Design of adaptive controllers using partial certainty equivalence principle

Optimal stochastic control problem for general non‐linear dynamic system with unknown parameters is considered. An approximative assumption, which has been named partial certainty equivalence (PCE) principle, is suggested for design of adaptive controllers of non‐linear and linear stochastic systems. For derivation of a suboptimal controller with the PCE principle the certainty equivalence (CE) assumption is used only for the part of the system states and unknown parameters. The PCE control policy has a simple form for linear systems with unknown parameters. It is suggested in the present paper to design adaptive dual control using the PCE assumption and bicriterial optimization to derive the adaptive controller with the optimal persistent excitation. Simulated examples are used to demonstrate the potential of the suggested method and its superiority over the generally used CE‐controllers. Copyright © 2004 John Wiley & Sons, Ltd.     

The performance of different propensity score methods for estimating marginal odds ratios

The propensity score which is the probability of exposure to a specific treatment conditional on observed variables. Conditioning on the propensity score results in unbiased estimation of the expected difference in observed responses to two treatments. In the medical literature, propensity score methods are frequently used for estimating odds ratios. The performance of propensity score methods for estimating marginal odds ratios has not been studied. We performed a series of Monte Carlo simulations to assess the performance of propensity score matching, stratifying on the propensity score, and covariate adjustment using the propensity score to estimate marginal odds ratios. We assessed bias, precision, and mean-squared error (MSE) of the propensity score estimators, in addition to the proportion of bias eliminated due to conditioning on the propensity score. When the true marginal odds ratio was one, then matching on the propensity score and covariate adjustment using the propensity score resulted in unbiased estimation of the true treatment effect, whereas stratification on the propensity score resulted in minor bias in estimating the true marginal odds ratio. When the true marginal odds ratio ranged from 2 to 10, then matching on the propensity score resulted in the least bias, with a relative biases ranging from 2.3 to 13.3 per cent. Stratifying on the propensity score resulted in moderate bias, with relative biases ranging from 15.8 to 59.2 per cent. For both methods, relative bias was proportional to the true odds ratio. Finally, matching on the propensity score tended to result in estimators with the lowest MSE.     

Temporal changes in the spatial pattern of disease rates incorporating known risk factors

Examining the geographical pattern of temporal changes in infant mortality rates illustrates the methodological problems of documenting and understanding temporal changes in any spatial pattern of disease. Early research on geographical differences in infant mortality rates showed strong ecological correlations with socio-economic factors such as poverty rates. More recent research established relationships between individual-level socio-economic values and probabilities of death. With geographic information available at the level of individuals, it is possible to estimate the probabilities of death on a person-by-person basis from knowledge of the relationships between individual factors and socio-economic measures. These estimated probabilities provide an expected geographic pattern of deaths. The difference between the observed spatial pattern and the expected pattern is the remaining spatial variation adjusted for this knowledge. For the study area, individual factors and some socio-economic measures were available for each year of the study period. Using data from the Iowa Birth Defects Registry and the Iowa Department of Public Health (USA), I tested the stability and continuity of these cross-sectional relationships and investigated whether any temporal lags in these variables relate to the unexplained spatial variations in infant mortality rates that remain. I accounted for the 'Change of Support Problem' [Gotway C. A. & Young L. J. (2002). Combining incompatible spatial data. Journal of the American Statistical Association, 97458, 632-648] inherent in frame-based geographical analysis. The analysis involved a generalized linear model (GLM) to estimate individual risks and a Monte Carlo simulation model to generate the non-linear probability density functions for disease rates whose densities are theoretically intractable. Results show the temporal changes in the observed spatial pattern and the expected spatial pattern differ by geographic location. In conclusion such differences are the result of a combination of unexplained place-based risk and unmeasured individual risks.     

