Trafficking and ethanol-induced inhibition of AMPA receptors

AMPA receptors are an important class of ionotropic glutamate receptors which participate in fast excitatory synaptic transmission in most brain areas. They have a pivotal role in adjustment of cell membrane excitability as their cell membrane expression levels is altered in brain physiology such as in learning and memory formation. AMPA receptor function and trafficking is regulated by several proteins, such as transmembrane AMPA receptor regulatory proteins (TARPs). NMDA-type glutamate receptors are important target molecules of ethanol. The role of AMPA receptors in the actions of ethanol has not been clarified as thoroughly. Furthermore, the regulation of AMPA receptor synthesis and their possible adaptation in neurons with altered inhibitory mechanisms are poorly understood. In this thesis work AMPA receptor pharmacology, trafficking and synaptic localization was studied using patch-clamp electrophysiology. Both native and recombinant AMPA receptors were studied. Hippocampal slices from transgenic Thy1alfa6 mice with altered inhibition were used to study adaptation of AMPA receptors. Ethanol was found to inhibit AMPA receptor function by increasing desensitization of the receptor, as the steady-state current was inhibited more than the peak current. Ethanol inhibition was reduced when cyclothiazide was used to block desensitization and when non-desensitizing mutant receptors were studied. Ethanol also increased the rate of desensitization, which was increased further by the coexpression of TARP-proteins. We found that the agonist binding capability is important for trafficking AMPA receptors from endoplasmic reticulum to the cell membrane. TARP rescues the surface expression of non-binding AMPA receptor mutants in HEK293 cells, but not in native neurons. Studies with Thy1alfa6 mice revealed that decreased inhibition decrease AMPA receptor mediated excitation keeping the neurotransmission in balance. Thy1alfa6 mice also had lower sensitivity to electroshock convulsions, presumably due to the decreased AMPA receptor function. The results suggest that during alcohol intoxication ethanol may inhibit AMPA receptors by increasing the rate and the extent of desensitization. TARPs appear to enhance ethanol inhibition. TARPs also participate in trafficking of AMPA receptors upon their synthesis in the cell. AMPA receptors mediate also long-term adaptation to altered neuronal excitability, which adds to their well-known role in synaptic plasticity.

Heparin-binding growth-associated molecule (HB-GAM) in activity-dependent neuronal plasticity in hippocampus

Cell adhesion and extracellular matrix (ECM) molecules play a significant role in neuronal plasticity both during development and in the adult. Plastic changes in which ECM components are implicated may underlie important nervous system functions, such as memory formation and learning. Heparin-binding growthassociated molecule (HB-GAM, also known as pleiotrophin), is an ECM protein involved in neurite outgrowth, axonal guidance and synaptogenesis during perinatal period. In the adult brain HB-GAM expression is restricted to the regions which display pronounced synaptic plasticity (e.g., hippocampal CA3-CA1 areas, cerebral cortex laminae II-IV, olfactory bulb). Expression of HB-GAM is regulated in an activity-dependent manner and is also induced in response to neuronal injury. In this work mutant mice were used to study the in vivo function of HB-GAM and its receptor syndecan-3 in hippocampal synaptic plasticity and in hippocampus-dependent behavioral tasks. Phenotypic analysis of HBGAM null mutants and mice overexpressing HB-GAM revealed that opposite genetic manipulations result in reverse changes in synaptic plasticity as well as behavior in the mutants. Electrophysiological recordings showed that mice lacking HB-GAM have an increased level of long-term potentiation (LTP) in the area CA1 of hippocampus and impaired spatial learning, whereas animals with enhanced level of HB-GAM expression have attenuated LTP, but outperformed their wild-type controls in spatial learning. It was also found that GABA(A) receptor-mediated synaptic transmission is altered in the transgenic mice overexpressing HB-GAM. The results suggest that these animals have accentuated hippocampal GABAergic inhibition, which may contribute to the altered glutamatergic synaptic plasticity. Structural studies of HB-GAM demonstrated that this protein belongs to the thrombospondin type I repeat (TSR) superfamily and contains two β-sheet domains connected by a flexible linker. It was found that didomain structure is necessary for biological activity of HB-GAM and electrophysiological phenotype displayed by the HB-GAM mutants. The individual domains displayed weaker binding to heparan sulfate and failed to promote neurite outgrowth as well as affect hippocampal LTP. Effects of HB-GAM on hippocampal synaptic plasticity are believed to be mediated by one of its (co-)receptor molecules, namely syndecan-3. In support of that, HB-GAM did not attenuate LTP in mice deficient in syndecan-3 as it did in wild-type controls. In addition, syndecan-3 knockout mice displayed electrophysiological and behavioral phenotype similar to that of HB-GAM knockouts (i.e. enhanced LTP and impaired learning in Morris water-maze). Thus HB-GAM and syndecan-3 are important modulators of synaptic plasticity in hippocampus and play a role in regulation of learning-related behavior.

