function, and structure. This study offers a new viewpoint on how the most recent findings in these areas can be used to explore the impact of mutations on protein sequence, stability, and evolvability. Preliminary results indicate that: (1) mutations can be viewed as sensitive probes to identify 'typos' in the amino-acid sequence, and also to assess the resistance of naturally occurring proteins to unwanted sequence alterations; (2) the presence of 'typos' in the amino acid sequence, rather than being an evolutionary obstacle, could promote faster evolvability and, in turn, increase the likelihood of higher protein stability; (3) the mutation site is far more important than the substituted amino acid in terms of the marginal stability changes of the protein, and (4) the unpredictability of protein evolution at the molecular level-by mutations-exists even in the absence of epistasis effects. Finally, the Darwinian concept of evolution "descent with modification" and experimental evidence endorse one of the results of this study, which suggests that some regions of any protein sequence are susceptible to mutations while others are not. This work contributes to our general understanding of protein responses to mutations and may spur significant progress in our efforts to develop methods to accurately forecast changes in protein stability, their propensity for metamorphism, and their ability to evolve.
The Structure of the LysR-type Transcriptional Regulator, CysB, Bound to the Inducer, N-acetylserine
In Escherichia coli and Salmonella typhimurium, cysteine biosynthesis requires the products of 20 or more cys genes co-ordinately regulated by CysB. Under conditions of sulphur limitation and in the presence of the inducer, N-acetylserine, CysB binds to cys promoters and activates the transcription of the downstream coding sequences. CysB is a homotetramer, comprising an N-terminal DNA binding domain (DBD) and a C-terminal effector binding domain (EBD). The crystal structure of a dimeric EBD fragment of CysB from Klebsiella aerogenes revealed a protein fold similar to that seen in Lac repressor but with a different symmetry in the dimer so that the mode of DNA binding was not apparent. To elucidate the subunit arrangement in the tetramer, we determined the crystal structure of intact CysB in complex with N-acetylserine. The tetramer has two subunit types that differ in the juxtaposition of their winged helix-turn-helix DNA binding domains with respect to the effector binding domain. In the assembly, the four EBDs form a core with the DNA binding domains arranged in pairs on the surface. N-acetylserine makes extensive polar interactions in an enclosed binding site, and its binding is accompanied by substantial conformational rearrangements of surrounding residues that are propagated to the protein surface where they appear to alter the arrangement of the DNA binding domains. The results are (i) discussed in relation to the extensive mutational data available for CysB and (ii) used to propose a structural mechanism of N-acetylserine induced CysB activation.
Mechanisms of stationary voltage fluctuation in the neuromuscular junction endplate and corresponding denoising paradigms
The neuromuscular junction (NMJ) has an elaborate anatomy to ensure agile and accurate signal transmission. Based on our formerly obtained expressions of the thermal and conductance induced voltage fluctuations, in this paper, the mechanisms underlying the conductance-induced voltage fluctuation are characterized from two aspects: the scaling laws with respect to either of the two system-size factors, the number of receptors or the membrane area; and the "seesaw effect" with respect to the intensive parameter, the concentration of acetylcholine. According to these mechanisms, several aspects of the NMJ anatomy are explained from a denoising perspective. Finally, the power spectra of the two types of voltage fluctuations are characterized by their specific scaling laws, based on which we explain why the endplate noise has the low-frequency property that is described by the term "seashell sound".