Molecular lock regulates binding of glycine to a primitive NMDA receptor

The earliest metazoan ancestors of humans include the ctenophore Mnemiopsis leidyi. The genome of this comb jelly encodes homologs of vertebrate ionotropic glutamate receptors (iGluRs) that are distantly related to glycine-activated NMDA receptors and that bind glycine with unusually high affinity. Using ligand-binding domain (LBD) mutants for electrophysiological analysis, we demonstrate that perturbing a ctenophore-specific interdomain Arg-Glu salt bridge that is notably absent from vertebrate AMPA, kainate, and NMDA iGluRs greatly increases the rate of recovery from desensitization, while biochemical analysis reveals a large decrease in affinity for glycine. X-ray crystallographic analysis details rearrangements in the binding pocket stemming from the mutations, and molecular dynamics simulations suggest that the interdomain salt bridge acts as a steric barrier regulating ligand binding and that the free energy required to access open conformations in the glycine-bound LBD is largely responsible for differences in ligand affinity among the LBD variants.Glutamate receptor ion channels (iGluRs) are membrane proteins that mediate excitatory synaptic transmission in the brain by detecting release of the amino acid glutamate from nerve terminals (1). In combination with GluN2 subunits, which bind glutamate, NMDA subtype iGluRs use glycine as a coagonist, which binds to GluN1, GluN3A, and GluN3B subunits (2–6). NMDA receptors play key roles in synaptic plasticity and memory formation, and mutations of NMDA receptor genes underlie a diverse set of neurological and psychiatric diseases (7). Like all iGluRs, NMDA receptors are assembled from modular subunits containing amino terminal and S1S2 ligand binding domains (LBDs), which can be genetically isolated and expressed as soluble proteins for biochemical and structural analysis (4, 8–10). The LBDs of both the glutamate and glycine binding subunits are clamshell-shaped proteins of molecular mass around 30 kDa in which two lobes are connected by a hinge formed by antiparallel β-strands; in the activated state, ligands are trapped in a cavity formed when the clamshell closes. Strikingly, the volume of the ligand binding cavity for the GluN1, GluN3A, and GluN3B subunits is just large enough to accommodate glycine, whereas iGluR glutamate binding subunits have cavities that are four to five times larger and bind both glutamate and up to six or seven water molecules (4, 10–13).We recently reported the discovery of glycine-activated iGluRs from the comb jelly Mnemiopsis leidyi and the sea gooseberry Pleurobrachia bachei, candidates for earliest lineage metazoans, for which ML032222a and PbGluR3 glycine complex crystal structures reveal a salt bridge at the perimeter of the ligand binding cleft (14). This salt bridge links the upper and lower lobes of the LBD in the closed cleft glycine-bound conformation. Ctenophore iGluR subunits bind glycine with such high affinity that the ligand cannot be removed by exhaustive dialysis, suggesting an unusually stable ligand-bound closed-cleft conformation, perhaps stabilized by the interdomain salt bridge. Prior electrophysiological and crystallographic studies on vertebrate AMPA and kainate subtype iGluRs revealed that the stability of the closed cleft conformation is determined not only by contacts of the LBD with the neurotransmitter ligand but also by contacts formed between the upper and lower lobes of the clamshell assembly that occur only in the ligand-bound closed-cleft conformation (15, 16). Comparison of crystal structures of ctenophore iGluR LBDs with those of vertebrate NMDA receptor GluN1 and GluN3 subunits that also bind glycine, but for which apo proteins can be prepared without difficulty (4, 10), reveals that the salt bridge is unique to ctenophore iGluRs, further suggesting that it might underlie the high stability of the glycine complex.To investigate this, we prepared ML032222a mutant proteins and analyzed their ligand binding properties using electrophysiological, biochemical, and crystallographic techniques. To gain further insight into how these mutants perturb large-scale LBD dynamics, we computed conformational free energy landscapes for the apo state and glycine complexes of wild-type (WT) ML032222a and the R703K and E423S mutants, which weaken and break the interdomain salt bridge, respectively. This analysis reveals that, similar to vertebrate GluN1 and GluN3 glycine binding subunits, the apo state for ML032222a can access closed cleft conformations, although it is more stable in slightly open conformations. The R703K and E423S mutants destabilize closed cleft conformations for the glycine complex. Conformational dynamics inferred from the free energy landscapes suggest that the interdomain salt bridge is positioned at the most likely point of ligand entry to (and exit from) the binding pocket and thus acts as a steric barrier regulating the binding and dissociation of glycine.     