Neurotrophins and neuronal plasticity in the action of antidepressants and morphine

Neuronal plasticity is a well characterized phenomenon in the developing and adult brain. It refers to capasity of a single neuron to modify morphology, synaptic connections and activity. Neuronal connections and capacity for plastic events are compromised in several pathological disorders, such as major depression. In addition, neuronal atrophy has been reported in depressive patients. Neurotrophins are a group of secretory proteins functionally classified as neuronal survival factors. Neurotrophins, especially brain derived neurotrophic factor (BDNF), have also been associated with promoting neuronal plasticity in dysfunctional neuronal networks. Chronic antidepressant treatment increases plastic events including neurogenesis and arborization and branching of neurites in distinct brain areas, such as the hippocampus. One suggested mode of action is where the antidepressants elevate the synaptic levels of BDNF thus further activating several signaling cascades via trkB-receptor. In our studies we have tried to clarify the mechanisms of action for antidepressants and to resolve the role of BDNF in this process. We found that chronic antidepressant treatment increases amount of markers of neuronal plasticity in both hippocampus and in the medial prefrontal cortex, both of which are closely linked to the etiology of major depression. Secondary actions of antidepressants include rapid activation of the trkB receptor followed by a phosphorylation of transcription factor CREB. In addition, activation of CREB by phosphorylation appears responsible for the regulation of the expression of the BDNF gene. Using transgenic mice we found that BDNF-induced trkB-mediated signaling proved crucial for the behavioral effects of antidepressants in the forced swimming test and for the survival of newly-born neurons in the adult hippocampus. Antidepressants not only increased neurogenesis in the adult hippocampus but also elevated the turnover of hippocampal neurons. During these studies we also discovered that another trkB ligand, NT-4, is involved in morphine-mediated anti-nociception and tolerance. These results present a novel role for trkB-mediated signaling in plastic events present in the opioid system. This thesis evaluates neuronal plasticity and trkB as a target for future antidepressant treatments.

A rationalisation of fatigue thresholds in pearlitic steels using a theoretical model

From a detailed re-examination of results in the literature, the effects of microstructure sizes, namely interlamellar spacing, pearlitic colony size and the prior austentitic grain size on the thresholds for fatigue crack growth (ΔKth) and crack closure (Kcl, th) have been illustrated. It is shown that while interlamellar spacing explicitly controls yield strength, a similar effect on ΔKth cannot be expected. On the other hand, the pearlitic colony size is shown to strongly influence ΔKth and Kcl, th through the deflection and retardation of cracks at colony boundaries. Consequently, an increase in ΔKth and Kcl, th with colony size has been found. The development of a theoretical model to illustrate the effects of colony size, shear flow stress in the slip band and macroscopic yield strength on Kcl, th and ΔKth is presented. the model assumes colony boundaries as potential sites for slip band pile-up formation and subsequent crack deflection finally leading to zig-zag crack growth. Using the concepts of roughness induced crack closure, the magnitude of Kcl, th is quantified as a function of colony size. In deriving the model, the flow stress in the slip band has been considered to represent the work hardened state in pearlite. Comparison of the theoretically predicted trend with the experimental data demonstrates very good agreement. Further, the intrinsic or closure free component of the fatigue threshold, ΔKeff, th is found to be insensitive to colony size and interlamellar spacing. Using a criterion for intrinsic fatigue threshold which considers the attainment of a critical fracture stress over a characteristic distance corresponding to interlamellar spacing, ΔKth values at high R values can be estimated with reasonable accuracy. The magnitude of ΔKth as a function of colony size is then obtained by summing up the average value of experimentally obtained ΔKeff, th values and the predicted Kcl, th values as a function of colony size. Again, very good agreement of the theoretically predicted ΔKth values with those experimentally obtained has been demonstrated.