Reciprocal effect on lateral diffusion of receptor for advanced glycation endproducts and toll-like receptor 4 in the HEK293 cell membrane
Receptor for advanced glycation endproducts (RAGE) and toll-like receptor 4 (TLR4) are pattern-recognition receptors that bind to molecular patterns associated with pathogens, stress, and cellular damage. Diffusion plays an important role in receptor functionality in the cell membrane. However, there has been no prior investigation of the reciprocal effect of RAGE and TLR4 diffusion properties in the presence and absence of each receptor. This study reports how RAGE and TLR4 affect the mobility of each other in the human embryonic kidney (HEK) 293 cell membrane. Diffusion properties were measured using single-particle tracking (SPT) with quantum dots (QDs) that are selectively attached to RAGE or TLR4. The Brownian diffusion coefficients of RAGE and TLR4 are affected by the presence of the other receptor, leading to similar diffusion coefficients when both receptors coexist in the cell. When TLR4 is present, the average Brownian diffusion coefficient of RAGE increases by 40%, while the presence of RAGE decreases the average Brownian diffusion coefficient of TLR4 by 32%. Diffusion in confined membrane domains is not altered by the presence of the other receptor. The mobility of the cell membrane lipid remains constant whether one or both receptors are present. Overall, this work shows that the presence of each receptor can affect a subset of diffusion properties of the other receptor without affecting the mobility of the membrane.
The conformational properties of alamethicin in ethanol studied by NMR
Alamethicin, a peptide consisted of 20 amino acid residues, has been known to function as an antibiotic. The peptides self-associate in biological membranes, form an ion channel, and then induce cell death by leaking intracellular contents through a transmembrane pore of an ion channel. We investigated conformation and its thermal stability of alamethicin-A6 and -U6 in ethanol using proton nuclear magnetic resonance (NMR) spectroscopy; alamethicin-A6 and -U6 have the amino acid sequences of UPUAUAQUVUGLUPVUUQQO and UPUAUUQUVUGLUPVUUQQO, respectively, where U and O represent α-aminoisobutyric acid and phenylalaninol, respectively. As indicated by the under bars in the sequences, only the residue 6 differs between the alamethicins. We show that the alamethicins in ethanol form helix conformation in the region of the residues 2-11 and a non-regular conformation in the regions of the N- and C-termini, and that the helices are maintained up to 66 °C at least. Conformations in the region of the residues 12-18 of the alamethicins, however, are not well identified due to the lack of NMR data. In addition, we demonstrate that the amide proton chemical shift temperature coefficients' method, which is known as an indicator for intramolecular hydrogen bonds in peptides and proteins in aqueous solutions, can be also applied to the alamethicins in ethanol. Further, we show that the conformation around the C-terminus of alamethicin-A6 is restrained by intramolecular hydrogen bonds, whereas that of alamethicin-U6 is either restrained or unrestrained by intramolecular hydrogen bonds; the alamethicin-U6 molecules having the restrained and unrestrained conformations coexist in ethanol. We discuss the two types of conformations using a model chain consisting of particles linked by rigid bonds called as the free jointed chain.
Modeling study of kinesin-13 MCAK microtubule depolymerase
Mitotic centromere-associated kinesin (MCAK) motor protein is a typical member of the kinesin-13 family, which can depolymerize microtubules from both plus and minus ends. A critical issue for the MCAK motor is how it performs the depolymerase activity. To address the issue, the pathway of the MCAK motor moving on microtubules and depolymerizing the microtubules is presented here. On the basis of the pathway, the dynamics of both the wild-type and mutant MCAK motors is studied theoretically, which include the full-length MCAK, the full-length MCAK with mutations in the α4-helix of the motor domain, the mutant full-length MCAK with a neutralized neck, the monomeric MCAK and the mutant monomeric MCAK with a neutralized neck. The studies show that a single dimeric MCAK motor can depolymerize microtubules in a processive manner, with either one tubulin or two tubulins being removed per times. The theoretical results are in agreement with the available experimental data. Moreover, predicted results are provided.
Erythrocytes membrane fluidity changes induced by adenylyl cyclase cascade activation: study using fluorescence recovery after photobleaching
In this study, fluorescence recovery after photobleaching (FRAP) experiments were performed on RBC labeled by lipophilic fluorescent dye CM-DiI to evaluate the role of adenylyl cyclase cascade activation in changes of lateral diffusion of erythrocytes membrane lipids. Stimulation of adrenergic receptors with epinephrine (adrenaline) or metaproterenol led to the significant acceleration of the FRAP recovery, thus indicating an elevated membrane fluidity. The effect of the stimulation of protein kinase A with membrane-permeable analog of cAMP followed the same trend but was less significant. The observed effects are assumed to be driven by increased mobility of phospholipids resulting from the weakened interaction between the intermembrane proteins and RBC cytoskeleton due to activation of adenylyl cyclase signaling cascade.