NMR structure and dynamics of the agonist dynorphin peptide bound to the human kappa opioid receptor

The structure of the dynorphin (1–13) peptide (dynorphin) bound to the human kappa opioid receptor (KOR) has been determined by liquid-state NMR spectroscopy. ¹H and ¹⁵N chemical shift variations indicated that free and bound peptide is in fast exchange in solutions containing 1 mM dynorphin and 0.01 mM KOR. Radioligand binding indicated an intermediate-affinity interaction, with a K_d of ∼200 nM. Transferred nuclear Overhauser enhancement spectroscopy was used to determine the structure of bound dynorphin. The N-terminal opioid signature, YGGF, was observed to be flexibly disordered, the central part of the peptide from L5 to R9 to form a helical turn, and the C-terminal segment from P10 to K13 to be flexibly disordered in this intermediate-affinity bound state. Combining molecular modeling with NMR provided an initial framework for understanding multistep activation of a G protein-coupled receptor by its cognate peptide ligand.G protein-coupled receptors (GPCRs) are the largest superfamily of membrane proteins in the human genome and play a critical role in human physiology by initiating signal transduction in response to extracellular stimuli (1, 2). Since 2007, 89 GPCR crystal structures have been reported, including receptors in inactive and active states, as well as the beta-2 adrenergic receptor (β₂-AR) bound to heterotrimeric G proteins (3). NMR spectroscopy has revealed that the intrinsic conformational heterogeneity of GPCRs is influenced by ligand pharmacology, membrane composition, and effector interactions (4–6). These structural biology studies have provided atomic-resolution insights of systems defined by dynamic structural rearrangements that are correlated with diverse cellular and physiological outcomes.The classic opioid receptors (δ/κ/μ) are GPCRs activated in response to binding enkephalin-like peptide agonists and are the primary targets of widely prescribed pain medications (7). The kappa opioid receptor (KOR) and its cognate peptide dynorphin are implicated in neuronal pathways associated with addiction, pain, reward, mood, cognition, and perception (8, 9). Nonselective KOR antagonists such as naltrexone have been prescribed for alcohol dependence with limited efficacy in humans, and next-generation KOR antagonists continue to be developed to treat drug addiction and other disorders. Although much is known regarding the antagonist-bound, inactive state of GPCRs, including the crystal structure of JDTic-bound KOR, the interaction of these receptors with neuropeptide agonists remains largely unknown (10). Peptide agonist-bound structures have thus far been limited to a conformationally stabilized neurotensin receptor, likely corresponding to a low-energy peptide-receptor state (11–13).Dynorphin was discovered by Goldstein and Chavkin as the endogenous activating neuropeptide for KOR, with a “low-resolution” structural model of interaction proposed to PNAS in 1981 (14, 15). Dynorphins are derived from the precursor prodynorphin, with dynorphin A(1–17), dynorphin B(1–13), and alpha neoendorphin sharing a highly conserved N-terminal sequence and charge distribution (16). Dynorphin A(1–13) was shown to act as an agonist on opioid kappa receptors in vivo (17). Physiological activation of KOR is mainly associated with unwanted effects such as dysphoria, anhedonia, and hallucinations, and a current hypothesis in the field is that KOR functionally selective ligands may produce analgesia without dysphoria (18, 19). Functional selectivity has emerged as the leading model to understand the ability of a ligand to activate a subset of signaling cascades, providing a framework for developing next-generation drugs with rationally designed pharmacological profiles (20).The seminal work of Schwyzer in the 1970s and 1980s led to a model of KOR activation by dynorphin that proceeds via a multistep binding mechanism (14, 21, 22). Thereby, low- to intermediate-affinity binding states of dynorphin correspond to binding to cell-surface membranes or to extracellular loops of the GPCR. A “message–address” paradigm has been formulated based on structure–activity relations observed with dynorphin analogs (21–26). Accordingly, the N-terminal YGGF “message” sequence, which is common to all opioid peptides, was found to be responsible for receptor activation. A C-terminal “address” sequence was further found to contribute via electrostatically driven interactions to KOR subtype specificity. In the context of this paradigm, the present study yields intriguing data on the N-terminal segment of the KOR-bound opioid peptide dynorphin. The methods used, NMR in solution and molecular dynamics simulations, enabled us to define structural ensembles of KOR-bound dynorphin and to characterize internal peptide motions in the presently prepared low-affinity receptor-bound state.     