Intraspecific variation in brain size and architecture : population divergence and phenotypic plasticity

Brain size and architecture exhibit great evolutionary and ontogenetic variation. Yet, studies on population variation (within a single species) in brain size and architecture, or in brain plasticity induced by ecologically relevant biotic factors have been largely overlooked. Here, I address the following questions: (i) do locally adapted populations differ in brain size and architecture, (ii) can the biotic environment induce brain plasticity, and (iii) do locally adapted populations differ in levels of brain plasticity? In the first two chapters I report large variation in both absolute and relative brain size, as well as in the relative sizes of brain parts, among divergent nine-spined stickleback (Pungitius pungitius) populations. Some traits show habitat-dependent divergence, implying natural selection being responsible for the observed patterns. Namely, marine sticklebacks have relatively larger bulbi olfactorii (chemosensory centre) and telencephala (involved in learning) than pond sticklebacks. Further, I demonstrate the importance of common garden studies in drawing firm evolutionary conclusions. In the following three chapters I show how the social environment and perceived predation risk shapes brain development. In common frog (Rana temporaria) tadpoles, I demonstrate that under the highest per capita predation risk, tadpoles develop smaller brains than in less risky situations, while high tadpole density results in enlarged tectum opticum (visual brain centre). Visual contact with conspecifics induces enlarged tecta optica in nine-spined sticklebacks, whereas when only olfactory cues from conspecifics are available, bulbus olfactorius become enlarged.Perceived predation risk results in smaller hypothalami (complex function) in sticklebacks. Further, group-living has a negative effect on relative brain size in the competition-adapted pond sticklebacks, but not in the predation-adapted marine sticklebacks. Perceived predation risk induces enlargement of bulbus olfactorius in pond sticklebacks, but not in marine sticklebacks who have larger bulbi olfactorii than pond fish regardless of predation. In sum, my studies demonstrate how applying a microevolutionary approach can help us to understand the enormous variation observed in the brains of wild animals a point-of-view which I high-light in the closing review chapter of my thesis.

A Calcium-Dependent Plasticity Rule for HCN Channels Maintains Activity Homeostasis and Stable Synaptic Learning

Theoretical and computational frameworks for synaptic plasticity and learning have a long and cherished history, with few parallels within the well-established literature for plasticity of voltage-gated ion channels. In this study, we derive rules for plasticity in the hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, and assess the synergy between synaptic and HCN channel plasticity in establishing stability during synaptic learning. To do this, we employ a conductance-based model for the hippocampal pyramidal neuron, and incorporate synaptic plasticity through the well-established Bienenstock-Cooper-Munro (BCM)-like rule for synaptic plasticity, wherein the direction and strength of the plasticity is dependent on the concentration of calcium influx. Under this framework, we derive a rule for HCN channel plasticity to establish homeostasis in synaptically-driven firing rate, and incorporate such plasticity into our model. In demonstrating that this rule for HCN channel plasticity helps maintain firing rate homeostasis after bidirectional synaptic plasticity, we observe a linear relationship between synaptic plasticity and HCN channel plasticity for maintaining firing rate homeostasis. Motivated by this linear relationship, we derive a calcium-dependent rule for HCN-channel plasticity, and demonstrate that firing rate homeostasis is maintained in the face of synaptic plasticity when moderate and high levels of cytosolic calcium influx induced depression and potentiation of the HCN-channel conductance, respectively. Additionally, we show that such synergy between synaptic and HCN-channel plasticity enhances the stability of synaptic learning through metaplasticity in the BCM-like synaptic plasticity profile. Finally, we demonstrate that the synergistic interaction between synaptic and HCN-channel plasticity preserves robustness of information transfer across the neuron under a rate-coding schema. Our results establish specific physiological roles for experimentally observed plasticity in HCN channels accompanying synaptic plasticity in hippocampal neurons, and uncover potential links between HCN-channel plasticity and calcium influx, dynamic gain control and stable synaptic learning.