Site-directed mutagenesis at the Glu78 in Ec-NhaA transporter impacting ion exchange: a biophysical study
Na/H antiporters facilitate the exchange of Na for H across the cytoplasmic membrane in prokaryotic and eukaryotic cells. These transporters are crucial to maintain the homeostasis of sodium ions, consequently pH, and volume of the cells. Therefore, sodium/proton antiporters are considered promising therapeutic targets in humans. The Na/H antiporter in Escherichia coli (Ec-NhaA), a prototype of cation-proton antiporter (CPA) family, transports two protons and one sodium (or Li) in opposite direction. Previous mutagenesis experiments on Ec-NhaA have proposed Asp164, Asp163, and Asp133 amino acids with the significant implication in functional and structural integrity and create site for ion-binding. However, the mechanism and the sites for the binding of the two protons remain unknown and controversial which could be critical for pH regulation. In this study, we have explored the role of Glu78 in the regulation of pH by Ec-NhaA. Although we have created various mutants, E78C has shown a considerable effect on the stoichiometry of NhaA and presented comparable phenotypes. The ITC experiment has shown the binding of ~ 5 protons in response to the transport of one lithium ion. The phenotype analysis on selective medium showed a significant expression compared to WT Ec-NhaA. This represents the importance of Glu78 in transporting the H across the membrane where a single mutation with Cys amino acid alters the number of H significantly maintaining the activity of the protein.
The effect of ionic redistributions on the microwave dielectric response of cytosol water upon glucose uptake
The sensitivity of cytosol water's microwave dielectric (MD) response to D-glucose uptake in Red Blood Cells (RBCs) allows the detailed study of cellular mechanisms as a function of controlled exposures to glucose and other related analytes like electrolytes. However, the underlying mechanism behind the sensitivity to glucose exposure remains a topic of debate. In this research, we utilize MDS within the frequency range of 0.5-40 GHz to explore how ionic redistributions within the cell impact the microwave dielectric characteristics associated with D-glucose uptake in RBC suspensions. Specifically, we compare glucose uptake in RBCs exposed to the physiological concentration of Ca vs. Ca-free conditions. We also investigate the potential involvement of Na/K redistribution in glucose-mediated dielectric response by studying RBCs treated with a specific Na/K pump inhibitor, ouabain. We present some insights into the MD response of cytosol water when exposed to Ca in the absence of D-glucose. The findings from this study confirm that ion-induced alterations in bound/bulk water balance do not affect the MD response of cytosol water during glucose uptake.
Two-layer elastic models for single-yeast compressibility with flat microlevers
Unicellular organisms such as yeast can survive in very different environments, thanks to a polysaccharide wall that reinforces their extracellular membrane. This wall is not a static structure, as it is expected to be dynamically remodeled according to growth stage, division cycle, environmental osmotic pressure and ageing. It is therefore of great interest to study the mechanics of these organisms, but they are more difficult to study than other mammalian cells, in particular because of their small size (radius of a few microns) and their lack of an adhesion machinery. Using flat cantilevers, we perform compression experiments on single yeast cells (S. cerevisiae) on poly-L-lysine-coated grooved glass plates, in the limit of small deformation using an atomic force microscope (AFM). Thanks to a careful decomposition of force-displacement curves, we extract local scaling exponents that highlight the non-stationary characteristic of the yeast behavior upon compression. Our multi-scale nonlinear analysis of the AFM force-displacement curves provides evidence for non-stationary scaling laws. We propose to model these phenomena based on a two-component elastic system, where each layer follows a different scaling law..