Regulation and aggregation of intrinsically disordered peptides

Intrinsically disordered proteins (IDPs) are a unique class of proteins that have no stable native structure, a feature that allows them to adopt a wide variety of extended and compact conformations that facilitate a large number of vital physiological functions. One of the most well-known IDPs is the microtubule-associated tau protein, which regulates microtubule growth in the nervous system. However, dysfunctions in tau can lead to tau oligomerization, fibril formation, and neurodegenerative disease, including Alzheimer’s disease. Using a combination of simulations and experiments, we explore the role of osmolytes in regulating the conformation and aggregation propensities of the R2/wt peptide, a fragment of tau containing the aggregating paired helical filament (PHF6*). We show that the osmolytes urea and trimethylamine N-oxide (TMAO) shift the population of IDP monomer structures, but that no new conformational ensembles emerge. Although urea halts aggregation, TMAO promotes the formation of compact oligomers (including helical oligomers) through a newly proposed mechanism of redistribution of water around the perimeter of the peptide. We put forth a “superposition of ensembles” hypothesis to rationalize the mechanism by which IDP structure and aggregation is regulated in the cell.Most proteins in the human body have a well-defined, stable three-dimensional structure that is intimately tied to their physiological function. In the past few decades however, researchers have also identified a class of proteins that are natively unstructured. The latter, often referred to as intrinsically disordered proteins (IDPs) (1), are widespread and have the ability to quickly change their conformations to participate in a variety of biological processes. IDPs typically contain multiple charged side chains and few hydrophobic residues. Despite these characteristics, IDPs are not typically found in extended states but rather populate compact states due to hydrogen bonds and salt bridges (2, 3). IDP structures are highly regulated in the cell, and aberrant regulation often results in protein aggregation.In this paper we consider the effect of external agents, specifically osmolytes, in regulating IDP structure and aggregation properties. To carry out this study, we focused on the microtubule-associated protein tau, a soluble (4), archetypical IDP found in the nervous system that helps regulate and stabilize microtubules (5, 6). When the regulation of tau structure and activity is compromised, tau loses its ability to bind to microtubules, and disassociated tau proteins can aggregate into supramolecular assemblies with a cross-β structure (7–9) typical of amyloid fibers. This aggregation process is a pathological hallmark of Alzheimer’s disease and other forms of dementia known as tauopathies (10, 11). We consider here a segment of tau, the R2/wt fragment ₂₇₃GKVQIINKKLDL₂₈₄, which contains the highly aggregation prone paired helical filament (PHF6*) (VQIINK) region. R2/wt aggregates in vitro in a manner qualitatively similar to full-length tau, therefore we expect that the effects of osmolytes on R2/wt are similar to those on full-length tau.Our earlier work on this peptide showed that R2/wt is unstructured in solution, populating an ensemble of interconverting conformations (12). Two primary structural families emerged: a family consisting of extended conformations and a family consisting of compact conformations. The latter included structures that were stabilized by hydrogen bonding (primarily hairpins and, to a lesser extent, helices) or by salt bridges between aspartic acid (D) and lysine (K) groups, with salt bridges between K274 and D283 (located at opposite ends of the peptide) more prevalent than between adjacent residue pairs K280 and D283 or K281 and D283. Hydrogen bonded conformations are stabilized for enthalpic reasons, however, salt bridge ensembles are stabilized by both energetic and entropic contributions, as multiple conformations of the backbone are possible for any given salt bridge. The competition between salt bridge formation and hydrogen bonding is the reason that this peptide is intrinsically disordered, unable to find a unique structure. Conformations stabilized by hydrogen bonds are continually disrupted by the formation of salt bridges, and vice versa.Here, we propose a new hypothesis that we term “superposition of ensembles.” We propose that external regulating agents (osmolytes, crowders, etc.) or internal regulating mechanisms (mutations, posttranslational modifications, etc.) can shift the population of protein conformations, but do not necessarily introduce fundamentally new structures, and can thus define the basis of regulation. The subtle conformational shifts caused by these regulatory effects can then either enhance or suppress particular states, such as those possessing different levels of normal activity, or states with propensities to aggregate into abnormal pathological conformations. To explore this idea further, we consider the effect of the following external agents on the R2/wt tau conformation: (i) urea, an osmolyte used to denature globular proteins through presumed perturbations in peptide hydrogen bonding (13), and (ii) trimethylamine N-oxide (TMAO), an osmolyte that is known to stabilize globular proteins and act as a crowding agent (13). The effect of these agents on the monomeric state of R2/wt is studied using replica exchange molecular dynamics simulations, a methodology that enables efficient sampling of the diverse conformations populated by this peptide. The ability of R2/wt to aggregate in the presence of these external factors, in turn, is assayed experimentally using Thioflavin T (ThT) fluorescence spectroscopy to quantify aggregation rates and transmission electron microscopy (TEM) to determine aggregate morphologies. By combining statistics from molecular simulations with experimental observations, it becomes possible to study, at an atomic level, the intrinsic origins of protein disorder and regulation that play a leading role in most physiological processes.     