Quantitative interactions between the A-type K+ current and inositol trisphosphate receptors regulate intraneuronal Ca2+ waves and synaptic plasticity

Key points center dot Active calcium signal propagation occurs when an initial calcium trigger elicits calcium release through endoplasmic reticulum (ER) receptors. A high concentration of the calcium trigger in thin-calibre dendrites would suppress release of calcium through hippocampal inositol trisphosphate receptors (InsP3Rs). center dot Could the high-density expression of A-type K+ channels in thin-calibre dendrites be a mechanism for inhibiting this suppression, thereby restoring the utility of the ER as a substrate for active calcium propagation? center dot Quantitative analyses involving experimentally constrained models reveal a bell-shaped dependence of calcium released through InsP3Rs on the A-type K+ channel density, during the propagation of a calcium wave. center dot A-type K+ channels regulated the relative contribution of ER calcium to the induction of synaptic plasticity in the presence of model metabotropic glutamate receptors. center dot These results identify a novel form of interaction between active dendrites and the ER membrane and suggest that A-type K+ channels are ideally placed for inhibiting the suppression of InsP3Rs in thin-calibre dendrites. Abstract The A-type potassium current has been implicated in the regulation of several physiological processes. Here, we explore a role for the A-type potassium current in regulating the release of calcium through inositol trisphosphate receptors (InsP3R) that reside on the endoplasmic reticulum (ER) of hippocampal pyramidal neurons. To do this, we constructed morphologically realistic, conductance-based models equipped with kinetic schemes that govern several calcium signalling modules and pathways, and constrained the distributions and properties of constitutive components by experimental measurements from these neurons. Employing these models, we establish a bell-shaped dependence of calcium release through InsP3Rs on the density ofA-type potassium channels, during the propagation of an intraneuronal calcium wave initiated through established protocols. Exploring the sensitivities of calcium wave initiation and propagation to several underlying parameters, we found that ER calcium release critically depends on dendritic diameter and that wave initiation occurred at branch points as a consequence of a high surface area to volume ratio of oblique dendrites. Furthermore, analogous to the role ofA-type potassium channels in regulating spike latency, we found that an increase in the density ofA-type potassium channels led to increases in the latency and the temporal spread of a propagating calcium wave. Next, we incorporated kinetic models for the metabotropic glutamate receptor (mGluR) signalling components and a calcium-controlled plasticity rule into our model and demonstrate thatthe presence of mGluRs induced a leftward shift in a BienenstockCooperMunro-like synaptic plasticity profile. Finally, we show that the A-type potassium current could regulate the relative contribution of ER calcium to synaptic plasticity induced either through 900 pulses of various stimulus frequencies or through theta burst stimulation. Our results establish a novel form of interaction between active dendrites and the ER membrane, uncovering a powerful mechanism that could regulate biophysical/biochemical signal integration and steer the spatiotemporal spread of signalling microdomains through changes in dendritic excitability.

Depression biased non-Hebbian spike-timing-dependent synaptic plasticity in the rat subiculum

The subiculum is a structure that forms a bridge between the hippocampus and the entorhinal cortex (EC), and plays a major role in the memory consolidation process. Here, we demonstrate spike-timing-dependent plasticity (STDP) at the proximal excitatory inputs on the subicular pyramidal neurons of juvenile rat. Causal (positive) pairing of a single EPSP with a single back-propagating action potential (bAP) after a time interval of 10 ms (+10 ms) failed to induce plasticity. However, increasing the number of bAPs in a burst to three, at two different frequencies of 50 Hz (bAP burst) and 150 Hz, induced long-term depression (LTD) after a time interval of +10 ms in both the regular-firing (RF), and the weak burst firing (WBF) neurons. The LTD amplitude decreased with increasing time interval between the EPSP and the bAP burst. Reversing the order of the pairing of the EPSP and the bAP burst induced LTP at a time interval of -10 ms. This finding is in contrast with reports at other synapses, wherein prebefore postsynaptic (causal) pairing induced LTP and vice versa. Our results reaffirm the earlier observations that the relative timing of the pre- and postsynaptic activities can lead to multiple types of plasticity profiles. The induction of timing-dependent LTD (t-LTD) was dependent on postsynaptic calcium change via NMDA receptors in the WBF neurons, while it was independent of postsynaptic calcium change, but required active L-type calcium channels in the RF neurons. Thus the mechanism of synaptic plasticity may vary within a hippocampal subfield depending on the postsynaptic neuron involved. This study also reports a novel mechanism of LTD induction, where L-type calcium channels are involved in a presynaptically induced synaptic plasticity. The findings may have strong implications in the memory consolidation process owing to the central role of the subiculum and LTD in this process.