Robust network oscillations during mammalian respiratory rhythm generation driven by synaptic dynamics

How might synaptic dynamics generate synchronous oscillations in neuronal networks? We address this question in the preBötzinger complex (preBötC), a brainstem neural network that paces robust, yet labile, inspiration in mammals. The preBötC is composed of a few hundred neurons that alternate bursting activity with silent periods, but the mechanism underlying this vital rhythm remains elusive. Using a computational approach to model a randomly connected neuronal network that relies on short-term synaptic facilitation (SF) and depression (SD), we show that synaptic fluctuations can initiate population activities through recurrent excitation. We also show that a two-step SD process allows activity in the network to synchronize (bursts) and generate a population refractory period (silence). The model was validated against an array of experimental conditions, which recapitulate several processes the preBötC may experience. Consistent with the modeling assumptions, we reveal, by electrophysiological recordings, that SF/SD can occur at preBötC synapses on timescales that influence rhythmic population activity. We conclude that nondeterministic neuronal spiking and dynamic synaptic strengths in a randomly connected network are sufficient to give rise to regular respiratory-like rhythmic network activity and lability, which may play an important role in generating the rhythm for breathing and other coordinated motor activities in mammals.Central pattern generators (CPGs) are neuronal circuits that generate coordinated activity in the absence of sensory input (1). One such mammalian CPG, the preBötzinger complex (preBötC), gives rise to the eupneic respiratory rhythm (2, 3). Located in the medulla, the preBötC preserves a spontaneous respiratory-like rhythm when isolated in transverse slices, but the precise nature of the cellular and synaptic mechanisms underlying rhythmogenesis remains elusive (3–7). An early hypothesis was that the neuronal activity is driven by intrinsically bursting pacemaker neurons synchronized via excitatory synaptic connections (2, 6, 8, 9). However, electrophysiological and modeling studies (7, 10–12) now suggest the rhythm emerges through stochastic activation of intrinsic currents conveyed by recurrent synaptic connections, without the need for pacemaker neurons (3, 4, 11, 13, 14). In either case, excitatory synapses are required for rhythm generation; the possibility that synaptic properties also underlie periodic burst initiation and termination is yet to be demonstrated.Synaptic transmission relies on the release of vesicles, which can be modulated at the presynaptic terminal. Synaptic depression (SD), based on vesicular release, consists of decaying release probability after sustained activity, which subsequently decreases excitability within the underlying connected network. Conversely, synaptic facilitation (SF) enhances vesicular release probability and promotes neuronal synchronization. These synaptic dynamics are critical for short-term synaptic plasticity, and here they are explored in the context of preBötC rhythm generation.We first consider a randomly connected network where each neuron is modeled using a generalized Hodgkin–Huxley system of equations and exhibits spontaneous spiking activity based on a random process, but the neurons do not have intrinsic bursting mechanisms. These neurons are sparsely connected within a realistically sized network by excitatory synapses. The distinction of this model, from previous preBötC models, is that synapses express SF and SD that is implemented using two separate pools of vesicles and creates dynamic synapses. The first pool is the readily releasable pool (RRP) and the other is the recycling pool (RP) (15), modeled with mass-action kinetics. Synaptic dynamics has been repeatedly used to describe changes in spike rates in neural network populations (16) and emergence of gamma oscillations (17). Furthermore network connectivity can also participate to define bursting or the oscillation frequency in neural networks (18, 19).We show here that random networks connected with these synaptic properties, with random spiking, are sufficient for periodic bursting and examine a variety of experimental scenarios testing this model. The present model shows that an ensemble of excitatory neurons driven by synaptic dynamics can generate population-wide rhythmic activity and behaves in a manner similar to the preBötC under different conditions observed in vitro. Finally, we show experimentally that excitatory inputs to preBötC neurons often exhibit dynamically changing excitatory postsynaptic currents (EPSCs), supporting the modeled concept that SF/SD occurs on a timescale relevant to influence respiratory periods.     