Calcium Permeable AMPA Receptor-Dependent Long Lasting Plasticity of Intrinsic Excitability in Fast Spiking Interneurons of the Dentate Gyrus Decreases Inhibition in the Granule Cell Layer

The local fast-spiking interneurons (FSINs) are considered to be crucial for the generation, maintenance, and modulation of neuronal network oscillations especially in the gamma frequency band. Gamma frequency oscillations have been associated with different aspects of behavior. But the prolonged effects of gamma frequency synaptic activity on the FSINs remain elusive. Using whole cell current clamp patch recordings, we observed a sustained decrease of intrinsic excitability in the FSINs of the dentate gyrus (DG) following repetitive stimulations of the mossy fibers at 30 Hz (gamma bursts). Surprisingly, the granule cells (GCs) did not express intrinsic plastic changes upon similar synaptic excitation of their apical dendritic inputs. Interestingly, pairing the gamma bursts with membrane hyperpolarization accentuated the plasticity in FSINs following the induction protocol, while the plasticity attenuated following gamma bursts paired with membrane depolarization. Paired pulse ratio measurement of the synaptic responses did not show significant changes during the experiments. However, the induction protocols were accompanied with postsynaptic calcium rise in FSINs. Interestingly, the maximum and the minimum increase occurred during gamma bursts with membrane hyperpolarization and depolarization respectively. Including a selective blocker of calcium-permeable AMPA receptors (CP-AMPARs) in the bath; significantly attenuated the calcium rise and blocked the membrane potential dependence of the calcium rise in the FSINs, suggesting their involvement in the observed phenomenon. Chelation of intracellular calcium, blocking HCN channel conductance or blocking CP-AMPARs during the experiment forbade the long lasting expression of the plasticity. Simultaneous dual patch recordings from FSINs and synaptically connected putative GCs confirmed the decreased inhibition in the GCs accompanying the decreased intrinsic excitability in the FSINs. Experimentally constrained network simulations using NEURON predicted increased spiking in the GC owing to decreased input resistance in the FSIN. We hypothesize that the selective plasticity in the FSINs induced by local network activity may serve to increase information throughput into the downstream hippocampal subfields besides providing neuroprotection to the FSINs. (c) 2014 Wiley Periodicals, Inc.

Stress-facilitated LTD induces output plasticity through a synchronized-spikes and spontaneous unitary discharges the CA1 region of the hippocampus

Long-term potentiation (LTP) and long-term depression (LTD) of the excitatory synaptic inputs plasticity in the hippocampus is believed to underlie certain types of learning and memory. Especially, stressful experiences, well known to produce long-lasting strong memories of the event themselves, enable LTD by low frequency stimulation (LFS, 3 Hz) but block LTP induction by high frequency stimulation (HFS, 200 Hz). However, it is unknown whether stress-affected synaptic plasticity has an impact on the output plasticity. Thus, we have simultaneously studied the effects of stress on synaptic plasticity and neuronal output in the hippocampal CA1 region of anesthetized Wistar rats. Our results revealed that stress increased basal power spectrum of the evoked synchronized-spikes and enabled LTD induction by LFS. The induction of stress-facilitated LTD but not LFS induced persistent decreases of the power spectrum of the synchronized-spikes and the frequency of the spontaneous unitary discharges; However, HFS induced UP in non-stressed animals and increased the power spectrum of the synchronized-spikes, without affecting the frequency of the spontaneous unitary discharges, but HFS failed to induce UP in stressed animals without affecting the power spectrum of the synchronized-spikes and the frequency of the spontaneous unitary discharges. These observations that stress-facilitated LTD induces the output plasticity through the synchronized-spikes and spontaneous unitary discharges suggest that these types of stress-related plasticity may play significant roles in distribution, amplification and integration of encoded information to other brain structures under stressful conditions. (C) 2004 Elsevier Ireland Ltd and The Japan Neuroscience Society. All rights reserved.

Glucocorticoid receptor and protein/RNA synthesis-dependent mechanisms underlie the control of synaptic plasticity by stress