Multiple stiffening effects of nanoscale knobs on human red blood cells infected with Plasmodium falciparum malaria parasite

During its asexual development within the red blood cell (RBC), Plasmodium falciparum (Pf), the most virulent human malaria parasite, exports proteins that modify the host RBC membrane. The attendant increase in cell stiffness and cytoadherence leads to sequestration of infected RBCs in microvasculature, which enables the parasite to evade the spleen, and leads to organ dysfunction in severe cases of malaria. Despite progress in understanding malaria pathogenesis, the molecular mechanisms responsible for the dramatic loss of deformability of Pf-infected RBCs have remained elusive. By recourse to a coarse-grained (CG) model that captures the molecular structures of Pf-infected RBC membrane, here we show that nanoscale surface protrusions, known as “knobs,” introduce multiple stiffening mechanisms through composite strengthening, strain hardening, and knob density-dependent vertical coupling. On one hand, the knobs act as structural strengtheners for the spectrin network; on the other, the presence of knobs results in strain inhomogeneity in the spectrin network with elevated shear strain in the knob-free regions, which, given its strain-hardening property, effectively stiffens the network. From the trophozoite to the schizont stage that ensues within 24–48 h of parasite invasion into the RBC, the rise in the knob density results in the increased number of vertical constraints between the spectrin network and the lipid bilayer, which further stiffens the membrane. The shear moduli of Pf-infected RBCs predicted by the CG model at different stages of parasite maturation are in agreement with experimental results. In addition to providing a fundamental understanding of the stiffening mechanisms of Pf-infected RBCs, our simulation results suggest potential targets for antimalarial therapies.The most virulent human malaria parasite, Plasmodium falciparum (Pf), causes ∼700,000 deaths each year (1, 2). Following entry into red blood cells (RBCs), the parasite matures through the ring (0–24 h), trophozoite (24–36 h), and schizont stages (40–48 h). This intraerythrocyte maturation is accompanied by striking changes in the surface topography and membrane architecture of the infected RBC (3–5). A notable modification is the formation of nanoscale protrusions, commonly known as knobs, at the RBC surface during the second half (24–48 h) of the asexual cycle. These protrusions mainly comprise the knob-associated histidine-rich protein (KAHRP) and the membrane-embedded cytoadherence protein, Pf-erythrocyte membrane protein 1 (PfEMP1). KAHRP binds to the fourth repeat unit of the spectrin α-chain, to ankyrin, to spectrin–actin–protein 4.1 complexes, and to the cytoplasmic domain of PfEMP1 (6–9). These attachments enhance the vertical coupling between the lipid bilayer and the spectrin network. Another striking modification in the Pf-infected RBC membrane is the reorganization of the cytoskeletal network caused by parasite-induced actin remodeling (10). As a result of these molecular-level modifications, the Pf-infected RBC exhibits markedly increased stiffness [the shear modulus increases on average from ∼4−10 µN/m in normal/uninfected RBCs, to ∼40 µN/m at the trophozoite stage, and to as high as 90 µN/m at the schizont stage (11–13)] and cytoadherence to the vascular endothelium, which enable sequestration from circulation in vasculature, and evasion from the surveillance mechanisms of the spleen. Although in vitro experimental studies have revealed roles of particular parasite-encoded proteins in remodeling the host RBC (14–22), the mechanism by which Pf-infected RBCs gain dramatically increased stiffness has remained unclear. Indeed, uncertainty remains as to whether the loss of deformability arises from the structural reorganization of the host membrane components or from the deposition of parasite proteins. That is, it is not clear whether the stiffening is due to remodeling of the spectrin network, or to the formation of the knobs, or both. As experimental studies alone have heretofore not been able to determine the molecular details, numerical modeling, combined with a variety of experimental observations and measurements, offers an alternative approach to reveal the underlying mechanisms.We present here a coarse-grained (CG) molecular dynamics (MD) RBC membrane model to correlate structural modifications at the molecular ultrastructure level with the shear responses of the Pf-infected RBC membrane, focusing on the second half of the parasite’s intra-RBC asexual cycle (24–48 h), i.e., the trophozoite and schizont stages. The CG model is computationally efficient, and able to capture the molecular structures of the RBC membrane in both normal and infected states. CGMD simulations reveal that spectrin network remodeling accounts for a relatively small change in shear modulus. Instead, the knobs stiffen the membrane by multiple mechanisms, including composite strengthening, strain hardening, and knob density-dependent vertical coupling. Our findings provide molecular-level understanding of the stiffening mechanisms operating in Pf-infected RBCs and shed light on the pathogenesis of falciparum malaria.