Learning and memory are exquisitely sensitive to behavioral stress, but the underlying mechanisms are still poorly understood. Because activity-dependent persistent changes in synaptic strength are believed to mediate memory processes in brain areas such as the hippocampus we have examined the means by which stress affects synaptic plasticity in the CA1 region of the hippocampus of anesthetized rats, Inescapable behavioral stress (placement on an elevated platform for 30 min) switched the direction of plasticity, favoring low frequency stimulation-induced decreases in synaptic transmission (long-term depression, LTD), and opposing the induction of long-term potentiation by high frequency stimulation, We have discovered that glucocorticoid receptor activation mediates these effects of stress on LTD and longterm potentiation in a protein synthesis-dependent manner because they were prevented by the glucocorticoid receptor antagonist RU 38486 and the protein synthesis inhibitor emetine. Consistent with this, the ability of exogenously applied corticosterone in non-stressed rats to mimic the effects of stress on synaptic plasticity was also blocked by these agents, The enablement of low frequency stimulation-induced LTD by both stress and exogenous corticosterone was also blocked by the transcription inhibitor actinomycin D, Thus, naturally occurring synaptic plasticity is liable to be reversed in stressful situations via glucocorticoid receptor activation and mechanisms dependent on the synthesis of new protein and RNA, This indicates that the modulation of hippocampus-mediated learning by acute inescapable stress requires glucocorticoid receptor-dependent initiation of transcription and translation.

Enriched environment experience overcomes the memory deficits and depressive-like behavior induced by early life stress

Stress in early life is believed to cause cognitive and affective disorders, and to disrupt hippocampal synaptic plasticity in adolescence into adult, but it is unclear whether exposure to enriched environment (EE) can overcome these effects. Here, we rep

GABA Transporter-1 Activity Modulates Hippocampal Theta Oscillation and Theta Burst Stimulation-Induced Long-Term Potentiation

The network oscillation and synaptic plasticity are known to be regulated by GABAergic inhibition, but how they are affected by changes in the GABA transporter activity remains unclear. Here we show that in the CA1 region of mouse hippocampus, pharmacolog

Opioid Withdrawal for 4 Days Prevents Synaptic Depression Induced by Low Dose of Morphine or Naloxone in Rat Hippocampal CA1 Area In Vivo

The formation of memory is believed to depend on experience- or activity-dependent synaptic plasticity, which is exquisitely sensitive to psychological stress since inescapable stress impairs long-term potentiation (LTP) but facilitates long-term depression (LTD). Our recent studies demonstrated that 4 days of opioid withdrawal enables maximal extents of both hippocampal LTP and drug-reinforced behavior; while elevated-platform stress enables these phenomena at 18 h of opioid withdrawal. Here, we examined the effects of low dose of morphine (0.5 mg kg(-1), i.p.) or the opioid receptor antagonist naloxone (1 mg kg(-1), i.p.) on synaptic efficacy in the hippocampal CA1 region of anesthetized rats. A form of synaptic depression was induced by low dose of morphine or naloxone in rats after 18 h but not 4 days of opioid withdrawal. This synaptic depression was dependent on both N-methyl-D-aspartate receptor and synaptic activity, similar to the hippocampal long-term depression induced by low frequency stimulation. Elevated-platform stress given 2 h before experiment prevented the synaptic depression at 18 h of opioid withdrawal; in contrast, the glucocorticoid receptor (GR) antagonist RU38486 treatment (20 mg kg(-1), s.c., twice per day for first 3 days of withdrawal), or a high dose of morphine reexposure (15 mg kg(-1), s.c., 12 h before experiment), enabled the synaptic depression on 4 days of opioid withdrawal. This temporal shift of synaptic depression by stress or GR blockade supplements our previous findings of potentially correlated temporal shifts of LTP induction and drug-reinforced behavior during opioid withdrawal. Our results therefore support the idea that stress experience during opioid withdrawal may modify hippocampal synaptic plasticity and play important roles in drug-associated memory. (C) 2009 Wiley-Liss, Inc.

A mechanistic model of algal photoinhibition induced by photodamage to Photosystem-II

Photoinhibition is a central problem for the understanding of plasticity in photosynthesis vs. irradiance response. It effectively reduces the photosynthetic rate. In this contribution, we present a mechanistic model of algal photoinhibition induced by photodamage to photosystem-II. Photosystem-IIs (PSIIs) are assumed to exist in three states: open, closed and inhibited. Photosynthesis is closely associated with the transitions between the three states. The present model is defined by four parameters: effective cross section of PSII, number of PSIIs, turnover time of electron transfer chains and the ratio of rate constant of damage to that of repair of D1 proteins in PSIIs. It gives a photosynthetic response curve of phytoplankton to irradiance (PI-curve). Without photoinhibition, the PI-curve is in hyperbola with the first three parameters. The PI-curve with photoinhibition can be simplified to the same form as the hyperbola by replacing either the number of PSIIs with the number of functional PSIIs or the turnover time of electron transfer chains with the average turnover time.